Transcript Math Slides

Place
Value
Page 5 – 12
Pages 6 – 8
Understanding Place Value


What do these four numbers have in common?
4,321
1,234
3,412
2,143
• All are four-digit numbers
• All are made up of the same digits: 1, 2, 3, & 4
The digits are the same, but each number has a
different value. This is because the digits are in
different places in each number. In our number
system the place of the digit tells you its value. In
other words, each digit in a number has a place
value.
Pages 6 – 8
Understanding Place Value: Cont.
thousands
hundreds
tens
units or ones
4
1
3
2
,
,
,
,
3
2
4
1
2
3
1
4
1
4
2
3
Pages 6 – 8
Example
 Which
of the following numbers has a 5 in the
hundreds place?
a) 6,235
b) 5,623
c) 3,265
d) 2,536
 What is the value of the digit 9 in the number
9,204?
Pages 6 – 8
Group Work
 Use
the number 7,856 to answer questions 1 to 6.
1. Which digit is in the thousands place?
2. Which digit is in the hundreds place?
3. What is the value of the digit 7?
4. What is the value of the digit 8?
5. What is the value of the digit 5?
6. What is the value of the digit 6?
Pages 11 – 12
Rounding Whole Numbers

A round number – a number that ends with zero
– is easy to work with.

Later, when you learn to estimate answers, you
will often round the numbers in problems to
similar numbers that end with zeros.
Pages 11 – 12
Rounding Whole Numbers: Cont.

To round a whole number do the following steps:
1. Underline the digit in the place you are
rounding to.
a) If the digit to the right of the underlined digit
is greater than or equal to 5, add 1 to the
underlined digit
b) If the digit to the right of the underlined digit
is less than 5, leave the underlined digit as it
is.
2. Change all the digit to the right of the
underlined digit to zero.
Pages 11 – 12
Example
 Round
1. 3,614
2. 8,469
3. 9,530
each number to the nearest thousand
Pages 11 – 12
Group Work
 Round
1. 294
2. 2,319
3. 927
4. 6,859
5. 371
6. 661
each number to the nearest hundred.
Addition
Pages 13 - 32
Pages 17 – 18
Adding Larger Numbers
 Parts
of an Addition Problem
4 addend
+5 addend
9 sum or total
 Add the column at the right first, & then move to
the next column to the left.
 Continue
until you have added each column of
figures
 To
check an addition problem, you can add the
numbers in each column from the bottom
Pages 17 – 18
Example
1) 7
+2
2) 9
+5
Pages 17 – 18
Group Work
1) 4
+4
2) 6
+5
5) 2
+4
6) 5
+0
3) 2
+3
4) 7
+1
Pages 19 – 22
Adding & Carrying
 When
the sum of the numbers in a column has a
2-digit answer. Write the digit on the right under
the column you just added & carry the left digit to
the next column.
 Writing
a digit in the next column is sometimes
called regrouping or renaming. It is also called
carrying. The idea is to add units with units, tens
with tens, hundreds with hundreds, & so on.
Pages 19 – 22
Example
1) 57
+83
2) 9
37
+ 8
Pages 19 – 22
Group Work
1) 43
+29
2) 82
+68
3) 683
+417
4) 257
+683
5) 5
47
+8
6) 2
81
+5
Page 23
Adding Numbers Written Horizontally
 When
the numbers you want to add are not in
vertical columns, rewrite them so that the units
are under the units, the tens are under the tens, &
so on.
 Always
line up the units column first.
Page 23
Example
1. 93 + 55 + 34 =
2. 4,596 + 8,892 + 4,625 =
Page 23
Group Work
1. 53 + 618 + 9 + 47 =
2. 26 + 745 + 66 + 4,329 =
3. 232 + 80,465 + 19 + 1,591 =
4. 8,779 + 2,286 + 5,269 =
5. 7,630 + 4,108 + 7,068 =
Page 24
Addition Shortcuts
 compatible
pairs = Two numbers whose sum
ends in zero.
 The
numbers in an addition problem may be
added in any order so look for any that make a
compatible pairs.
 Adding
these will make your addition faster
Page 24
Example
 Find
a compatible pair. Rewrite the problem.
Then add.
1. 62 + 8 + 5 =
2. 17 + 11 + 5 + 9 + 3 =
Page 24
Group Work
 Find
a compatible pair. Rewrite the problem.
Then add.
1. 19 + 27 + 3 =
2. 12 + 9 + 6 + 21 + 8 =
3. 4 + 35 + 13 + 26 + 5 =
4. 21 + 14 + 42 + 8 + 6 =
5. 43 + 7 + 8 + 62 + 5 =
Pages 25 – 26
Rounding, Estimating, & Using a Calculator
 When
the digit to the right of the number you are
rounding to is greater than or equal to 5, you must
add 1 to the underlined digit.
 If
the underlined digit is a 9, the digit to the left of
the 9 changes.
Pages 25 – 26
Example
 Round
each number to the nearest hundred. Then
add the rounded numbers.
1. 3,948 + 758 + 6,799 + 437 =
2. 714 + 7,465 + 302 + 4,974 =
Pages 25 – 26
Group Work
 Round
each number to the nearest hundred & find
the sum of the rounded numbers. Then find the
exact sum of the original numbers.
1. 518 + 782 + 764 + 207 + 843 =
2. 114 + 2,726 + 3,953 + 199 + 4,727 =
3. 6,806 + 992 + 5,528 + 4,666 + 894 =
Pages 27 – 26
Applying Your Addition Skills
 Watch
 In
for words such as sum, total, & combined
solving money problems, be sure to add dollars
in the dollars columns & cents in the cents
columns.
Subtraction
Page 33 - 59
Pages 37 – 38
Subtracting Larger Numbers
 Parts
of a Subtraction Problem
6 minuend
-2  subtrahend
4  difference
 Subtract the column at the right first, & then
move to the next column to the left. Continue
until you have subtracted each column of figures.
 To check a subtraction problem, add the answer to
the bottom number of the original problem. The
sum should be the top number of the original
problem.
Pages 37 – 38
Example
 Subtract
& Check
1) 34
– 22
2) 874,395
– 211,243
Pages 37 – 38
Group Work
 Subtract
& Check
1) 916
– 503
2) 567
–356
3) 9,161
–5,031
4) 5,467
–3,245
5) 255,694
–241,454
6) 860,956
–360,224
Pages 39 – 43
Subtracting & Borrowing
 When
a digit in the subtrahend (the bottom
number) is too large to subtract from the digit
above it, you have to borrow from the next
column to the left in the minuend (the top
number). Borrowing is sometimes called
regrouping or renaming.
 Sometimes
you have to borrow more than once in
the same problem.
Pages 39 – 43
Example
 Subtract
& Check.
1) 67
–8
2) 685,978
–498,369
Pages 39 – 43
Group Work
 Subtract
& Check.
1) 2,328
–1,489
2) 3,633
– 794
3) 7,792
–4,829
4) 9,113
–2,058
5) 7,488
–2,499
6) 8,233
–7,148
Page 44
Subtracting Numbers Written Horizontally
 When
the numbers you want to subtract are not in
vertical columns, rewrite them with the larger
number on top.
 Make
sure that you line up the units under the
units, the tens under the tens, & so on.
 Always
line up the units column first.
Page 44
Example
 Subtract
& Check.
1. 7,522 – 971 =
2. 15, 697 – 14, 938 =
Page 44
Group Work
 Subtract
& Check.
1. 9,330 – 827 =
2. 5,942 – 307 =
3. 6,752 – 4,397 =
4. 24,143 – 5,048 =
5. 43,524 – 22,685 =
Pages 45 – 48
Subtracting from Zeros
 You
cannot borrow from zeros.
 When
the digit in the column you want to borrow
from is zero, move to the next column to the left
that does not contain a zero.
Pages 45 – 48
Example
 Subtract
& check
1. 205 – 86 =
2. 40,000 – 6,417 =
Pages 45 – 48
Group Work
 Subtract
& Check.
1. 5,020 – 438 =
2. 1,006 – 307 =
3. 9,004 – 2,916 =
4. 50,002 – 23,875 =
5. 8,000 – 927 =
Page 49
Subtraction Shortcuts
 When
the subtrahend (the number you subtract
from another number) ends in zero, you can
subtract in your head.
 Any
number minus zero is that number.
 Sometimes
you can change a subtraction problem
to a similar problem that is easier to subtract.
Page 49
Example
 Rewrite
each problem as a similar problem with a
subtrahend (the bottom number) that ends in zero.
Remember to add to both numbers in the problem.
Then subtract the new numbers.
1. 83 – 26 =
2. 131 – 47 =
Page 49
Group Work
 Rewrite
each problem as a similar problem with a
subtrahend (the bottom number) that ends in zero.
Remember to add to both numbers in the problem.
Then subtract the new numbers.
1. 92 – 45 =
2. 96 – 38 =
3. 104 – 88 =
4. 71 – 35 =
5. 85 – 56 =
6. 64 – 19 =
Pages 52 – 56
Applying Your Subtraction Skills
 Pay
close attention to the language that tells you
to subtract.
 Watch
for words such as difference, balance, how
many more, how much larger, & how much
change.
 Line
up money problems carefully.
Multiplication
Pages 60 - 86
Pages 62 - 64
Basic Multiplication Facts

Parts of a Multiplication Problem
82 multiplicand (also called a factor)
x 3 multiplier (also called a factor)
246 product
Page 65
The Multiplication Table

It is very important to know the multiplication
table.
•

If you do not know it, take the time to memorize
it. The time you spend memorizing the table
now will be saved later on because you will be
able to do long multiplication & division
problems quickly.
any number multiplied by 0 is 0.
Page 66
Multiplying by One-Digit Numbers

Multiply each digit in the top number by the
bottom number. The answer should be written
from right to left, starting with the product of the
ones column, then the tens column, & so on.

Checking a multiplication problem:
•
go over your steps carefully to find any errors
you might have made.
•
divide the answer you got by the bottom
number in the problem.
Page 66
Example

Multiply & Check
1) 71
x9
2) 8,011
x 7
Page 66
Group Work
Multiply & Check
1) 321
x 4
2) 700
x 5
3) 200
x 6
5) 4,201
x 4
6) 3,102
x 3
4) 110
x 9
Pages 67 – 68
Multiplying by Larger Numbers

When you multiply by a 2-digit number, be sure
to begin your answer (the first partial product)
directly under the ones columns of the numbers
being multiplied. Begin the second partial product
directly under the tens columns of the numbers
being multiplied & the first partial product.
Always multiply from right to left.
 When multiplying by zero, write the answer 0
directly under the 0 in the problem. Then multiply
by the next digit in the bottom number & continue
to the left.
Pages 67 – 68
Example
Multiply & Check
62
x 23
31,212
x 443
Pages 67 – 68
Group Work
Multiply & Check
1) 73
2) 812
x 22
x 34
4) 411
x 80
5) 641
x 20
3) 43
x 31
6) 10,220
x 123
Pages 69 – 70
Multiplying Numbers Written Horizontally

To multiply numbers written horizontally, rewrite
the problem vertically with the shorter number on
the bottom. Whether you put the shorter number
on the top or the bottom, you will get the same
answer. However, by putting the shorter number
on the bottom, you will have fewer partial
products to add.
 Three ways to indicate multiplication.
Pages 69 – 70
Example
1.
(941)(20) =
2.
713(30) =
Pages 71 – 73
Multiply & Carrying

Carrying in multiplication is very much like
carrying in addition. Be sure to multiply first &
then add the number being carried. Carrying is
sometimes called regrouping or renaming.

Remember: Any number multiplied by 0 is 0, &
you must always multiply before you carry.
Pages 71 – 73
Example
Multiply & Check
1.
17(4) =
2.
738(9) =
Pages 71 – 73
Group Work
1.
26(59) =
2.
36(27) =
3.
39(42) =
4.
56(83) =
5.
84(38) =
6.
27(73) =
Pages 74 – 75
Multiply by 10, 100, & 1,000

To multiply a number by 10, add a 0 to the right
of the number

To multiply a number by 100, add two 0’s to the
right of the number

To multiply a number by 1,000, add three 0’s to
the right of the number.
Pages 74 – 75
Example
Multiply
1.
47 x 10 =
2.
1,000 x 499 =
Pages 74 – 75
Group Work
Multiply
1.
92 x 10 =
2.
261 x 10 =
3.
209 x 100 =
4.
32 x 1,000 =
5.
100 x 26 =
6.
1,000 x 62 =
Pages 76 – 78
Rounding, Estimating, & Using a Calculator

Zeros make many multiplication problems easier.

front-end rounding = To estimate an answer to a
multiplication problem, try rounding the larger
number to the left-most place.
Pages 76 – 78
Example

1.
In the following problems, use the rounding to
select the correct answer from the choices. Then
check.
36(425) =
a) 8,700
b) 9,600
c) 15,300
d) 21,900
2.
798(657) =
a) 642,826
b) 524,286
c) 414,346
d) 382,156
Pages 76 – 78
Group Work

Round the larger number in each problem to the
nearest thousand & multiply.
1.
2(4,281) =
2.
7(2,963) =
3.
3(6,059) =
4.
7,516(4) =
5.
5(3,772) =
6.
4(5,693) =
Pages 79 – 83
Applying Your Multiplication Skills

In each problem, pay close attention to the
language that tells you to multiply. In most cases,
you will be given information about one thing &
you will be asked to apply it to several things.
Division
Page 87 – 119
Pages 90 – 92
Basic Division Facts

Parts of a Division Problem
 Dividend = The number being divided.
 Divisor = The number that divides into the
dividend.
 Quotient = The answer.
 There are four common ways to write division.
Pages 93 – 95
Dividing by One-Digit Numbers

Divide 156 by 4
1. Divide 15 ÷ 4 = 3. Put the 3 over the 5 in the
dividend.
2. Multiply 3 x 4 = 12. Put the 12 directly under the
15.
3. Subtract 15 – 12 = 3
4. Bring down the next number from the dividend
5. Divide 36 ÷ 4 = 9. Put the 9 directly over the 6 in
the dividend.
6. Multiply 9 x 4 = 36. Put the 36 directly under the
36 in the problem.
7. Subtract 36 – 36 = 0
Pages 93 – 95
Dividing by One-Digit Numbers: Cont.

When dividing by a 1-digit number, most of the
work can be done by multiplying & subtracting
mentally. Write each digit that you carry in the
dividend. This procedure is called short division.

To check a division problem, multiply the
quotient by the divisor. The product should be the
dividend.
Pages 93 – 95
Example
Divide & Check
1.
252 ÷ 6 =
2.
540/9 =
Pages 93 – 95
Group Work
Divide & Check
1.
360 ÷ 4 =
2.
8,874 ÷ 9 =
3.
1,746/6 =
4.
2,065 ÷ 5 =
5.
2,325 ÷ 3 =
6.
1,940 ÷ 5 =
Pages 96 – 98
Dividing with Reminders

Division problems do not always come out
evenly. The amount left over is called the
reminder.

To check a division problem with a remainder,
multiply the quotient by the divisor. Then add the
remainder. The result should equal the dividend.
Pages 96 – 98
Example
Divide & check
1.
12,503 ÷ 6 =
2.
52,022 ÷ 8 =
Pages 96 – 98
Group Work
Divide & check
1.
1,449 ÷ 6 =
2.
2,431 ÷ 4 =
3.
1,619 ÷ 2 =
4.
2,059 ÷ 7 =
5.
8,197 ÷ 9 =
6.
2,867 ÷ 4 =
Page 99
Mental Math & Properties of Numbers

Commutative property of addition = the
numbers in an addition problem can be added in
any order.

Commutative property of multiplication = the
numbers in a multiplication problem can be
multiplied in any order
•
Subtraction & division are NOT commutative!
Page 99
Mental Math & Properties of Numbers: Cont.

Any number multiplied by one is that number &
any number divided by one is that number

Any number multiplied by zero is zero & any
number divide into zero is zero.

You cannot divide a number by zero! Any
number divided by zero is undefined.
Pages 100 – 106
Dividing by Two-digit & Three-digit Numbers

Dividing by two-digit & three-digit numbers is a
tricky process.

It requires practice & a skill called estimating:
that is, guessing how many times one number
goes into another.
Pages 100 – 106
Example
Divide & check
1.
336 ÷ 42 =
2.
18,130 ÷ 37 =
Pages 100 – 106
Group Work
Divide & check
1.
465 ÷ 93 =
2.
217 ÷ 31 =
3.
200 ÷ 31 =
4.
683 ÷ 82 =
5.
538 ÷ 74 =
6.
136/29 =
Pages 107 – 108
Rounding & Estimating

Numbers that end in zeros are often easy to work
with.

When both the dividend & the divisor end in
zeros, you can cancel the zeros one-for-one.

Sometimes you can round the dividend to a
number that is easy to divide into, You can use the
rounded number to estimate an answer to the
original division problem.
Pages 107 – 108
Example
Round each dividend to the nearest ten & the
nearest hundred. Then decide which number is
easier to divide. Use the easier rounded number to
estimate the answer.
1.
423 ÷ 7 =
2.
716 ÷ 9 =
Pages 109 – 110
Two-Digit Accuracy & Using a Calculator

Another way to estimate answers is to do a partial
division.

Instead of completing a division problem, try for
two-digit accuracy.

Divide until you have three digits in the quotient.

Then round your answer.
Pages 109 – 110
Example
Calculate each problem to two-digit accuracy.
1.
7,936 ÷ 62 =
2.
569,439 ÷ 93 =
Pages 109 – 110
Group Work
Calculate each problem to two-digit accuracy.
1.
18,316 ÷ 76 =
2.
14,798 ÷ 49 =
3.
34,506 ÷ 81 =
4.
20,909 ÷ 29 =
5.
45,724 ÷ 92 =
6.
18,444 ÷ 53 =
Pages 111 – 116
Apply Your Division Skills

Pay close attention to the language that tells you
to divide. You may be asked how many of one
thing are contained in something else.

You may be given information about several
things & ask for information about one of those
things.

You may be asked to find an average, or mean, is
a total number divided by the number of things
that make up the total.
Fractions
Pages 8 – 59
Page 11
What is a Fraction?
Fraction = Part of a Whole
Top Number?
Bottom Number?
3
4
Numerator =
tells how many parts
you have
Denominator =
tells how many parts
are in the whole
Note: the fraction bar means to divide the numerator
by the denominator
Page 11
One Way To Remember
Numerator
=
North
# of parts in
whole
3
4
Denominator
=
Down
# you have
Divided by
Page 11
What Fraction is Shaded?
¾
⅝
7/
16
Page 13
Identifying Forms of Fractions
There are three forms of fractions:
 Proper fraction: The numerator (top number) is
always less than the denominator. The value of a
proper fraction is less than 1 whole.
 Improper fraction: The numerator is equal to or
greater than the denominator. When the numerator
is equal to the denominator, an improper fraction
is equal to 1 whole.
 Mixed Number: A whole number & a proper
fraction are written next to each other. A mixed
number always has a value of more than 1 whole.
Page 13
Example
Tell whether each of the following is a proper
fraction (P), an improper fraction (I) or a mixed
number (M).
1
2
9
7
2
110
75
3
10
10
Page 13
Group Work
Tell whether each of the following is a proper
fraction (P), an improper fraction (I) or a mixed
number (M).
1
9
6
2
1
4
2
3
17
17
Page 14
Thinking About the Size of Fractions
 The
size of the numerator compared to the size of
the denominator tells you:
• A fraction is equal to ½ when the numerator is
exactly half of the denominator
• A fraction is less then ½ when the numerator is
less than half of the denominator
• A fraction is greater than ½ when the numerator
is more than half of the denominator
 The symbol = means “is equal to”
 The symbol < means “is less than”
 The symbol > means “is greater than”
Page 14
Example
In the box between each pair of fractions, write a
symbol that makes the statement true.
3
5
1
2
8
16
1
2
Page 14
Group Work
In the box between each pair of fractions, write a
symbol that makes the statement true.
7
20
1
2
9
15
1
2
Pages 15 – 17
Reducing Fractions
 Reducing
a fraction means dividing both the
numerator & the denominator (top & bottom) by a
number that goes into each evenly.
 Reducing changes the numbers in a fraction, but
reducing does not change the value of a fraction.
 When both the numerator & the denominator of a
fraction end with zeros, you can cancel the zeros
one-for-one. This is a shortcut for reducing ten.
Always check to see if you can continue to reduce.
 Sometimes a fraction can be reduced more than
once to reach the lowest terms
Pages 15 – 17
Questions When Reducing
 Are
the numerator & denominator both even?
Divide by 2
 Add
the digits of the numerator separate from the
digits of the denominator. Do they add up to a
number that is divisible by 3? Divide by 3
 Do
the numerator & the denominator end in a 0 or
5? Divide by 5
 If
no to all previous questions: You just have to
try 7, 11, 13 & so on
Pages 15 – 17
Example

Reduce each fraction to lowest terms
1 6
=
12
2 25
=
30
3 33
=
77
Pages 15 – 17
Example

Reduce each fraction to lowest terms
1 75
=
80
2 25
=
50
3 35
=
49
Page 18
Raising Fractions to Higher Terms
 An
important skill in the addition & subtraction of
fractions is raising a fraction to higher terms.
 Raising
to higher terms is the opposite of
reducing.
 To
reduce a fraction, you must divide both the
numerator & denominator by the same number.
 To
raise a fraction to higher terms, multiply both
the numerator & the denominator by the same
number.
Page 18
Example
Raise each fraction to higher terms by filling in the
missing numerator.
1 4
=
5
30
2 4
=
7
35
Page 18
Group Work
Raise each fraction to higher terms by filling in the
missing numerator.
1 1
=
3
45
2 5
=
6
42
Pages 19 – 20
Changing Improper Fractions to
Whole or Mixed Numbers
 The
answers to many fraction problems are
improper fractions.
•
These answers are easier to read if you change
them to whole numbers or mixed numbers.
 To
change an improper fraction, divide the
denominator into the numerator.
Pages 19 – 20
Example
Change each fraction to a whole number or a mixed
number. Reducing any remaining fractions.
1 14
=
8
2 30
=
9
Pages 19 – 20
Group Work
Change each fraction to a whole number or a mixed
number. Reducing any remaining fractions.
1 13
=
12
2 36
=
12
Page 21
Changing Mixed Numbers to
Improper Fractions
 When
you multiply & divide fractions, you will
have to change mixed numbers to improper
fractions. To change a mixed number to an
improper fraction, follow these steps:
1. Multiply the denominator (bottom number) by
the whole number.
2. Add that product to the numerator (top number)
3. Write the sum over the denominator.
Page 21
Example
Change each mixed number to an improper fraction
1
3
=
2
4
2
1
9
=
2
Page 21
Group Work
Change each mixed number to an improper fraction
1
1
=
10
3
2
4
3
=
5
Pages 22 – 24
Addition of Fractions with
the Same Denominators
 To
add fractions with the same denominators
(bottom numbers), first add the numerators.
 Then
write the total (or sum) over the
denominator.
 Don’t
forget to check to see if you can reduce
your answer.
Pages 22 – 24
Example
Add
1
7
8
13
4
+6
13
3
12
2
8
1
9
8
2
+ 10
8
Page 25
Addition of Fractions with
Different Denominators
 If
the fractions in an addition problem do not have
the same denominators, you must find a common
denominator.
 common denominator = a number that can be
divided evenly by every denominator in the
problem.
 lowest common denominator or LCD = The
lowest denominator that can be divided evenly by
every denominator in the problem.
Pages 26 – 28
Finding a Common Denominator
 Method
1: Multiply the denominators together.
 Brute force method: List the multiples of the
larger number until you find a multiple of the
smaller number
 Prime factorization method: find prime factors of
both numbers. Circle the numbers they have in
common. Write those once then write in the rest
of the numbers and multiply to find the LCM
Pages 26 – 28
Example
Add
2
1
+
7
10
3
4
+
11
16
1
3
7
8
Pages 26 – 28
Group Work
2
1
+
5
12
5
9
+
5
7
4
9
2
3
Page 31
Subtracting Fractions with
the Same Denominators
 To
subtract fractions, subtract the numerators &
put the difference (the answer) over the
denominator.
Page 31
Example
2
1
–
5
9
2
9
5
23
6
1
– 7
6
Pages 32 – 33
Subtracting Fractions with
Different Denominators
 When
fractions do not have the same
denominators, first find a common denominator.
 Change each fraction to a new fraction with the
common denominator.
 Then subtract.
Pages 32 – 33
Example
Subtract & Reduce
1
11
13
18
1
– 8
2
2
5
25
8
2
– 22
5
Pages 32 – 33
Group Work
Subtract & Reduce
1
5
16
6
7
– 9
10
2
3
18
5
3
– 9
10
Pages 34 – 36
Borrowing & Subtracting Fractions
 Sometimes
there is no top fraction to subtract the
bottom fraction from. Other times the top fraction
is not big enough to subtract the bottom fraction
from. To get something in the position of the top
fraction, you must borrow. To borrow means to
write the whole number on top as a whole number
& an improper fraction.
8
 For example, 12 = 11 8 . The numerator &
denominator of the improper fraction should be
the same as the denominator of the other fraction
in the problem.
Pages 34 – 36
Example
Subtract & Reduce
1
3
24
16
2
– 9
3
2
2
13
9
5
– 7
6
Pages 34 – 36
Group Work
Subtract & Reduce
1
1
30
3
8
– 16
11
2
1
12
6
7
– 10
12
Page 39
Multiplication of Fractions
 When
you multiply whole numbers (except 1 &
0), the answer is bigger than the two numbers you
multiply.
 When you multiply two proper fractions, the
answer is smaller than either of the two fractions.
When you multiply two fractions, you find a
fraction of a fraction or a part of a part.
 To multiply fractions, multiply the numerators
together & the denominators. Then reduce.
Page 39
Example
Multiply & Reduce
1
2
4
x
=
3
5
2
1
4
2
x
x
=
3
7
3
Page 39
Group Work
Multiply & Reduce
1
5
2
x
=
7
9
2
2
7
1
x
x
=
5
9
3
Pages 40 – 41
Canceling & Multiplying Fractions
 Canceling
is a way of making multiplication of
fractions problems easier.
 Canceling is similar to reducing.
 To cancel, divide a numerator & denominator by a
number that goes evenly into both of them.
 You don’t have to cancel to get the right answer,
but it makes the multiplication easier.
Pages 40 – 41
Example
Multiply & Reduce
1
15
7
12
x
x
=
28
16 45
2
17
14
7
x
x
=
21
51 11
Pages 40 – 41
Group Work
Multiply & Reduce
1
11
10 13
x
x
=
39
11 18
2
19
7
3
x
x
=
36
10
7
Page 42
Multiplying Fractions &
Whole Numbers
 To
multiply a whole number & a fraction, first
write the whole number as a fraction.
 Write the whole number as the numerator & 1 a
the denominator.
Page 42
Example
Multiply & Reduce
1
9
=
2 x
10
2
7
x 36 =
12
Page 42
Group Work
Multiply & Reduce
1
5
=
16 x
24
2
7
x
35 30 =
Page 43
Multiplying Mixed Numbers
 To
multiply mixed numbers, first change the
mixed numbers to improper fractions.
 Then
multiply the improper fractions.
 Reduce
the answer.
Page 43
Example
Multiply & Reduce
1
2
1
1
2
x 5
x 7
=
15
4
2
2
2
3
7
2
x 3
x 2
=
5
8
9
Page 43
Group Work
Multiply & Reduce
1
3
3
x
4
2
1
x 2
16
3
8
1
x 1
=
9
5
5
=
14
Pages 47 – 48
Dividing Fractions by Fractions
 To
divide fractions, take the reciprocal (or
inverse) of the divisor (the number at the right of
the ÷ sign) & follow the rules for multiplying
fractions.
 To make a reciprocal means to write the
numerator on the bottom & the denominator on
the top.
Pages 47 – 48
Example
Divide & Reduce
1
16
3
÷
=
21
4
2
12
18
÷
=
19
38
Pages 47 – 48
Group Work
Divide & Reduce
1
3
6
÷
=
10
7
2
5
25
÷
=
11
33
Pages 49 – 54
Dividing Whole Numbers by Fractions
&
Dividing Fractions by Whole numbers
&
Dividing with Mixed Numbers
 In
fraction division problems, change whole
numbers & mixed numbers to improper fractions.
 Then take the reciprocal of the fraction you are
dividing by & follow the rules for multiplying
fractions.
Pages 49 – 54
Example
Divide & Reduce
1
2
24
=
56 ÷
25
3
5
1
÷ 4
10
=
7
8
2
÷ 35 =
24
Pages 49 – 54
Group Work
Divide & Reduce
1
21
=
7 ÷
25
3
2
5
÷ 15 =
18
5
5
÷ 3
5
=
6
12
Page 55
Finding a Number When a
Fraction of It Is Given
 There
is a kind of division problem that is
sometimes hard to recognize. Think about the
question ½ of what number is 12? Without using
pencil & paper, you can probably come up with
the answer 24. You know that ½ of 24 is 12.
 To solve the problem, you find a solution to the
statement ½ x ? = 12. The statement asks you to
find the missing number in a multiplication
problem. To find the missing number, divide 12
by ½.
Page 55
Example
Solve
1
7
of what number is 35?
12
2
3
of what number is 45?
10
Page 55
Group Work
Solve
1
8
of what number is 32?
9
2
4
of what number is 80?
5
Pages 62 – 63
Understanding Decimals
 Like
a fraction, a decimal shows a part of
a whole. Decimals divide a whole into 10
parts or 100 parts or 1,000 parts and so
on. If you have used money you’ve used
decimals.
 Decimals get their names from the
number of places on the right side of the
decimal point. The decimal point
separates whole numbers from decimals.
A place is the position for a digit. The
decimal point itself does not take up a
Pages 62 – 63
Pages 62 – 63
Pages 62 – 63
Mixed decimals are numbers with digits on both
sides of the decimal point. $4.95 is a mixed decimal.
It means 4 whole dollars and 95/100 of a dollar.
 As you move to the right in the decimal system,
each place means that the whole has been divided
into more parts, therefore, the values of the
decimal places get smaller.
Pages 62 – 63
Example
For each number, underline the digit that is
in the place named
1.
Tenths place
297.18
2.
Thousandths place
0.04107
Circle the correct answer for the following
question
3.
Which of the following tells the value of
the digit 9 in the number 2.936?
9 tenths
9 hundredths
9 thousandths 9 ten-thousands
Pages 62 – 63
Group Work
For each number, underline the digit that is
in the place named
1.
Hundredths place
0.1389
2.
Tenths place
0.5864
Circle the correct answer for the following
question
3.
Which of the following tells the value of
the digit 7 in the number 12.047?
7 tenths
7 hundredths
7 thousandths 7 ten-thousands
Page 64
 Remember
that a decimal gets its name from the
number of places at the right of the decimal
point.
 To read a decimal, count the places at the right of
the decimal point.
 With mixed decimals, watch for the word &
which separates whole numbers from decimal
fractions.
Page 64
 Write
Example
each decimal or mixed decimal in
words
1. 0.5
= Five tenths
2.
0.07
= Seven hundredths
3.
10.402 = Ten and four hundred two
thousandths
Page 65
 To
write decimals from words, be sure that you
have the correct number of decimal places.
 Use zeros to hold places where necessary.
 Remember, again, that the word & separates
whole numbers from decimal fractions in mixed
decimals.
 Watch where zeros hold places.
Page 65
Example
 Write
the following as a decimal or a
mixed decimal.
1.
Five hundredthousandths
= 0.00005
= 0.047
Forty-seven thousands =48.9
3. Forty-eight and nine
tenths
2.
Page 66
 Consider
the number 020.060 & decide whether
each zero is necessary.
• The zero left of the digit 2 is unnecessary
• The zero right of the 2 is necessary because it
keeps the 2 in the tens place.
• The zero right of 6 is unnecessary
• The number can be correctly written as 20.06
 A decimal with no whole number is often written
with a zero in the units place. The decimal .8 &
0.8 are both correct forms for eight tenths.
Page 66
Example
For each number, choose the correctly
rewritten number.
1. 5.0060
a) 50.6 b) 50.06 c) 5.006 d) 5.06
2. 003.1050
a) 3.105
b) 30.105 c) 3.15
d) 30.015
3. 0700.40
a) 70.04
b) 70.4
c) 700.04 d) 700.4
4. 0040.0920
a) 40.92
b) 40.092 c) 4.092 d) 4.92

Page 67
 To
change a decimal to a fraction (or to change a
mixed decimal to a mixed number), write the
digits in the decimals as the numerator.
 Write
the denominator according to the number of
decimal places.
 Then
reduce the fraction.
Page 67
Example
 Write
each number as a common
fraction or a mixed number & reduce.
1.
0.08
2.
3.6
3.
0.00324
4.
16.00004
Page 67
Group Work
 Write
each number as a common
fraction or a mixed number & reduce.
1.
0.085
2.
7.2
3.
2,036.8
4.
7.22
5.
0.375
Page 68
 Remember
that a fraction can be understood as a
division problem.
 To
change a fraction to a decimal, divide the
denominator into the numerator.
•
To divide, add a decimal point & zeros to the
numerator.
•
Usually two zeros are enough.
 Then
bring the point up in the answer.
Page 68
Example
 Write
1.
¼
2. 2/9
3. 3/5
each fraction as a decimal.
Page 68
Group Work
 Write
1. 2/5
2. 6/25
3. 1/6
4. 3/8
5. 5/12
each fraction as a decimal.
Page 70
 When
you look at a group of decimals, it is
sometimes difficult to tell which decimal is the
largest. To compare decimals, give each decimal
the same number of places by adding zeros. This
is the same as giving each decimal a common
denominator. The zeros you add do not change the
value of the decimals.
 Don’t write the extra zeros in the final answer.
Page 70
Example
 In
each pair, tell which decimal is larger.
1.
0.04 or 0.008
2.
0.328 or 0.33
3.
0.0057 or 0.006
Page 70
Group Work
 Arrange
each list in order from the smaller
to the largest.
1.
0.03,0.33, 0.033, 0.303
2.
0.106, 0.16, 0.061, 0.6
3.
0.4, 0.405, 0.45, 0.045
4.
0.0072, 0.07, 0.027, 0.02
Pages 71 – 72
 To
round a number, you must know the place
value of each digit in the number.
 To round a decimal:
1. Underline the digit in the place to which you
want to round.
2. If the digit to the right of the underlined digit is
5 or more, add one to the underlined digit.
3. If the digit to the right of the underlined digit is
4 or less, do not change the underlined digit.
4. Drop the digits to the right of the underlined
digit.
Pages 71 – 72
Example
 Round
each decimal to the nearest
place value given.
1.
Tenth
4.29
2.
Hundredth
0.582
3.
Whole number
5.4068
Pages 71 – 72
Group Work
 Round
each decimal to the nearest
place value given.
1.
Tenth
516.24
2.
Hundredth
0.0946
3.
Whole number
1.89
Page 73

To add decimals, line up the decimal points under
each other. (Remember that whole numbers have
a decimal point at its right.)
• This makes it so that you are adding the same
place values to each other.
 Then add
Page 73
Example
 Add
1.
0.8 + 0.047 + 0.36
2.
123 + 2.6 + 9.04
3.
9.043 + 0.27 + 15
Page 73
Group Work
 Add
1.
0.849 + 1.6 + 73
2.
7.563 + 0.08 + 124.9
3.
12.3 + 0.908 + 6 + 4.25
4.
1.6 + 23 + 12.73 + 0.485
Page 75
 To
subtract decimals line up the decimals with the
points under each other just like in addition.
• Remember to put a point to the right of a whole
number. Put zeros at the right until each decimal
has the same number of places.
• You will need the zeros for borrowing.
Page 75
Example
 Subtract
1.
4.2 – 3.76
2.
0.804 – 0.1673
3.
3.2 – 2.68
Page 75
Group Work
 Subtract
1.
0.08 – 0.0156
2.
1.4 – 0.978
3.
0.6 – 0.059
Pages 79 – 81

Multiply as you would any whole numbers.
•
To find the placement of the decimal in the
product (the answer)
 Count
the decimal places in each factor (the
numbers you multiplied).
 Put
the total number of decimal places in the
product. (Sometimes you will need to put
extra zeros in your answer.)
Pages 79 – 81
Example
 Multiply
1.
2.8 x 4.3
2.
(0.81)(0.69)
3.
45.21(5.6)
Pages 79 – 81
Group Work
 Multiply
1.
5.6 x 0.82
2.
(0.94)(1.8)
3.
34.7(209)
Page 82

To multiply a decimal by 10, move the decimal
point one place to the right.

To multiply a decimal by 100, move the decimal
point two places to the right.

To multiply a decimal point by 1,000, move the
decimal point three places to the right.

You may have to add zeros to get
enough places.
Page 82
Example
 Multiply
1.
0.8 x 10
2.
0.721 x 10
3.
0.06 x 1,000
Page 82
Group Work
 Multiply
1.
$1.25 x 10
2.
$0.60 x 100
3.
$0.03 x 1,000
Page 86
 To
divide a decimal by a whole number, line up
the problem carefully.
 Then
divide as you would a whole number &
bring the decimal point up into quotient (the
answer) above its position in the problem.
 Sometimes
answers.
you will need to put zeros in your
Page 86
Example
 Divide
1.
33.605 ÷ 65
2.
464.31 ÷ 77
3.
1,565.2 ÷ 43
Page 86
Group Work
 Divide
1.
1.52 ÷ 19
2.
216.6 ÷ 38
3.
9.516 ÷ 52
Pages 87 – 88
 To
divide a decimal by a decimal, first make a
new problem.
• Change the number you are dividing by (the
divisor) into a whole number.
• You can change the divisor into a whole number
by moving the decimal point to the right end.
• Then move the decimal point in the other
number (the dividend) the same number of
places.
 Sometimes you will have to put extra zeros in the
dividend.
Pages 87 – 88
Example
 Divide
1.
0.11648 ÷ 0.64
2.
145.44 ÷ 3.6
3.
0.3933 ÷ 0.19
Pages 87 – 88
Group Work
 Divide
1.
0.522 ÷ 8.7
2.
558.6 ÷ 0.06
3.
4.48 ÷ 0.008
Page 89
 To
divide a whole number by a decimal,
remember to put a decimal point at the right of the
whole number.
• Then move the points in both the divisor and the
dividend.
• You will have to put zeros in the dividend.
 Not every division problem comes out even.
When this happens, choose a place to round to
(unless it is chosen for you in the directions).
Then divide one place beyond the place you want
to round to.
Page 89
Example
 Divide
1.
3,237 ÷ 0.039
2.
33,040 ÷ 5.6
3.
37,440 ÷ 0.48
Page 89
Group Work
 Divide
1.
1,178 ÷ 0.019
2.
21,546 ÷ 51.3
3.
2,135 ÷ 4.27
Page 90
 To
divide a decimal by 10, move the decimal
point one place to the left
 To
divide a decimal by 100, move the
decimal point two place to the left
 To
divide a decimal by 1,000, move the
decimal point three place to the left
 You
may have to add zeros to get
enough places.
Page 90
Example
 Divide
1.
$20 ÷ 1,000
2.
$540 ÷ 1,000
3.
$650 ÷ 100
Page 90
Group Work
 Divide
1.
$2.19 ÷ 10
2.
15.8 ÷ 1,000
3.
6,954 ÷ 1,000
Page 91
 Adding
zeros to a division of decimals problem
does not always result in a problem that divides
evenly.
 To
get a division answer that is accurate to the
nearest tenth, divide to the hundredths place &
round the answer to the nearest tenth.
 This
is called dividing to fixed place accuracy.
Page 91
Example
 Divide.
tenth.
Find the answer to the nearest
1.
6.3 ÷ 0.8
2.
72.6 ÷ 50.3
3.
12.3 ÷ 7
Page 91
Group Work
 Divide
1.
204 ÷ 9.2
2.
10.3 ÷ 0.35
3.
49.5 ÷ 36
Percents
Pages 96 – 122
Page 98
Understanding Percents
 A percent
shows a part of a whole.
 Remember
• Fractions: the denominator tells how many
parts a whole is divided into. Any whole
number except for zero can be a denominator.
• Decimals: a whole is divided into tenths,
hundredths, thousandths, & so on.
 Percent: the whole is always divided into 100
parts. The word percent means “by the hundred or
per one hundred.” Percent is shown with the sign
%.
Page 98
Example
 Fill
in the blank
1.
Percent means that a whole has been divided into
___________ equal parts.
2.
49¢ is 49/100 of a dollar or __________% of a
dollar.
3.
75% of something means 75 of the _________
equal parts of something.
Page 98
Group Work
 Fill
1.
2.
3.
in the blank
If every registered student attends a night class,
you can say that ______% of the students are
there.
If Gloria gets every problem right on a math
quiz, you can say she got ______% of the
problems right
If Bernard gets only half of the problems right on
the math quiz, you can say that he got ______%
of the problems right.
Page 99
Changing Decimals to Percents
 Percent
is similar to a two-place decimal.
•
To change a decimal to a percent, move the
decimal point two places to the right & write the
percent sign (%).
•
If the decimal point moves to the end of the
number, it is not necessary to write it.
•
You may have to add zeros.
Page 99
Example
 Write
each decimal as a percent
1.
0.32
2.
0.005
3.
0.125
Page 99
Group Work
 Write
each decimal as a percent
1.
0.09
2.
0.0375
3.
0.2
Page 100
Changing Percents to Decimals
 To
change a percent to a decimal, drop the percent
sign (%) & move the decimal point two places to
the left.
 You
may have to add zeros.
Page 100
Example
 Write
each percent as a decimal.
1.
62 ½%
2.
7%
3.
200%
Page 100
Group Work
 Write
each percent as a decimal.
1.
6 2/3%
2.
1.5%
3.
8%
Page 101
Changing Fractions to Percents
 There
are two ways to change a fraction to a
percent:
• Method 1: Multiply fraction by 100%
• Method 2: Divide the denominator of the
fraction into the numerator & move the point
two places to the right.
Page 101
Example
 Write
1
2
3
4
25
1
6
3
7
each fraction as a percent.
Page 101
Group Work
 Write
1
2
3
3
10
4
5
1
8
each fraction as a percent.
Page 102
Changing Percents to Fractions
 To
change a percent to a fraction, write the
percent as a fraction with 100 as the denominator
& reduce.
Page 102
Example
 Write
each percent as a common fraction.
1.
8 1/3%
2.
4%
3.
80%
Page 102
Group Work
 Write
each percent as a common fraction.
1.
66 2/3%
2.
12%
3.
90%
Pages 104 – 105
Finding a Percent of a Number
 To
find a percent of a number, change the percent
Method 1: to a decimal or
Method 2:to a fraction
• & multiply.
 If you want to multiply by a complex percent like
16 ⅔%, it is easiest to change the percent to the
fraction that it is equal to & then multiply.
• If you don’t know the fraction value of a
complex percent, multiply by the improper
fraction form of the percent, & put the other
number over 100.
Pages 104 – 105
Example
 Use
the method that you find easier to solve the
following:
1.
1.8% of 753
2.
0.8% of 56
3.
62 ½% of 176
Pages 104 – 105
Group Work
 Use
the method that you find easier to solve the
following:
1.
2.6% of 390
2.
1 ½% of 200
3.
50% of 418
Page 108
Solving Two-Step Problems
 Many
applications of finding a percent of a
number require two steps.
1. find the percent of a the number.
2. add it to or subtract it from the original number
Page 108
Example
 Read
1.
2.
each problem carefully to decide whether to
add or subtract in the second step
A computer that sold for $1,200 last year is now
on sale for 15% less. What is the price of the
computer this year?
Elizabeth earns $576 each week. If she gets an
8% raise, how much will she take home each
week?
Page 108
 Read
Group Work
each problem carefully to decide whether to
add or subtract in the second step
1. A jacket originally selling for $48 was on sale
at 20% off. Find the sale price of the jacket.
2. For lunch Brain bought a sandwich for $2.50.
The sale tax where Brain lives is 6%. What was
the price of the sandwich including sales tax?
3. Paul’s part-time job earns him $360 each week.
His employer withholds 18% of Paul’s pay for
taxes & social security. How much does Paul
take home each week?
Pages 110 – 111
Finding What Percent One
Number is of Another
 To
find what percent one number is of another,
make a fraction by putting the part (usually the
smaller number) over the whole.
 Reduce
the fraction & change it to a percent.
Pages 110 – 111
Example
 Solve
1. 792
the following:
is what percent of 200,000?
2. 2,600
3. 12
is what percent of 10,000?
is what percent of 72?
Pages 110 – 111
Group Work
 Solve
the following:
1. 15
is what percent of 75?
2. 84
is what percent of 105?
3. 27
is what percent of 120?
Page 114
Finding a Percent of Change
 A common
application of percent is to find a
percent of change.
•
First, find the amount of the change.
•
Next, make a fraction with the change over the
original (earlier) amount.
•
Finally, change that fraction to a percent.
Page 114
Example
 Solve
1.
2.
each problem. Remember to write the
amount of change over the original amount.
A color TV that originally sold for $380 was on
sale for $285. By what percent was the original
price discounted?
Anna’s weekly salary is $500, but she takes
home only $395. The deductions her employer
takes out are what percent of her weekly salary?
Page 114
Group Work
 Solve
1.
2.
each problem. Remember to write the
amount of change over the original amount.
At the beginning of the football season, 800
people attended a high school game. After the
team lost several games, the attendance was
down to 560 people. By what percent did the
attendance drop?
Last year a town budget was $2.4 million. This
year the budget will be 2.7 million. By what
percent did the budget increase from last year?
Pages 115 – 116
Finding A Number When a
Percent is Known
 If
a percent of a number is given & you are
looking for the whole number, change the percent
into either a fraction or a decimal & divide it into
the number you have.
Pages 115 – 116
Recognizing Types of Percent
Problems
 Three
parts of a percent problem: The part, the
whole, & the percent
 Three
types of problems from these number
•
Finding the part
•
Finding the percent
•
Finding the whole
Pages 115 – 116
Example
 Solve.
1.
2.
Of the 500 employees at Ajax Electronics, only
6% go to work by public transportation. How
many employees at Ajax use public
transportation to get to work?
The Moore family expects to spend $1,200 on
their summer vacation. So far they have saved
$900 toward their vacation. What percent of the
cost have they saved?
Pages 115 – 116
Group Work
 Solve.
1.
2.
3.
The sales tax rate in Linda’s state is 5%. How
much tax does she have to pay on a shirt that
costs $29?
Juan saves 10% of his take-home pay. He puts
$160 in his savings account each month. What is
his monthly take-home pay?
The total bill for Paul & Dorothy’s dinner was
$32. They left a tip of $4.80. The tip was what
percent of the total bill?
Using
Number
Power
Pages 130 – 161
Pages 130 – 134
Changing Units of Measurement

To change from a large unit of measurement to a
small unit, multiply by the number of a small
units contained in one large unit.

To change from a small unit of measurement to a
large unit, divide by the number of small units
contained in one large unit.
Pages 130 – 134
Example
1.
2.
192 ounces = ? pounds
420 quarts = ? gallons
3) 2 hr 38 min
4) 5 wk 4 day
+ 6hr 47 min
6 wk 6 day
+ 4 wk 5 day
5) 9 wk
- 4 wk 2day
7) 30 wk 6 days ÷ 12
6) 8 m 36 cm
x
4
Pages 130 – 134
Group Work
1.
5 miles = ? Feet
2) 10 min 15 sec
5 min 52 sec
+ 9 min 47 sec
4) 18 yd 2ft
x
7
5) 9 kg 420 g ÷ 4
3) 5 yd
- 2 yd 2ft
Pages 135 – 136
Perimeter

A rectangle is a flat figure with four sides. The
sides across from each other are equal in length &
are parallel, which means that they remain the
same distance from each other. The long side of a
rectangle = length, & the short side = width.
 Perimeter = The distance around a sided shape.
• To get the perimeter of a rectangular shape, add
all four sides together or double the length,
double the width, & add these two answers.
 formula: P = 2l + 2w (P = perimeter, l =
length, & w = width.)
Pages 135 – 136
Example
1.
How much fencing is required to enclose a
garden that is 18 feet wide & 23 feet long?
2.
Wire fencing costs $1.29 per foot. Find the cost
of the fencing for the garden in the problem
above.
Pages 135 – 136
Group Work
1.
2.
3.
Mr. Wiley wants to put weather stripping around
the large windows of his house. Each window is
3 feet wide & 5 feet high. There are 11 of these
windows in his house. How many feet of
weather stripping must Mr. Wiley buy?
If the weather stripping costs 39¢ per foot, how
much will it cost to buy weather stripping for the
windows of Mr. Wiley’s house?
Mr. Romney’s rectangular garden required 82
feet of fencing to completely enclose it. If the
garden is 27 feet long how wide is it?
Pages 137 – 139
Area

When you want to decide how much carpeting to
buy to cover your floor, or how much paint you
need to cover a wall, you find the area.
 Area = the measure of the amount of space inside
a flat figure. It’s measured in square units: square
inches, & so on. Rectangular shape: length x
width = area.
 To find the length or width of a rectangle when
the area & either the length or width are given,
divide the area by the side of the rectangle you
know.
Pages 137 – 139
Example
1.
What is the area of a room that is 12 feet wide &
18 feet long?
2.
Find the area in yards for the room in problem 1.
Pages 137 – 139
Group Work
3.
4.
5.
If a carpet costs $16.99 per square yard, how
much would it cost to buy carpet for the room in
problem 1?
A store charges $45 to deliver & install carpet.
Find the total cost including delivery &
installation for the carpet in the last problem?
Mr. Cortez wants to put tiles on his basement
floor. Each tile is 1 square foot in area. His
basement floor is 63 feet long & 24 feet wide.
How many tiles does he need to cover the
basement floor?
Pages 140 – 141
Volume

To find out how much space is inside things like
boxes, containers, suitcases, & rooms you have to
find volume. In order to find out the amount of
space inside a 3-D object, you have to find
volume. That means that, in addition to length &
width, they also have height or depth. Volume is
measured in cubic units: cubic inches, & so on.

Volume = length x width x height
Pages 140 – 141
Example
1.
Mr. Miller is adding a room to the back of his
home. For the foundation, he must dig a hole
that is 16 feet long, 12 feet wide, & 4 feet deep.
How many cubic feet of soil have to be
removed?
2.
Find the volume of a shoe box that is 9 inches
wide, 15 inches long, & 6 inches high.
Pages 140 – 141
Group Work
1.
2.
3.
Mrs. Rodriguez’s ice tray is 1 inch deep, 9 inches
long, & 3 inches wide. How many cubic inches
of ice will the tray hold?
Mrs. Rodriguez’s try makes ice cubes that are
each 1 cubic inch. How many cubes can be made
with five trays.
When the Corona Family goes on vacation, they
always pack one big trunk instead of a lot of
small suitcases. Their trunk measures 6 feet long
by 4 feet wide by 3 feet high. Find the volume of
the packing space of the trunk.
Pages 149 – 150
Finding an Average

To find the average of a group of numbers, add
the numbers together & divide by the number of
numbers you added.
Pages 149 – 150
Example
1.
At night, Pete drives a cab. Monday night he
drove for 3 hours, Tuesday night for 6 hours,
Wednesday night for 5 hours, Thursday night for
4 hours & Friday night for 7 hours. What was the
average number of hours he drove each night?
2.
On Monday night, Pete made $14.30 in tips; on
Tuesday $28.55; on Wednesday $26.15; on
Thursday, $21.65 & on Friday, $42.35. How
much did Pete average in tips per night.
Pages 149 – 150
Group Work
1.
During a basket ball tournament, the number of
tickets sold each night was: first night – 4,065
tickets; second night – 3,983 tickets; third night
– 4,117 tickets; and the last night – 5,267 tickets.
What was the average number of tickets sold for
each night of the tournament?
2.
Elizabeth received the following scores on math
tests: 86, 76, 93, 89, 68, & 92. What was the
average score of her math tests?
Didn’t get to
this set of
slides Last
time I taught
this class.
All set up just
have to enter
examples &
group work.
Using
Number
Power # 2
Pages 133 - 168
Pages 142 – 143
Circumference of a Circle
 Diameter
= The distance across a circle, which
can be shown by a straight line that goes through
the center of a circle.
 Circumference = The distance around a circle.
To find the circumference of a circle, multiply the
diameter of the circle by π (pi).
• Formula: C = πd. C is the circumference, π is
22/7 or 3.14, and d is the diameter.
Pages 142 – 143
Example
Pages 142 – 143
Group Work
Pages 144 – 145
Area of a Circle
 Radius
= The distance halfway across a circle.
r = 2d
 Area = The amount of space in closed in a circle.
To find the area of a circle, multiply the radius of
the circle by itself & then multiply the product by
π (pi).
• Formula: A = πr2. A is the area, π is 22/7 or 3.14,
and r is the radius.
Pages 144 – 145
Example
Pages 144 – 145
Group Work
Pages 150 – 151
Finding Interest for One Year

Interest is money that money earns. On a loan,
interest is the payment you must make for using the
lender’s money. On a savings account, interest is
the money the bank pays you for using your money.
•

Formula: i = prt (where i is the interest in dollars;
p is the principal, the money borrowed or saved; r
is the percent rate, which can be written either as a
fraction or a decimal; & t is the time in years
The formula is read as interest is equal to the
principal times the rate times the time.
Pages 150 – 151
Example
Pages 150 – 151
Group Work
Pages 152 – 153
Finding Interest for More or Less than One Year
 Interest rates are usually given for one year.

If you want to find interest for less or more than
one year, write the number of months over 12 (the
number of months in one year). Use this fraction
for t in the formula i = prt.
Pages 152 – 153
Example
Pages 152 – 153
Group Work
Pages 154 – 155
Finding Compound Interest
 In
most saving accounts, money earns compounds
interest.
 This means that your balance (the principal)
changes by the addition of interest on a regular
time basis such as quarterly (every three months),
monthly, or even daily.
Pages 154 – 155
Finding Compound Interest: Cont.
P =
principal amount (the initial amount you
borrow or deposit)
 r = annual rate of interest (as a decimal)
 t = number of years the amount is deposited or
borrowed for
 A = amount of money accumulated after n years,
including interest.
 n = number of times the interest is compounded
per year
Pages 154 – 155
Example
Pages 154 – 155
Group Work
Pages 156 – 157
Comparing Food Prices: Unit Pricing
 Similar
food items come in different package
sizes. It is not always easy to tell which package
is the best buy.
 Suppose you find two different brands of peas,
one in a 16-ounce can priced at 72 cents &
another in a 10 ounce can priced at 55 cents. To
find the best buy, calculate the price per ounce of
peas in each can.
 The word per suggests division. Finding this price
is called unit pricing.
Pages 156 – 157
Example
Pages 156 – 157
Group Work
Pages 158 – 159
Finding the Percent Saved at a Sale
 To
find what percent you saved by buying an item
on sale, put the amount saved over the original
price, reduce, & change the fraction into a
percent.
 To
find a sale price. After you find the percentage,
subtract it from the original selling price.
 Look
at your answer to see if it seems reasonable.
Pages 158 – 159
Example
Pages 158 – 159
Group Work
Pages 167 – 168
Buying on an Installment Plan
 Buying
on an installment plan is a way to make
partial payments for an item. However, by paying
in regular installments, a customer can end an up
paying much more than the list price of an item.
 Down
payment is a part of the total cost of an
item. It is paid at the time of purchase. The rest is
paid month by month. Down payment is a
percentage of the total cost. Calculate down
payment by converting the percent to a decimal &
multiplying the total cost.
Pages 167 – 168
Example
Pages 167 – 168
Group Work
Not in the Book
Percent of a Number: Sales Tax
 To
find the tax multiply the percent (changed into
decimal form) & the cost
 To find the total add the tax to the cost.
Not in the Book
Example
Not in the Book
Group Work