Transcript Document

Notes
8th Grade
Pre-Algebra
McDowell
LCM
LCM
9/25
Least common multiple
The smallest number that
is a multiple of both
numbers
Steps
To
Find
LCM
1. Make a multiplication table
for each number
2. Compare the multiplication
tables
3. Pick the smallest number
that both (all) tables have
Example
Find the LCM of 8 and 3
1
2
3
4
5
6
7
8
8
16
24
32
40
48
56
64
1. Make a
mult table
2. Compare
3
6
9
12
15
18
21
24
3. Find the
smallest
match
The LCM of 8 and 3 is 24
You Try
Find the LCM between
1. 10 and 45
2. 12 and 7
Comparing
And
Ordering
fractions
Manipulate the fractions so
each has the same
denominator
Compare/order the fractions
using the numerators (the
denominators are the same)
You try
Workbook
p 76
# all
Fractions and Decimals
9/28
Terminating
Decimal
a decimal that ends
Repeating
Decimal
When the same group of numbers
continues to repeat forever
1¼ or 1.25
4
4.3
or 4.33333333333
Converting
Fractions
To
decimals
Example
1. Keep the whole number a
whole number
2. Divide the numerator by the
denominator
Converting
Terminal
decimals
to
fractions
1. Find the place value of the
terminating decimal
2. Place the numbers after the
decimal over the place value
Keep whole numbers as whole
numbers
3. Simplify the fraction to
lowest terms
Example
6.925
925
1000
The 5 is in the thousandths
place so 1000 is the
denominator
6
925  25
6 1000  25
6
37
40
Simplify
Converting
Repeating
decimals
to
fractions
1. Let the decimal = n
0.6 = n
2. Multiply both sides by 100
0.6 x 100 = n x 100
66.6 = 100n
3. Subtract n from both sides
Remember n = 0.6
66.6 = 100n
-0.6 - n
66 = 99n
4. Divide both side by 99 to
solve for n
4. Divide both side by 99 to
solve for n
66 = 99n
99 99
66 = n
99
5. Reduce the fraction
66  11= n
99  11
2=n
3
You try
Workbook
p 78
# 3-21 every 3rd
Adding and Subtracting Fractions 9/29
Steps
1. Convert all mixed numbers into
improper fractions
2. Find a common denominator
3. Add or subtract the numerators
4. Keep the common denominator
5. Write in simplest form (change
all improper fractions back into
mixed numbers)
Example
Common
denominator
so add or
subtract the
numerator
Already in
simplest form
Example
Common
denominator
so add or
subtract the
numerator
Already in
simplest form
because we do
not know
what x is
Find a common
denominator
24
Example
x4
x4
Add or
Subtract
numerators
Already in
simplest form
Converting
A Mixed
Number
To an
Improper
MAD face
Multiply, Add, keep the Denominator
1. Multiply the denominator by
the whole number then add the
product to the numerator
2. That is the new numerator—
keep the old denominator
6x5+3
6
30 + 3
6
33
6
Converting
An
Improper
To a
Mixed #
1. Divide the numerator by the
dominator
2. The quotient is the whole
number
3. The remainder is the new
numerator
4. Keep the same denominator
Example
Convert 26 to a mixed number
3
8 R2
3 26
-24
2
Example
1. Convert all mixed
numbers into improper
fractions
2. Find a common
denominator
3. Add or subtract the
numerators
4. Keep the common
denominator
5. Write in simplest
form
Additional
Examples
1. .
2. .
You try
Workbook
p 80
# all
Multiplying and Dividing Fractions
Steps to
multiply
fractions
9/30
1. Convert all mixed numbers into
improper fractions
2. Simplify by taking common
factors out of the numerators and
denominators
3. Multiply numerators together
4. Multiply denominators together
5. Write in simplest form (change
all improper fractions back into
mixed numbers)
2. Simplify by taking
common factors out of the
numerators and
denominators
Example

5

5 3. Multiply numerators
together
4. Multiply denominators
together
5. In simplest form
2. Simplify by taking
common factors out of the
numerators and
denominators
Example

x

2

2

x
3. Multiply numerators
together
4. Multiply denominators
together
5. In simplest form
Additional
Examples
1. .
2. .
Steps to
divide
fractions
1. Convert all mixed numbers into
improper fractions
2. Keep
1st fraction
3. Change
Multiplication to division
4. Flip
Write the reciprocal of the
2nd fraction
5. Follow steps to multiply fractions
Example
Keep
Change
Flip
X

4
Multiply

4
You try
Workbook
p 82
# all
Chapter 5 Review
10/1
Chapter 5 Quiz
10/2