Transcript Number processes - Glen Urquhart High School

Aim Of The Power Point
• This power point has been produced as the
first step towards teaching numeracy across
the curriculum in a consistent manner.
• The power point has been designed for
teachers to use as a reference in advance of
teaching numeracy skills in their own subject or
for parents as an aid to helping their offspring.
• For any clarification on any of the topics please
consult a member of the maths department.
Our Mission Statement:
• Glen Urquhart High School is committed
to raising the standards of numeracy of
all of its students, so that they develop
the ability to use numeracy skills
effectively in all areas of the curriculum
and the skills necessary to cope
confidently with the demands of
further education, employment and
adult life.
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Contents
Number & Number Processes
Subtraction
Multiplication
Division
Decimals
Fractions
Equivalent & Simplifying
Fraction of a Quantity
Mixed Numbers & Improper Fractions
Addition & Subtraction
Multiplication & Division
Information Handling
Averages & Spread
Frequency Tables
Bar Graphs
Line Graphs & Scatter Graphs
Pie Charts
Contents
• Number & Number Processes
• Decimals
• Fractions
• Information Handling
• A current definition of numeracy:
• Numeracy is a proficiency which is developed mainly
in mathematics but also in othesubjects. It is more
than an ability to do basic arithmetic. It involves
developing confidence and competence with numbers
and measures. It requires understanding of the
number system, a repertoire of mathematical
techniques, and an inclination and ability to solve
quantitative or spatial problems in a range of
contexts.
• Numeracy also demands understanding of the ways in
which data are gathered by counting and measuring,
and presented in graphs, diagrams, charts and tables.
Number Processes
Addition
Subtraction by decomposition
Long Multiplication
Long Division
13-Apr-15
Decimals
Add & Subtract Decimals
Multiplying Decimals by 10,100,1000
Dividing Decimals by 10,100,100
Multiplying Decimals
Dividing Decimals
Rounding to Any Number of Decimal Places
Rounding to Significant Figures
13-Apr-15
Fractions
Simplifying Fractions
Fractions of a quantity
Percentages
Finding a Percentage (Calculator)
Finding (Simple) Percentages
Types of fractions
Add and Subtract fractions
Multipy and Divide fractions
Fractions
Simplifying Fractions
Fractions of a quantity
Percentages
Finding a Percentage (Calculator)
Finding (Simple) Percentages
Adding and subtracting fractions
Multiplying and Dividing fractions
26 + 57
Remember to keep all
Tens and Units in line!
26
+57
83
1
Write
down the 3
units
Start on the
right – add
up the units
6 + 7 = 13
Add up all
the tens
Carry the
1 ten to
the tens
column
Subtraction by decomposition
83 - 26
83 – 26
70
-
80
20
50



13
6
7
= 57
83 – 26
7
-
1
83
26
57
94 – 57
Borrow 10
from here
Put it here
80
-
90
50
30



14
7
7
= 37
94 - 57
8
-
1
4-7 we can’t do so
borrow from next
column and 9
goes down to 8
94
57
37
14-7=7
94 - 57
Quick way to set it out
8
-
1
94
57
37
300 - 59
0-9 we can’t do so borrow from
next column :can’t so borrow
from 3rd column which goes
down to 2 and can only give this
to adjacent column
2
1
9
1
300
- 59
2 4 1
2-0=0
9-5=4
10-9=1
We can now
borrow from
the second
column to give
one to the first
column
Written Method - Decomposition
Example
3482 - 1735
71
3482
-1735
7
711
3482
-1735
47
2
1
111 71
1
1
3482
-1735
1747
2-1=1
2-5,can’t do.
Borrow 1 from
the next
column. 12-5=7
7-3=4
4-7,can’t do.
Borrow 1 from
the next column.
14-7=7
Long multiplication
• Method 1 Chunking
18 x17
replace with 4 easy multiplications
• Split 18 into 10 and
8
• Split 17 into 10 and
7
• Total 4
multiplications
• 100+70+80+56
• answer=306
X
10
8
10
100
80
7
70
56
23 x46
replace with 4 easy multiplications
• Split 23 into 20 and
3
• Split 46 into 40 and
6
• Total 4
multiplications
• 800+120+60+18
• answer=1058
X
20
3
40
800
120
6
60
18
10
10
10 x 10
= 100
18
8
10 x 8
= 80
17
18x17
100
80
70
7
7 x 10
7x8
+56
= 70
= 56
306
Long Multiplication
Firstly write the sum correctly:
24
x34
That means units
over units and tens
over tens. This
makes the working
out easier.
Short Division
The quick way to divide by a single digit.
54 ÷ 3
We need to write this as:
3)5 4
1
3)5 4
2
5 divided by 3 is 1.
We can get 1 group of 3
out of 5 with 2 left over
3
6
9
12
15
18
21
24
27
.
30
2
5
18
3)5 4
2
24 divided by 3 is 8.
We can get 8 groups of 3
out of 24 with none left
over
3
6
9
12
15
18
21
24
27
.
30
8
2 3R2
4)9 4
1
9 divided by 4 is 2.
We can get 2 groups of 4
out of 9 with 1 left over
14 divided by 4 is 3.
We can get 3 groups of 4
out of 14 with 2 left over
.
4
8
12
16
20
24
28
32
36
40
1
9
14
2
2 3 .5
4)9 4 .0
1
2
9 tens divided by 4 is 2 tens.
There is 1 ten left over.
14 divided by 4 is 3.
There is a remainder of 2.
2 units divided by 4 is 0.5.
Long Multiplication
24
x34
96
1
Then the first part is
done as normal.
Bottom Unit x Top unit.
Bottom Unit x Top Tens.
Long Multiplication
Then, because we are
multiplying by ten we
write a 0 under the units
column.
24
x34
96
720
1
1
Then carry on as normal
Bottom Tens x Top Unit
Bottom Tens x Top Tens
Long Multiplication
24
x34
96
720
816
1
1
1
Then, underline the last
piece of working you did.
Then finally perform
a simple addition of
the two numbers
between the lines.
Long Division
• Long division is as simple as
memorizing the people in this family.
Dad
Mum
Sister
Rover
Brother
Long Division
• Each person represents a step in the
long division process.
3. Subtract
1. Divide
Sister
4. Bring down
Dad
Brother
2. Multiply
5. Repeat or
Remainder
Mum
Rover
• 947 divided by 2
• 947 is the dividend
• 2 is the divisor
• The whole number part of the answer is
the quotient and there may be a
remainder left over
Step 1 in Long Division
1. Divide
Dad
• Divide 2 into first
number
• Think how many 2’s
will fit into 9.
• Write that number
directly above the
number you
divided
into.
4
2)947
How many 2’s
will go into 9?
Step 2 in Long Division
4
2. Multiply
mum
• Multiply the divisor times
the first number in the
answer.
2)947
• Write your answer directly
under the 9 or the number you
just divided into.
8
2x4=8
Step 3 in Long Division
3. Subtract
Sister
• Draw a line under the 8.
• Write a subtraction sign
next to the 8.
4
2)947
8
1
• Subtract 8 from 9.
• Write your answer directly below the 8.
Step 4 in Long Division
4. Bring
down
4
2
)
9
4
7
• Go to the next number in
Brother
the dividend to the right
of the 9.
• Write an arrow under the 4.
8
14
• Bring the 4 down next to the 1.
Step 5 in Long Division
5. Repeat or
Remainder
Rover
• This is where you decide
whether you repeat the
5 steps of division.
4
2)947
8
14
• If your divisor can divide into your new number,
14, or if you have numbers in the dividend
that have not been brought down, you repeat
the 5 steps of division.
Step 5 in Long Division
5. Repeat or
Remainder
Rover
• Since there are no more
numbers to bring down & 2 will
not divide into 1, you do not
repeat the steps of division.
• The number left over, 1,
becomes the remainder.
47 3
2)947
8
14
14
07
6
1
R1
You did it!
47 3
R1
You’re
awesome!
2)947
You’re so
smart!
8
14
14
07
6
1
Cool
Dude!
Wolf!
Multiplying and Dividing
Decimals by 10, 100, and 1,000
The Basics:
• When you multiply by 10, 100, or 1,000, you
can move the decimal point to the right.
• The number of decimal places you move is
the same as the number of zeroes you are
multiplying by.
• When you divide by 10, 100, or 1,000, you
can move the decimal point to the left.
Move the decimal point once for each zero
you are dividing by.
1.492 x 100
Move the decimal to the right:
two spaces.
149.2
2,124.94 ÷ 1,000
Move the decimal to the left: three
spaces.
2.12494
4.2 ÷ 100
Move the decimal point to the left: two
spaces. Add a zero for the second space.
.042
15.36 x 1,000
Move the decimal point to the
right: three spaces. Add a zero
for the third space.
15,360
Decimals
Addition & Subtraction
Learning Intention
1.
To explain how to add and
subtract decimal numbers.
Success Criteria
1. Remember to keep decimal
point in line.
2. Make use of trailing 0’s
when needed.
13-Apr-15
Decimals
Addition & Subtraction
Example : 3.2 + 0.487 + 5.73
3.200
0.487
5.730
9.417
1 11
13-Apr-15
Keep point in
line
Decimals
Addition & Subtraction
Example : 6.2 – 3.19 + 1.783
6.200
+1.783
7.983
3.190
4.793
13-Apr-15
Add first
Then subtract
Steps for Multiplying Decimals
1.
Ignore decimals and multiply as before
2.
Count the number of digits after the
decimal in the original problem and make
sure the answer has the same number of
digits after the decimal.
Decimals
Simple Multiplication
Example 1 : 0.6 x 0.4
6 x 4 = 24
0. 24
2 digits after
decimal place
Example 2 : 0.09 x 0.3
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9 x 3 = 27
0. 027
3 digits after
decimal place
Decimals
Simple Multiplication
Example 3 : 0.071 x 0.5
71 x 5 = 355
4 digits after
decimal place
13-Apr-15
0. 0355
Simplify the following:
1.
0.07x0.03
2.
0.42x6
7x3
42 x 6
21
252
4 decimal places
0.0021
2 decimal places
2.52
3.
3.12x0.05
312 x 5
1560
4 decimal places
0.1560
4.
0.02x1.39
2 x 139
278
4 decimal places
0.0278
5.
1.22
1.2 x 1.2
12 x 12
6.
(0.3)2
0.3 x 0.3
3x3
144
9
1.44
0.09
7.
0.5x22
8.
10x0.314
5 x 22
10 x 314
110
3140
11.0
3.14
Steps for dividing by whole numbers
1. Use long division as if there were no decimal
point involved.
2. If necessary, add zeros after last digit in the
decimal.
3. Place decimal point directly above the
decimal point in the problem.
Divide the following:
4 65
1. 8 37 .2 0
32
52
48
40
40
0
7 87
2. 4 31.48
28
34
32
28
28
0
6 66
3. 33
3.3 219
21 .978
.78
198
217
198
19 8
198
0
Divide the following:
Divide the following:
33
4. 20.2
22 77.2
266
66
66
66
0
Decimals
Division of a Decimal
Do not attempt to divide by a decimal,
multiply the divisor so it is a whole number first.
Example 1 : 3.5 ÷ 0.7
35 ÷ 7 = 5
x 10
x 10
Example 2 : 0.8 ÷ 0.2
13-Apr-15
8÷2= 4
Decimals
Division of a Decimal
Do not attempt to divide by a decimal,
multiply the divisor so it is a whole number first.
Example 3 : 0.036 ÷ 0.04
3.6 ÷ 4 = 0.9
x 100
Example 4 : 24 ÷ 3000
13-Apr-15
24 ÷ 3÷1000 = 0.008
Steps for dividing by decimals numbers
1.
Change divisor to a whole number by
moving both numbers the same amount
of digits
2.
Divide as before
5.
.3778 ÷ .25 and round to the nearest
When rounding make
hundredth:
1 5 11 1.51
sure to calculate one digit
past required place value.
25
37.078
0.25
.3778
0
25
127
125
28
25
30
25
Decimals
Rounding to Any Number of Decimal Places
When rounding to :
1 decimal place look at 2nd decimal figure
e.g. 2.46
2 decimal place look at 3rd decimal figure e.g. 6.456
3 decimal place look at 4th decimal figure
e.g. 3.7846
4 decimal place look at 5th decimal figure
e.g. 13.1146
13-Apr-15
Decimals
Rounding to Any Number of Decimal Places
www.mathsrevision.com
Example : The number 4.2615937
Rounded to 1 decimal place, the number is 4.3
Rounded to 2 decimal place, the number is 4.26
Rounded to 3 decimal place, the number is 4.262
Rounded to 4 decimal place, the number is 4.2616
13-Apr-15
Created by Mr. Lafferty Maths Dept.
Significant Numbers
Learning Intention
1. To understand the
term significant number
for decimals and whole
numbers.
13-Apr-15
Success Criteria
1. To know the meaning of
significant number.
2. Apply knowledge to
problems.
Significant Numbers
In mathematics a figure or digit is significant
if it gives an idea of both:
(i) Quantity
(ii) Accuracy
IMPORTANT : If zero’s are employed just to position the decimal point
then they are considered NOT significant.
e.g.
506 cm
Has 3 significant figures.
50.6 cm Has 3 significant figures.
0.506 cm Has 3 significant figures.
0.00506 cm Has 3 significant figures.
13-Apr-15
Significant Numbers
IMPORTANT : When dealing with WHOLE NUMBERS you need
More information before you can tell if trailing zero’s are significant.
Question ? How many significant figures is this number to.
360
Is it 2 or 3 !!!
3
If I said 359 to the nearest ten is 360. How many significant figures. 2
If I said there are 360 deg. in a circle. How many significant figures.
YOU NEED TO KNOW THE CONTEXT OF THE QUESTION WHEN
DEALING WITH WHOLE NUMBERS WITH TRAILING ZEROS.
WORK OUT WHAT THE ZERO MEANS
Significant Figures
Decimals
0.001090
To the left of
The number
Middle of
the number
To the right of
the number
Always Significant
Not Significant
Always Significant
Whole Numbers
03060
To the left of
The number
Middle of
the number
? Depends
More Info.
Not Significant Always Significant Read Question
13-Apr-15
Fractions
A Fraction consists of 2 parts.
3
5
Top number is called the numerator
Bottom number is called the denominator
Fractions
2
4
3
6
Write down the fraction that is shaded in light blue.
Fractions
It is possible to find a fraction equivalent to any
fraction that you have by multiplying the numerator
and the denominator by any number.
Find a fraction equivalent to :
x3
6
2

x3
12
4
x2
2
1
x2 
10
5
Fractions
We can sometimes simplify a fraction by finding a HCF
between the numerator and denominator.
Simplify the fractions below :
1
2

÷2
2
4
÷2
1
3
÷3 
4
12
÷3
Fractions of a quantity
Learning Intention
1. To explain the 2 step
process of finding a
fraction of a quantity.
Success Criteria
1. To know the 2 step for
finding a fraction of a
quantity.
2. Be able to calculate the
fraction of a quantity.
Fractions of a quantity
Q.
Do the calculations below.
1
of 120
2
1
of 120
4
Simply divide by the bottom number
60
2 120
30
4 120
Fractions of a quantity
Q.
Do the calculation below.
2
of 24
3
Simply divide by the bottom number
Then multiply the answer by top number
Step 1:
8
3 24
Step 2:
8 x 2 = 16
Fractions of a quantity
Q.
Do the calculation below.
5
of 360
8
Simply divide by the bottom number
Then multiply the answer by top number
Step 1:
45
8 360
Step 2:
45 x 5 = 225
Percentages
Learning Intention
1. To explain what the term
percentage means and how
it is connected to a
fraction and a decimal.
Success Criteria
1. To understand the term
percentage.
2. Understand connection
between percentage,
fraction and decimal.
3. Find a percentage of a
quantity.
31 out
of a 100
Percentages
When a shape is divided into
100 ‘bits’ each bit is called
“ 1 percent”
31
= 0.31
31 % means
100
7
= 0.07
7 % means
100
7 out of
a 100
Percentages
Q. Write down the following as a fraction and a decimal.
27
= 0.27
27% 
100
15% 
15
= 0.15
100
2%
2
= 0.02
100

Percentages
Q.
Change the fractions to percentages
1
2
7
10
Simply do the division the multiply by 100
Step 1:
0.5
2 1.0
Step 1:
Step 2: 0.5 x 100 = 50% Step 2:
0.7
10 7.0
0.7 x 100 = 70%
Percentages
Q.
Paul scored 24 out of 30 in English and
36 out of 40 in Maths.
Find percentage of each and say which
he is best at?
Simply do the division the multiply by 100
24
Step 1:
30
Step 2: 0. 8x 100 = 80%
Step 1:
Step 2:
36 Maths
40
0.9 x 100 = 90%
Percentages
(Calculator)
Learning Intention
1. To understand how to
calculate a percentage
using a calculator.
Success Criteria
1. Use a calculator to
calculator.
2. Show all working.
of means
times
Q.
Percentages
Find 17% of £450
Remember
money 2
decimal
places
17
 450
100
17  100 x 450 = £76.50
1
7

Calculator Keys
1
0
0
x
4
5
0
=
76.5
of means
times
Q.
Percentages
Find 4% of £70
Remember
money 2
decimal
places
4
 70
100
4  100 x 70 = £2.80
4

Calculator Keys
1
0
0
x
7
0
=
2.8
Simple Percentages
Learning Intention
1. To explain some simple
percentages.
Success Criteria
1. To know the simple
percentages.
2. Calculate simple percentage
without a calculator.
Simple Percentages
Copy down and learn the following basic percentages
100% 50%
1
1
2
1
33 %
3
1
3
25% 20% 10% 5% 1%
1
4
1
5
1
10
1
1
20 100
Percentages
Q.
Find 25% of £40
1
 40
4
40 ÷ 4 = 10
Percentages
Q.
Find 5% of £300
1
 300
20
300 ÷ 20 = 15
Simple Percentages
Learning Intention
1. To explain some more basic
percentages.
Success Criteria
1. To know the basic
percentages.
2. Calculate basic percentage
without a calculator.
Simple Percentages
Copy down and learn the following basic percentages
100%
1
50%
1
2
1
33 %
3
1
3
2
66 % 20%
3
2
3
1
5
40% 60% 80%
2
5
3
5
10% 30% 70%
1
10
3
10
7
10
4
5
90%
9
10
Percentages
Q.
Find 30% of £40
3
 40
10
40 ÷ 10 x 3 = 12
Percentages
Q.
Find 75% of £600
3
 600
4
600 ÷ 4 x 3 = 450
These numbers are called
1
whole numbers
15
6
22
3
47
MALT©2006 Maths/Fractions Slide Show : Lesson 1
These numbers are called
1
2
fractions
3
15
5
6
2
3
12
22
4
7
MALT©2006 Maths/Fractions Slide Show : Lesson 1
Shout out
whole number or fraction
when you see each number
Ready ?
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number
or
fraction
25
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number
or
fraction
whole number
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number
or
fraction
3
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number
or
fraction
whole number
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number
or
fraction
2
3
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number
or
fraction
fraction
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number
or
fraction
1
8
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number
or
fraction
27
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number
or
fraction
whole number
MALT©2006 Maths/Fractions Slide Show : Lesson 1
When a number includes both
whole numbers and fractions
1
1
2
MALT©2006 Maths/Fractions Slide Show : Lesson 1
It is called a
mixed number
1
1
2
MALT©2006 Maths/Fractions Slide Show : Lesson 1
Here are some
mixed numbers
2
1
3
1
3
6
8
2
5
5
4
9
2
MALT©2006 Maths/Fractions Slide Show : Lesson 1
1
4
Shout out what the number is
either
whole number
fraction
mixed number
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number , fraction or mixed number
4
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number , fraction or mixed number
4
8
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number , fraction or mixed number
51
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number , fraction or mixed number
2
25
MALT©2006 Maths/Fractions Slide Show : Lesson 1
whole number , fraction or mixed number
14
1
4
MALT©2006 Maths/Fractions Slide Show : Lesson 1
So a mixed number
is both whole
numbers and
fractions together.
MALT©2006 Maths/Fractions Slide Show : Lesson 1
Mixed numbers
can be written
differently.
MALT©2006 Maths/Fractions Slide Show : Lesson 1
1
1
2
This number can
also be written as
3
2
MALT©2006 Maths/Fractions Slide Show : Lesson 1
1
1
2
can you
explain why?
3
2
MALT©2006 Maths/Fractions Slide Show : Lesson 1
1
1
2
3
2
MALT©2006 Maths/Fractions Slide Show : Lesson 1
2
1
4
9
4
MALT©2006 Maths/Fractions Slide Show : Lesson 1
Fractions
7
A fraction, like,
3
where the numerator is bigger
than the denominator is called a ‘Top-Heavy’ fraction.
A number,like, 5
3
consisting of
4
a ‘whole number’ part and a ‘fraction’ part
is called a Mixed fraction
13-Apr-15
Mixed to Top Heavy
Changing a mixed fraction to a top-heavy.
3
5 
4
1 1 1 1
1 1 1 1
1 1 1 1
   )(    )(    )
4 4 4 4
4 4 4 4
4 4 4 4
1 1 1 1
1 1 1 1
1 1 1
(    )(    )  
4 4 4 4
4 4 4 4
4 4 4
(
5 wholes are (5  4 ) 20 quarters and we have an extra 3 quarters
so
so
3
5
4
23
5  4  3  23 quarters 
4
37
2

7
7  5  2  37 fifths
5
5
7 wholes are (7  5 ) 35 fifths and we have an extra 2 fifths
13-Apr-15
here is the link
and you get 16 thirds
5
1
3
5 x 3 = 15
16
3
then add the 1
MALT©2006 Maths/Fractions Slide Show : Lesson 1
here is the link
and you get 12 fifths
2
2
5
2 x 5= 10
12
5
then add the 2
MALT©2006 Maths/Fractions Slide Show : Lesson 1
here is the link
and you get 29 sixths
4
5
6
4 x 6 = 24
29
6
then add the 5
MALT©2006 Maths/Fractions Slide Show : Lesson 1
And this one….
1
3
4
?
4
MALT©2006 Maths/Fractions Slide Show : Lesson 1
Try these
with a friend…..
2
2
3
?
3
MALT©2006 Maths/Fractions Slide Show : Lesson 1
And this one….
4
1
2
?
2
MALT©2006 Maths/Fractions Slide Show : Lesson 1
And this one….
2
4
5
?
5
MALT©2006 Maths/Fractions Slide Show : Lesson 1
And this one….
1
6
8
?
?
MALT©2006 Maths/Fractions Slide Show : Lesson 1
now try these
WALT: to understand mixed
numbers
1
2
3
3
3
6
2
2
4
5
1
3
2
5
6
four and a half
three and two thirds
five and a quarter
MALT©2006 Maths/Fractions Slide Show : Lesson 1
answers
5
3
21
6
10
4
16
3
17
6
nine halves
eleven thirds
twenty one quarters
MALT©2006 Maths/Fractions Slide Show : Lesson 1
Add / Sub Fractions
You can only add or subtract fractions if:
DENOMINATORS (bottom numbers) ARE THE SAME NUMBER
13-Apr-15
Example 1
Example 2
3 2 5
 
7 7 7
7 1 6
3
 

8 8 8
4
Adding Fractions of
the same type
Examples
1 3 4
 
7 7 7
3
1
5 3 
7
7
8 7
1
 
9
9 9
2
3
1
15  4  11
7
7
7
13-Apr-15
4
8
7
Adding Fractions of the same type
Examples
2
6 3 9
   1
7
7 7 7
16
5
9 7
15   15
 16
11 11
11
11
13-Apr-15
Add Fractions
When dealing with mixed fractions
deal with ‘whole’ part first then the fraction part
3
4
3 4
2 1  21 
5
5
5 5
3
2
4
5
13-Apr-15
7
5
Subtract Fractions
When dealing with mixed fractions
deal with ‘whole’ part first then the fraction part
5
1
7 4 74 
6
6
4
3
6
2
3
3
13-Apr-15
5 1

6 6
Harder Fractions
Learning Intention
1. To understand how to add
and subtract fractions
with different
denominators.
Success Criteria
1. Apply ‘ kiss and smile’ method.
2. Convert top heavy fractions
to mixed fractions.
3. Simplify fractions.
13-Apr-15
We are going
to
Harder
use the kiss and
smile method
Fractions
How can we add /subtract fractions that have
different denominators
Step 1 : Do the smile
Step 2 : Do the kiss
Step 3 : Add/Subtract
the numerator
and simplify
13-Apr-15
Harder Fractions
Step 1 : Do the smile
Step 2 : Do the kiss
Example 1
Step 3 : Add/Subtract
the numerator
and simplify
13-Apr-15
1 1

2 4
4 +2
8
6 ÷2
 ÷2
8
3

4
Harder Fractions
Step 1 : Do the smile
Step 2 : Do the kiss
Example 1
Step 3 : Add/Subtract
the numerator
and simplify
13-Apr-15
5 1

6 5
25 - 6
30
19

30
Harder Fractions
Step 1 : Do the smile
Step 2 : Do the kiss
Example 1
Step 3 : Add/Subtract
the numerator
and simplify
13-Apr-15
5 3

6 4
20 + 18
24
38

24
7
14
14 ÷2
1
 1 ÷2  1
12
24
24
Harder Fractions
1 2
1
2
2 3  23 
2 3
2
3
1 2
5 
2 3
1
 5 1
6
1
6
6
13-Apr-15
3 +4
6
7

6
1
1
6
Harder Fractions
7 2
7
2
7 4 74 
8 3
8
3
7 2
3 
8 3
5
3
24
5
3
24
13-Apr-15
21 - 16
24
5

24
Most Difficult
Fractions
3 5
3 5
4  4 
4 6
4 6
7
 5 1
12
7
6
12
18 + 20
24
38

24
7
14
1
1
12
24
13-Apr-15
Top Heavy to Mixed
Quick method
NUMERATOR  DENOMINATOR
7
can be written as 7  3
3
2 remainder 1
37
1
2
3
13-Apr-15
Top Heavy to Mixed
General
7
means seven thirds
3
7
1 1 1
1 1 1
1
(   )(   )
3
3 3 3
3 3 3 3
7 3 3 1
  
3 3 3 3
7
1
11
3
3
7
1
2
3
3
13-Apr-15
Top Heavy to Mixed
17
means seventeen fifths
5
17
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1
(     )(     )(     ) 
5
5 5 5 5 5
5 5 5 5 5
5 5 5 5 5 5 5
17 5 5 5 2
   
5 5 5 5 5
17
2
111
5
5
2
17
3
5
5
13-Apr-15
Top Heavy to Mixed
Quick method
NUMERATOR  DENOMINATOR
17
can be written as 17  5
5
3 remainder 2
5 17
2
3
5
13-Apr-15
Subtracting Fractions
1
2
1 2
6 2  62 
4
3
4 3
3
12 5

12 12
13-Apr-15
4
1 2

4 3
4
5
12
3
7
12
3 -8
12
5

12
Most Difficult
Fractions
1 1
1
1
7 1  7 1  
5 6
5
6
13-Apr-15
1 1
 6 
5 6
6 -5
30
1
 6
30
1
6
30
1

30
Subtract Fractions
When dealing with mixed fractions
deal with ‘whole’ part first then the fraction part
1 6 1
1  
6 6 6
5

6
13-Apr-15
Multiplying Fractions
How much is one-half of one-half?
we show one-half of a circle.
To find one- half of
one- half, we divide
the half in half.
We see this equals
one quarter.
Written out the Problem
looks like this:
1 X 1
2
2
=
1
4
Multiplying Fractions
• When you multiply two fractions
that are between 0 and 1 the
answer is smaller than both
fractions.
½x¾=
3
8
Look at the diagram on the
next slide to understand why.
Multiplying Fractions
Conceptual Understanding
½x¾=
3
8
¼
¼
¼
1/8
1/8
1/8
¼
How to Find a Fraction of a
Fraction
•
The first thing to remember is
“of” means multiply in
mathematics.
of = x
How to Find a Fraction of a
Fraction
•
Step 1 - When you see a fraction
problem you know when you read
“of” in the problem you multiply.
1 of
4
x
2
9
How to Find a Fraction of a
Fraction
•
Step 2 – Multiply your top
numbers (numerators) straight
across.
1 x 4 = 4
2
9
•
How to Find a Fraction of a
Fraction
Step 3 – Then multiply your bottom
numbers (denominators )straight across.
1 x 4 = 4
2
9 18
•
How to Find the Fraction of a
Fraction
Step 4 – Simplify your answer.
In this case we reduce.
1 x 4 = 4 ÷ 2= 2
2
9 18 ÷ 2 9
Multiply and Simplify
÷
1 of
9
9
3
3
x
=
=
6
5 30 ÷ 3 10
Multiply and Simplify
8 of
3
24
12
2
÷
x
=
=
9
4 36 ÷12 3
Example
2
3
4
2
6
1
x
=
=
9
36
6
This fraction can be reduced. Divide
the numerator and denominator by 6.
Multiplying by a Whole
Number
If you want to multiply a fraction by a
whole number, turn your whole number into
a fraction by putting it over 1. If your
answer is improper (top heavy), divide the
bottom into the top.
4
20
80
x
= 5 = 16
5
1
Multiplying Fractions
Multiplying basic fractions
1. Multiply the (numerators ) top numbers
2. Multiply the (denominators) bottom numbers
3 Simplify
Example 1
3 3 33
9
 

4 5 4  5 20
13-Apr-15
Example 2
4 5 4  5 20 2
 


5 6 5  6 30 3
Multiplying Fractions
Multiplying basic fractions
Example 3
3 2 3 6
5
2     1
5 1 5 5
6
Example 4
2 4 2 8
2
4     2
3 1 3 3
3
Another
Example
15 x 1
5
15
=
=
1
6
6
2
15 and 6 are in the 3 times table
2R1
2 5
Five halves is top heavy so we
divide the bottom into the top.
2
1
2
Simplifying Factors
• Before you multiply, you can make the
problem simpler.
• You can find the largest table both
numbers have in common
• divide the top number and bottom
number by this number, and rewrite the
problem.
Example 1
5 x 81
16 2
7
5
14
In the second fraction, 8
and 16 have table 8 in
common
8 ÷ 8 = 1 and 16 ÷ 8 = 2
Now, multiply with the
simpler numbers.
Top 5 x 1 = 5
and bottom 7 x 2 = 14.
Example 2
12
5
x
3
12 6
The top of the first fraction
and the bottom of the
second fraction have a table
in common , 2.
2 ÷ 2 = 1, and 12 ÷ 2 = 6.
Now, multiply:
5
18
How to Find a Fraction of a
Mixed Number
•
Step 1 - When you see a fraction
problem you know when you read
“of” in the problem you multiply.
1 of
4
x
3
2
9
How to Find a Fraction of a
Mixed Number
• Step 2 – Change the mixed number to an
improper ( top heavy) fraction.
27 + 4
+
x
1 x 3 4 31
2 27 9 9
How to Find a Fraction of a
Mixed Number
•
Step 3 – Multiply the
numerators straight across.
1 x 31 = 31
2
9
How to Find a Fraction of a
Mixed Number
•
Step 4 – Multiply the
denominators straight across.
1 x 31 = 31
2
9 18
How to Find a Fraction of a
Mixed Number
•
Step 5 – Simplify your answer. In
this case change the improper
fraction to a mixed number.
1R13
1 x 31 = 31 18)31
2 9 18 13
= 1 18
Multiply and Simplify
35 + 4
R11
1
+
1 x 5 x4 28) 39
4 35 7
11
39
39
1x
=
= 1 28
28
7
4
Multiply and Simplify
24 + 3
4 x 6 3 27 = 108
5 24 4 4 ÷ 20
8 4= 2
5 20 ÷ 4 5
20)108
+
x
Multiply and Simplify You’re
24 + 1
2 x6 1
4
5 24
2 x 25 = 50
20
5 4
+
x
shining!
Multiply and
You’re
Simplify shining!
50
2
20 20)50
10
2
20
R 10
1
10 ÷10 =
2
20 ÷10
2