MTH 3-07bMTH 3-07cMTH 4-07b
FractionsFractions
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Add & Subtract basic Fractions
Multiplying Fractions
Add & Sub Harder Fractions
Dividing Fractions
MTH 3-07bMTH 3-07cMTH 4-07b
StarterStarter
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
1. Solve the inequality 3x- 6=12
2. Calculate (- 29)+(- 11)+9
3. What fraction is x:
4. Simplify the fraction
5. What is the coordinate C(- 2,- 2) reflected in the x- axis?
25200
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X
MTH 3-07bMTH 3-07cMTH 4-07b
Mixed FractionsMixed Fractions
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. Understand what the Understand what the terms fraction, top-heavy terms fraction, top-heavy and mixed fraction are.and mixed fraction are.
1. We are learning theterm Fraction and Mixed Fraction.
2.2. Convert between top-Convert between top-heavy and mixed fraction.heavy and mixed fraction.
3.3. Solve problems Solve problems involving fractions.involving fractions.
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Fraction Fraction ReminderReminder
A Fraction consists of 2 parts.
Top number called the NUMERATOR
Bottom number called the DENOMINATOR
35
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
FractionsFractions
We can sometimes ‘simplify’ a fraction by dividing by the HCF of the numerator and denominator
F15 1 and 153 and 5
F27 1 and 273 and 9
1527
33
1527
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
FractionsFractions
A fraction, like, where the numerator is bigger
than the denominator is called a ‘Top-Heavy’ fraction.
73
A number like, consisting of
a ‘whole number’ part and a ‘fraction’ part is called a Mixed fraction
35
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Top Heavy to Top Heavy to MixedMixed
means seven thirds73
7 1 1 1 1 1 1 13 3 3 3 3 3 3 3
7 3 3 13 3 3 3
7 12
3 3
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
NUMERATOR DENOMINATOR
Top Heavy to Top Heavy to MixedMixed
can be written as 7 373
23 7
remainder 1
12
3
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
NUMERATOR DENOMINATOR
Top Heavy to Top Heavy to MixedMixed
can be written as 17 5175
35 17
remainder 2
23
5
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Changing a mixed fraction to a top-heavy.
WHOLE NUMBER DENOMINATORthen add NUMERATOR
5 4 3
7 5 2
Mixed to Top Mixed to Top HeavyHeavy
35
4
27
5
234
375
23 quarters
37 fifths
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Exercise 1Ch31 (page 128)
Mixed FractionsMixed FractionsMTH 3-07bMTH 3-07cMTH 4-07b
MTH 3-07bMTH 3-07cMTH 4-07b
Starter QuestionsStarter Questions
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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2. Simplify ?
3. Write 2% as a decimal
4. List the prime numbers between 20 and 30
5. Calculate
1284
7 5+2 2
5cm
7cm
MTH 3-07bMTH 3-07cMTH 4-07b
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. Understand that to add Understand that to add and subtract fractions and subtract fractions the denominators must the denominators must be the same.be the same.
1. We are learning how toadd and subtract basic fractions.
2.2. To be able to do simple To be able to do simple fraction calculations.fraction calculations.
Add / Sub Fractions
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Add / Sub Fractions
You can only add or subtract fractions if:
DENOMINATORS ARE THE SAME NUMBER
Example 1 Example 2
3 27 7
7 18 8
57
68
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Add Fractions
When dealing with mixed fractions deal with ‘whole’ part first then the fraction part
3 42 1
5 5
3 42 1
5 5
73
5
24
5
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Subtract Fractions
When dealing with mixed fractions deal with ‘whole’ part first then the fraction part
5 1
7 46 6
5 1
7 4 6 6
43
6
23
3
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Exercise 2Ch31 (page 131)
Add / Sub FractionsMTH 3-07bMTH 3-07cMTH 4-07b
MTH 3-07bMTH 3-07cMTH 4-07b
Starter QuestionsStarter Questions
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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(2 3 4)
4 149 9
y y x
1. Calculate
2. Expand
3. Write 72% as a decimal
4. Find the LCM of 2 and 3
5. 2.5% of £600
MTH 3-07bMTH 3-07cMTH 4-07b
Harder FractionsHarder Fractions
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. Understand and apply rules Understand and apply rules for adding and subtracting for adding and subtracting fractions.fractions.
1. We are learning how to add and subtract fractions with different denominators. 2.2. Convert top heavy Convert top heavy
fractions to mixed fractions to mixed fractions.fractions.
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MTH 3-07bMTH 3-07cMTH 4-07b
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Harder FractionsHarder Fractions
How can we add or subtract fractions that have different denominators
Step 1 : Find the LCM for the denominators
Step 2 : Convert to equivalent fractions
Step 3 : Add or Subtract the numerator and simplify
Before we can add or subtract they MUST
have the same denominator
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Harder FractionsHarder Fractions
Example 1
Step 1 : Find LCM
Step 2 : Equivalent Fractions
Step 3 : Add/Subtract the numerator
and simplify
MTH 3-07bMTH 3-07cMTH 4-07b
LCM of 2 and 4
4
4 4+2 1
43
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1225
5 26 5
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Harder FractionsHarder Fractions
Example 1
Step 1 : Find LCM
Step 2 : Equivalent Fractions
Step 3 : Add/Subtract the numerator
and simplify
MTH 3-07bMTH 3-07cMTH 4-07b
LCM of 5 and 6
30
30 30-
1330
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910
5 36 4
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Harder FractionsHarder Fractions
Example 1
Step 1 : Find LCM
Step 2 : Equivalent Fractions
Step 3 : Add/Subtract the numerator
and simplify
MTH 3-07bMTH 3-07cMTH 4-07b
LCM of 4 and 6
12
12 12+
1912
= =7
121
112 19 R7
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Exercise 3Ch31 (page 133)
Q1 and Q2
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Harder FractionsHarder Fractions
How can we add /subtract mixed fractions that have different denominators
When dealing with mixed fractions deal with ‘whole’ part first then the fraction part
Simple !
MTH 3-07bMTH 3-07cMTH 4-07b
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Harder FractionsHarder Fractions
1 22 3
2 3
1 22 3
MTH 3-07bMTH 3-07cMTH 4-07b
5
43
1 22 3
6 6+
16
1
16
1= 5 +
16
= 6 76
=
LCM of 2 and 3
61
6 7 R1
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Harder FractionsHarder Fractions
7 2
7 48 3
7 28 3
MTH 3-07bMTH 3-07cMTH 4-07b
3
1621
7 28 3
24 24-
524
524
= 3 +
524
= 3 =
LCM of 8 and 3
24
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Harder FractionsHarder Fractions
3 5
44 6
3 54 6
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4
109
3 54 6
12 12+
712
1
712
1= 4 +
712
= 5 1912
=
LCM of 4 and 6
121
12 19 R7
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Exercise 3Ch31 (page 134)
Q4 to Q8
Harder FractionsHarder FractionsMTH 3-07bMTH 3-07cMTH 4-07b
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Most Difficult Most Difficult FractionsFractions
1 2
6 24 3
1 24 3
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4
83
1 24 3
12 12-= 4 +
712
= 3 =
LCM of 4 and 3
12
512
-
512
-
= 45
12-
Adding a negative is the
same as subtracting
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Most Difficult Most Difficult FractionsFractions
1 2
7 15 3
1 25 3
MTH 3-07bMTH 3-07cMTH 4-07b
6
103
1 25 3
15 15-= 6 +
815
= 5 =
LCM of 5 and 3
15
715
-
715
-
= 67
15-
Adding a negative is the
same as subtracting
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Exercise 3Ch31 (page 134)
Q9 to Q15
Harder FractionsHarder FractionsMTH 3-07bMTH 3-07cMTH 4-07b
MTH 3-07bMTH 3-07cMTH 4-07b
Starter QuestionsStarter Questions
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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24 , 3 2
5
3 14 3
(2 )
56
x y and z z z xy
1. Calculate
2. I f . Find
3. Calculate 60% of £360
4. Make the following top- heavy
MTH 3-07bMTH 3-07cMTH 4-07b
Multiplying Multiplying FractionsFractions
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. Understand the simply Understand the simply rules for multiplying rules for multiplying basic and mixed basic and mixed fractions.fractions.
1. We are learning how to multiply basic and mixed fractions.
2.2. Apply rules correctly.Apply rules correctly.
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Multiplying Multiplying FractionsFractions
Example 1 Example 2
Multiply basic fractions
3 34 5
9
20
4 55 6
2030
23
1. Multiply the numerators
2. Multiply the denominators
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Exercise 4Ch31 (page 136)
Q1 to Q4
Multiplying Multiplying FractionsFractions
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Multiplying Multiplying FractionsFractions
1. Make fractions top-heavy
Multiplying Mixed Fractions
2. Multiply the numerators
3. Multiply the denominators
MTH 3-07bMTH 3-07cMTH 4-07b
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Multiplying Multiplying FractionsFractions
1 13 1
2 3
7 42 3
286
4
46
Example
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2
23
1. Make fractions top-heavy
2. Multiply the numerators
3. Multiply the denominators
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Multiplying Multiplying FractionsFractions
3 1
4 14 5
19 64 5
11420
14
520
Example
MTH 3-07bMTH 3-07cMTH 4-07b
7
510
1. Make fractions top-heavy
2. Multiply the numerators
3. Multiply the denominators
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Exercise 4Ch31 (page 136)
Q5 to Q10
Multiplying Multiplying FractionsFractions
MTH 3-07bMTH 3-07cMTH 4-07b
MTH 3-07bMTH 3-07cMTH 4-07b
Starter QuestionsStarter Questions
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1
3 (4 -3 ) - 12
1 132 3
2 33 2
a a b ab
1. Calculate
2. Simplify
3. Multiply
MTH 3-07bMTH 3-07cMTH 4-07b
Dividing FractionsDividing Fractions
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1. We are learning how to divide basic and mixed fractions.
1.1. Understand how the Understand how the simply rules for dividing simply rules for dividing basic and mixed basic and mixed fractions.fractions.
2.2. Apply rules correctly.Apply rules correctly.
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Always = 1
Dividing FractionsDividing Fractions
It is almost impossible to divide fractions like
by actually dividing.
Instead we change it into a multiplication by:
2335
2 53 33 55 3
2 53 3
109
1
19
2 33 5
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Dividing FractionsDividing Fractions
Easy rule to remember :
Example Example
Instead of dividing by , multiply by ab
ba
5 28 3
35
8 2
1516
4 55 6
64
5 5
2425
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Exercise 5Ch31 (page 138)
Q1 to Q4
Dividing FractionsDividing FractionsMTH 3-07bMTH 3-07cMTH 4-07b
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Dividing FractionsDividing Fractions
For mixed fractions YOU MUST make them top-heavy first !!
Example
1 13 2
2 3
7 72 3
37
2 7
2114
3 1
12 2
Instead of dividing by , multiply by ab
ba
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Dividing FractionsDividing Fractions
Example 2 3 23 1
4 3
15 54 3
3154 5
4520
52
20
12
4
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Exercise 5Ch31 (page 138)
Q5 to Q10
Dividing FractionsDividing FractionsMTH 3-07bMTH 3-07cMTH 4-07b