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Transcript of 21-Aug-14 Compiled by Mr. Lafferty Maths Dept. Fractions Simplifying Fractions Fractions of a...
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
FractionsFractionsw
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Simplifying Fractions
Fractions of a quantity
Finding (Simple) Percentages
More Simple Percentages
Reminder of Mixed Fractions
Add & Subtract Fractions
Multiplying Fractions
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
1. Find the missing value
2. I f you know the length of the side of a square describe in words how to calculate the perimeter.
3. 4x + 10 = 46
3 ?=4 20
Starter Starter QuestionsQuestions
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General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
FractionsFractionsw
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1.1. To know what the terms To know what the terms fraction.fraction.
1. To understand theterm Fraction and be able to simplify fraction.
2.2. Be able to simply fractions.Be able to simply fractions.
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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.com A Fraction consists of 2 parts.
35
Top number is called the numerator
Bottom number is called the denominator
FractionsFractions
The denominator tells us the type of fraction we have
The numerator tells us the how many we have
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Write down the fraction that is shaded in light blue.
24
36
FractionsFractionsGeneral
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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.com It is possible to find a fraction equivalent to any
fraction that you have by multiplying the numeratorand the denominator by any number.
24
15
Find a fraction equivalent to :
x3
x3
612
210
x2
x2
FractionsFractionsGeneral
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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.com We can sometimes simplify a fraction by finding a HCF
between the numerator and denominator.
24
312
Simplify the fractions below :
÷2
÷2
12
14
÷3
÷3
FractionsFractionsGeneral
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 1Ch11(page 126)
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FractionsFractionsGeneral
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Starter Starter QuestionsQuestions
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2. Simplify
3. 8.52 + 4.6
4.
25150
1 of 2355
6cm
10cm
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Fractions of a Fractions of a quantityquantity
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1.1. To know the 2 step for To know the 2 step for finding a fraction of a finding a fraction of a quantity.quantity.
1. To explain the 2 step process of finding a fraction of a quantity.
2.2. Be able to calculate the Be able to calculate the fraction of a quantity.fraction of a quantity.
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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12
Fractions of a Fractions of a quantityquantity
of 12014
of 120
Simply divide by the bottom number
602 120
304 120
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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23
Fractions of a Fractions of a quantityquantity
of 24
Simply divide by the bottom numberThen multiply the answer by top number
83 24 8 x 2 = 16Step 1: Step 2:
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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58
Fractions of a Fractions of a quantityquantity
of 360
Simply divide by the bottom numberThen multiply the answer by top number
458 360 45 x 5 = 225Step 1: Step 2:
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 2Ch11 (page 126)
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Fractions of a Fractions of a quantityquantity
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Starter Starter QuestionsQuestions
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of 120
1. Find the LCM of 2 and 3
2. Find HCF of 4 and 1
3. Find
4. Simplify
45
85200
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. Calculate basic simple Calculate basic simple percentages.percentages.
1. To understand how to calculate simple percentages without a calculator. 2.2. Show all working.Show all working.
Simple Simple PercentagesPercentages
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Copy down and learn the following basic percentages
Simple Simple PercentagesPercentages
100% 50%1
33 %3 25% 20% 10% 5% 1%
112
13
14
15
110
120
1100
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Q. Find 25% of £40
PercentagesPercentages
1 40
4
40 ÷4 =10
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Q. Find 5% of £300
PercentagesPercentages
1 300
20
300 ÷20 =15
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 3Ch11 (page 128)
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PercentagesPercentages
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Starter Starter QuestionsQuestions
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75200
1. Calculate 1200 300
2. Simplify
3. Find 10% of 65
4. Find LCM and HCF for 7 and 35
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. To know the basic To know the basic percentages.percentages.
1. To explain some more basic percentages.
2.2. Calculate basic percentage Calculate basic percentage without a calculator.without a calculator.
Extended Extended PercentagesPercentages
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Copy down and learn the following basic percentages
100% 50%1
33 %3
266 %
3 20% 40%60% 80%
112
13
23
15
25
35
45
10% 30%70% 90%
110
310
710
910
Extended Extended PercentagesPercentages
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Q. Find 30% of £40
3 40
10
40 ÷10 x 3 =12
Extended Extended PercentagesPercentages
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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Q. Find 75% of £600
3 600
4
600 ÷4 x 3 =450
Extended Extended PercentagesPercentages
General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Ex 4Ch11 (page 129)
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Extended Extended PercentagesPercentages
General
Starter Starter QuestionsQuestions
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
1. Solve the inequality 4x+5>29
2. Calculate 3+(- 10)+(- 7)
3. Simplify the fraction 4
200
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General
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. To know that to add and To know that to add and subtract fractions the subtract fractions the denominators must be denominators must be the same.the same.
1. To understand 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 FractionsGeneral
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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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.com A Fraction consists of 2 parts.
35
Top number is called the numerator
Bottom number is called the denominator
FractionsFractions
The denominator tells us the type of fraction we have
The numerator tells us the how many we have
General
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11 Apr 202311 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
4
General
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11 Apr 202311 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
General
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11 Apr 202311 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
General
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11 Apr 202311 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
General
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11 Apr 202311 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
General
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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Top Heavy to Top Heavy to MixedMixed
Examples
1 37 7
47
General
8 79 9
19
3 15 3
7 7
48
7
3 115 4
7 7
211
7
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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Top Heavy to Top Heavy to MixedMixed
Examples
6 37 7
97
General
9 715
11 11
1615
11
217
516
11
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11 Apr 202311 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
34
General
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11 Apr 202311 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
General
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11 Apr 202311 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
General
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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now tryExtension BookletEx 5E (page 46)
Mixed FractionsMixed FractionsGeneral
Starter QuestionsStarter Questions
11 Apr 202311 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
General
Starter Starter QuestionsQuestions
11 Apr 202311 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
General
Harder FractionsHarder Fractions
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. Apply ‘ rules for adding and Apply ‘ rules for adding and subtracting fractions.subtracting fractions.
1. To understand how to add and subtract fractions with different denominators. 2.2. Simplify fractions.Simplify fractions.
General
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MTH 3-07bMTH 3-07cMTH 4-07b
11 Apr 202311 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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2 4
11 Apr 202311 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
11 Apr 202311 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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1820
5 36 4
11 Apr 202311 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
24
24 24+
3824
1912
= =7
121
112 19 R7
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11 Apr 202311 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 !
General
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11 Apr 202311 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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11 Apr 202311 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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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Harder FractionsHarder Fractions
3 5
44 6
3 54 6
MTH 3-07bMTH 3-07cMTH 4-07b
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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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Most Difficult Most Difficult FractionsFractions
1 2
6 24 3
1 24 3
MTH 3-07bMTH 3-07cMTH 4-07b
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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11 Apr 202311 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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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Extension Booklet
Ex 6E (page 48)
Multiplying Multiplying FractionsFractions
General
Starter QuestionsStarter Questions
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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4 , 3 2
5
3 14 3
2
56
1. Calculate
2. I f . Find
3. Calculate 60% of £360
4. Make the following top- heavy
x y and z z xy
General
Multiplying Multiplying FractionsFractions
11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.ww
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1.1. To know the simply rule To know the simply rule for multiplying basic for multiplying basic fractions.fractions.
1. To show how to multiply basic fractions.
2.2. Apply fraction rules Apply fraction rules correctly.correctly.
General
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11 Apr 202311 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
MTH 3-07bMTH 3-07cMTH 4-07b
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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Multiplying Multiplying FractionsFractions
Example 3 Example 4
Multiplying basic fractions
32
5
2 31 5
65
4 21 3
2
43
83
2
23
General
516
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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
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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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Multiplying Multiplying FractionsFractions
1 13 1
2 3
7 42 3
286
4
46
Example
MTH 3-07bMTH 3-07cMTH 4-07b
2
23
1. Make fractions top-heavy
2. Multiply the numerators
3. Multiply the denominators
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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
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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11 Apr 202311 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Now try Extension Booklet
Ex 7E (page 50)
Multiplying Multiplying FractionsFractions
General