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Starter Questions. Multiply out the brackets and simplify: a) 4(x + 3) + 2b) 3 + 2( x + 4)c) 10 + 2(3x + 4). 2. Find the highest common factor of: a) 8 and 12b) 16 and 18c) 18x and 24. 3. Factorise the following: a) 10p + 15qb) 8d – 12fc) 4a + 10b +14c. Fractions. - PowerPoint PPT Presentation
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Starter Questions
1. Multiply out the brackets and simplify:
a) 4(x + 3) + 2 b) 3 + 2( x + 4) c) 10 + 2(3x + 4)
2. Find the highest common factor of:
a) 8 and 12 b) 16 and 18 c) 18x and 24
3. Factorise the following:
a) 10p + 15q b) 8d – 12f c) 4a + 10b +14c
FractionsFractions
Learning IntentionLearning Intention
To understand the term Fraction and be able to simplify fraction.
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
It is possible to find a fraction equivalent to any fraction that you have by multiplying the numerator
and the denominator by any number.
24
15
Find a fraction equivalent to :
x3
x3
612
210
x2
x2
FractionsFractions
We can sometimes simplify a fraction by finding a HCFbetween the numerator and denominator.
24
312
Simplify the fractions below :
÷2
÷2
12
14
÷3
÷3
FractionsFractions
Fractions of a quantityFractions of a quantity
Learning IntentionLearning Intention
To explain the 2 step process of finding a fraction of a quantity.
Q. Do the calculations below.
12
Fractions of a Fractions of a quantityquantity
of 12014
of 120
Simply divide by the bottom number
602 120
304 120
Q. Do the calculation below.
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:
Q. Do the calculation below.
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:
Learning IntentionLearning Intention
To understand how to calculate simple percentages without a
calculator.
Simple Simple PercentagesPercentages
Remember money 2 decimal places
Q. Find 17% of £450
17 100 x 450
PercentagesPercentages
17 450
100
= £76.50
of means times
Calculator Keys
1 1 x 4 = 76.57 0 0 5 0
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
Q. Find 25% of £40
PercentagesPercentages
1 40
4
40 ÷4 =10
Q. Find 5% of £300
PercentagesPercentages
1 300
20
300 ÷20 =15
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
Q. Find 30% of £40
3 40
10
40 ÷10 x 3 =12
Extended Extended PercentagesPercentages
Q. Find 75% of £600
3 600
4
600 ÷4 x 3 =450
Extended Extended PercentagesPercentages
Learning IntentionLearning Intention
To understand how to add and subtract basic fractions.
Add / Sub Fractions
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
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
NUMERATOR DENOMINATOR
Top Heavy to Top Heavy to MixedMixed
can be written as 7 373
23 7
remainder 1
12
3
NUMERATOR DENOMINATOR
Top Heavy to Top Heavy to MixedMixed
can be written as 17 5175
35 17
remainder 2
23
5
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
Top Heavy to Top Heavy to MixedMixed
Examples
1 37 7
47
8 79 9
19
3 15 3
7 7
48
7
3 115 4
7 7
211
7
Top Heavy to Top Heavy to MixedMixed
Examples
6 37 7
97
9 715
11 11
1615
11
217
5
1611
5
15 111
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
Harder FractionsHarder Fractions
Learning IntentionLearning Intention
To understand how to add and subtract fractions with different
denominators.
Harder FractionsHarder 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
We are going to use the kiss
and smile method
2+
Harder FractionsHarder Fractions
1 12 4
68
Example 1
Step 1 : Do the smile
Step 2 : Do the kiss
Step 3 : Add/Subtract the numerator
and simplify
84
34
÷2
÷2
6-
Harder FractionsHarder Fractions
5 16 5
3025
1930
18+
Harder FractionsHarder Fractions
5 36 4
3824
2420
14124
÷2
÷214
124
7
112
General
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 !
Harder FractionsHarder Fractions
1 22 3
2 3
1 22 3
2 3
1 25
2 3 4+
76
63
116
15 1
6
16
6
Harder FractionsHarder Fractions
7 27 4
8 3
7 27 4
8 3
7 23
8 3 16-
524
2421
53
24
53
24
3 54
4 6 3 5
44 6
20+
3824
2418
14124
75 1
12
76
12
7112
Most Difficult Most Difficult FractionsFractions
Subtracting Subtracting FractionsFractions
1 26 2
4 3
1 26 2
4 3
1 24
4 3 8-
512
123
54
12
12 5
312 12
7
312
Most Difficult Most Difficult FractionsFractions
1 17 1
5 6
1 17 1
5 6
1 16
5 6 5-
130
306
16
30
16
30
Subtract Fractions
When dealing with mixed fractions deal with ‘whole’ part first then the fraction part
11
6
6 16 6
56
Multiplying FractionsMultiplying Fractions
Learning IntentionLearning Intention
To show how to multiply basic fractions.
Multiplying Multiplying FractionsFractions
Example 1 Example 2
Multiplying basic fractions
3 34 5
3 34 5
9
20
4 55 6
4 55 6
2030
23
1. Multiply the numerators
2. Multiply the denominators
Multiplying Multiplying FractionsFractions
Example 3 Example 4
Multiplying basic fractions
32
5
2 31 5
65
4 21 3
2
43
83
2
23
5
16