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Fractions, Decimals and Fractions, Decimals and PercentagesPercentages
Maths Revision & Maths Revision & Practice BookletPractice Booklet
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ReviseUsing Common Factors to Simplify FractionsFractions that have the same value but represent this using different denominators and numerators are equivalent. We can recognise and find equivalent fractions by multiplying or dividing the numerator and denominator by the same amount. When we simplify a fraction, we use the highest common factor of the numerator and denominator to reduce the fraction to the lowest term equivalent fraction (simplest form).
2136
2136
35
35
47
47
712
Factors of 21:
Factors of 36:
The highest common factor
is 3.
1 3 7
1 2 3 4 6 9 12 18 36
÷ 3 = 7
÷ 3 = 12
Using Common Multiples to Express Fractions in the Same Denomination
To compare or calculate with fractions, we often need to give them a common denominator. We do this by looking at the denominators and finding their lowest common multiple.
5 × 7 = 3535 is the lowest common multiple.
3 × 7 = 21 4 × 5 = 205 × 7 = 35 7 × 5 = 35
Remember that whatever we do to the denominator, we have to do to the numerator.
Maths Revision & Practice Booklet
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Maths Revision & Practice Booklet
Comparing and Ordering Fractions, Including Fractions > 1
To compare and order fractions with the same
denominators…
To compare and order fractions with different
denominators…
To compare and order fractions with
mixed numbers…
...look at the numerators.
…change the fractions into
equivalent fractions with the lowest common denominator.
…change the mixed number
into an improper fraction and
continue as needed.
59
59
59
59
59
119
29
23
23
69
69
2797
2721
2545
29
35
1343
2821
2745
>
<
<
and
+
+
+
=
= = 1
and
and
× 5 × 9
1 1
× 3 × 7
Add and Subtract Fractions with Different Denominators and Mixed Numbers
When we add and subtract fractions with different denominators, we need to give them a common denominator. We use the lowest common multiple as the common denominator to create equivalent fractions which we can then add and subtract.
If one of the fractions is a multiple of the other, use multiplication to change the smaller denominator to the same denominator as the other fraction.
× 3 =× 3 =
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Maths Revision & Practice Booklet
89
89
34
34
3236
3236
2736
536
2736
-
- =
=
× 4 = × 9 =× 4 = × 9 =
If the fractions aren’t multiples of each other, use multiplication to change them both to the lowest common denominator.
If the fractions involve adding or subtracting mixed numbers, there are two methods that can be used:
Add the whole numbers and the fractions separately.
Convert the mixed numbers to improper fractions.
35
1220
35
56
176
14
15
1930
65
8530
3630
4930
4930
14
520
1720
1720
1720
+ +
+ -
--
+
= =
=
=
=
=
=
=
2 2
5 5
2 + 3 = 5
3 1
1
Multiplying Simple Pairs of Proper Fractions, Writing the Answer in its Simplest Form
Multiply a Proper Fraction by a
Whole Number
Multiply Proper Fractions Together
Write the whole number with a denominator of 1. Multiply the
numerators together and multiply the
denominators together.
Multiply the numerators together and multiply
the denominators together. Simplify the
answer if needed.
57
41
35
38
207
67
940
=
=
=
=
×
×
2
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Fraction
Decimal
Maths Revision & Practice Booklet
79
12
14
110
15
58
16
47
14
754
532
79
47
58
7 × 19 × 6
5 × 18 × 4
÷ ÷
× ×
= =
=
=
=
=
= =
0.5 0.25 0.1 0.2
6 4
Dividing Proper Fractions by Whole Numbers
Multiplication and division are inverse operations of each other.
÷ ×51
15is the same as
Calculating Decimal Equivalents of FractionsEvery proper fraction has a decimal number equivalent, which we can calculate by dividing the numerator by the denominator.
Common decimal equivalents of fractions can be learnt as facts:
We can calculate the decimal equivalents of trickier fractions using written methods of division.
Sometimes, a decimal equivalent will be a long number. In these cases, you can round the decimal to one or two decimal places.
0 5 7 17 4 0 0 04 5 1
0.57 rounded to two decimal places.
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Maths Revision & Practice Booklet
Identify the Value of Each Digit in Numbers to Three Decimal PlacesIn order to be able to read, write and calculate with decimal numbers, we need to understand the place value of each digit after the decimal point.
As the place value position moves right of the decimal point, the digits become ten times smaller.
ones tenths hundredths thousandths
110
1100
11000
Recall and Use Equivalences between Simple Fractions, Decimals and PercentagesFractions, decimals and percentages are equivalent ways of expressing the same proportion.
Fraction Percentage Decimal
50% 0.5
25% 0.25
75% 0.75
20% 0.2
10% 0.1
12
34
14
15110
60100
610
35
35
35
To calculate trickier equivalents, we can use the rules in this diagram to help us:
Percentage to FractionWrite the percentage as a fraction with a denominator of 100 and then simplify.
Decimal to PercentageMultiply the decimal by 100 and add the % sign.
0.6 × 100 = 60%
Fraction to DecimalDivide the numerator by the denominator.
60% 0.6Percentage Decimal
Fraction
= == 3 ÷ 5 = 0.6
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PractiseSupercharge your powers by answering these questions.
1. Put these fractions in order of size, starting with the smallest.
2. The numbers in this sequence increase by the same amount each time. Write the missing numbers.
3. In each box, circle the number that is greater.
4. Write the missing fraction in this calculation.
34
37
1214
16
712
23
smallest greatest
1
1.55
1.9
1.8
1.67
1 1
35
9100
23
15
13
710
1
1
1
1
+ + = 1
total for this page
1 mark
1 mark
1 mark
1 mark
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Practise5. Write the missing numbers in these equivalent fractions.
6. Circle the improper fraction that is equivalent to
7. Tick the calculation that is the best estimate.
4 - 1 + 2 5 - 2 + 2
5 - 1 + 2 4 - 1 + 1
8. I spent £1.40 on a drink and £1.70 on a sandwich. I have three fifths of my money left. How much money did I have to start with?
45
1112
79
15
409
419
429
439
449
90
5 6
12=
-4
4
1 1
=
+
£
Show your
method
total for this page
1 mark
1 mark
2 marks
1 mark
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Practise9. Yesterday, I read 3
7 of my book. Today, I read the remaining 152 pages to finish the book. How many pages are there in my book?
10. One fruit smoothie contains of a carton of orange juice. I make 7 smoothies. Calculate, as a mixed number, how much orange juice I use altogether.
11. In this circle, and are shaded. What fraction of the whole circle is not shaded?
pages
cartons
Show your
method
Show your
method
Show your
method
23
14
316
total for this page
2 marks
2 marks
2 marks
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12. What fraction of this diagram is shaded?
13. I make a model out of 25 cubes. What percentage of the cubes in the model are blue?
Practise
%
Show your
method
Show your
method
18 2
3?
total for this page
2 marks
2 marks
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14. I have £380. I spend 18% of my money on a new bike. How much money do I spend on my new bike?
Practise
£
Show your
method
total for this page
Colour in the superhero strength-o-meter to show how you feel about each of these statements:
Self-Assessment
I can use common factors to simplify fractions and use common multiples to express fractions in the same denomination.
I can compare and order fractions, including fractions > 1.
I can add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions.
I can multiply simple pairs of proper fractions, writing the answer in its simplest form.
I can divide proper fractions by whole numbers.
I associate a fraction with division and calculate decimal fraction equivalents.
I can recall and use equivalences between simple fractions, decimals and percentages.
2 marks
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