Fractions
decimals and
percentages
Spring Term Block 4
Answers
Y6 – Spring – Block 4 – Step 1 – Decimal and fraction equivalents Answers
Question Answer
a) The whole has been divided into 10 equal parts.
Each part is worth 0.1
1
This is equivalent to 10
b) The whole has been divided into 100 equal parts.
1
Each part is worth 0.01
10 parts out of 100 are shaded.
10 1
This is equivalent to 100 (or 10)
a)
17 parts out of 100 are shaded.
17
0.17 = 100
2 b)
20 parts out of 100 are shaded.
1
0.2 = 5
a)
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
b)
1 3 2 3 7 4 9
3 5 10 5 5 10 5 10
Both number lines go up in tenths.
The number line is part a) is labelled with decimals and the number line in part b) is
labelled with fractions in their simplest form.
Y6 – Spring – Block 4 – Step 1 – Decimal and fraction equivalents Answers (continued)
Question Answer
28 56
a) 50 = 100 = 0.56
6 30
b) 20 = 100 = 0.30
9 36
c) 25 = 100 = 0.36
4 24 12
d) 200 = 100 = 0.12
27 54
e) 500 = 1000 = 0.054
62 248
f) 250 = 1000 = 0.248
Eva
60 30
Tommy’s method: 200 = 100 = 0.30 = 0.3
5 60 300
Alex’s method: 200 = 1000 = 0.300 = 0.3
They get the same answer.
multiple possible answers, e.g.
2 10
6 4, 20
In all the fractions that the children find, the denominator must be twice the numerator.
Y6 – Spring – Block 4 – Step 2 – Fractions as division Answers
Question Answer
1
a) 3 = 1 ÷ 3
2
b) 3 = 2 ÷ 3
4
c) 7 = 4 ÷ 7
1 3
d) 5 = 3 ÷ 5
3
e) 7 = 3 ÷ 7
1
f) 10 = 1 ÷ 10
0.4
2
a) 0.25
b) 0.8
3
c) 0.375
a) 0.875
b) 1.4
4 c) 0.0625
d) 0.5625
0.98
5
Tiny worked out 2 ÷ 1 instead of 1 ÷ 2
6 The correct answer is 0.5
multiple possible answers, e.g.
9 41 21
7 20 100 50
There is an infinite number of possible answers.
0.333333…
8 Some children may not have realised that the sequence goes on forever.
Y6 – Spring – Block 4 – Step 3 – Understand percentages Answers
Question Answer
a) There are 8 parts out of a hundred shaded.
This is 8%.
b) There are 37 parts out of a hundred shaded.
1 This is 37%.
c) There are 81 parts out of a hundred shaded.
This is 81%.
45%
2 89%
a), b)
c) 36%
a) No
The bar is divided into 10 equal parts, so each part is 10%.
b) 40%
4
90%
25%
a)
5 b)
Y6 – Spring – Block 4 – Step 3 – Understand percentages Answers (continued)
Question Answer
6 They have all made 75 using difference methods. This works with percentages, as well as
with standard numbers.
multiple possible answers, e.g.
a) 4 × 20%
100% − 20%
50% + 10% + 10% + 10%
b) 60% + 5%
50% + 10% + 5%
7
4 × 10% + 25%
c) 90% + 9%
100% − 1%
50% + 40% + 9%
Children are likely to have some different ways.
Y6 – Spring – Block 4 – Step 4 – Fractions to percentages Answers
Question Answer
3
a) 10
7
b) 10
1 c) 30%
d) 70%
e) They add up to 100%.
a)
40%
b)
50%
c)
2
65%
d)
70%
The grids all have the same number of squares, and the percentage is the number of
shaded squares.
The denominators of the fractions are not all the same.
Y6 – Spring – Block 4 – Step 4 – Fractions to percentages Answers (continued)
Question Answer
9 90
a) 10 = 100 = 90%
9 45
b) 20 = 100 = 45%
3 9 18
c) 50 = 100 = 18%
9 36
d) 25 = 100 = 36%
a) 25%
50%
75%
b) 20%
40%
80%
c) 80%
40%
20%
4 d) 90%
90%
90%
Children may recognise various patterns:
1
Part a): As the fraction goes up by 4, the percentage goes up by 25%.
Part b): When the numerator of the fraction is doubled, the percentage is doubled.
Part c): When the numerator of the fraction is halved, the percentage is halved.
Part d): All the fractions are equivalent and give the same percentage.
No. Tiny has doubled the percentage when he should have divided it by 2
5 The correct answer is 5%.
a)
b) 6%
1 3 3
a) 2 > 40% 5 < 65%
75%= 4
7 b) This is the only solution.
Y6 – Spring – Block 4 – Step 5 – Equivalent fractions, decimals and percentages Answers
Question Answer
1
a) fraction = 100
decimal = 0.01
percentage = 1%
1
b) fraction = 10
1 decimal = 0.1
percentage = 10%
100
c) fraction =
100
decimal = 1
percentage = 100%
a)
24 6
b) fraction = 100 = 25
decimal = 0.24
percentage = 24%
Y6 – Spring – Block 2 – Step 5 – Equivalent fractions, decimals and percentages Answers (continued)
Question Answer
21
21%
100
12 3
0.12
100 or 25
0.2 20%
4 2
or 40%
4 10 5
44 11
or 44%
100 25
4 1 0.04
100 or 25
0.75 75%
99
99%
100
a) He has not converted the numbers to the same form.
14% = 0.14 or 0.4 = 40%
5
b) <
multiple possible answers, e.g.
0.24 0.35
There are eight possible answers:
7
0.21 0.23 0.24 0.25
0.31 0.32 0.34 0.35
Y6 – Spring – Block 4 – Step 6 – Order fractions, decimals and percentages Answers
Question Answer
a) >
b) <
c) >
1 d) =
e) <
f) >
a) 9
9% 19% 10 0.99
2
9
b) 9% 19% 0.99
10
a) 2 45%
0.2 0.25 5
2
b) 45% 0.25 0.2
5
13 7
a) 100 21% 10 0.9
37
b) 0.6 61% 0.66 50
63
c) 12% 47% 100 0.89
4 Children’s answers may vary. Possibly part c), because the fraction already has a
denominator of 100, so is easy to convert it to either a decimal or a percentage.
Children’s answers may vary. Possibly part b), because the fraction requires converting to
a fraction with a denominator of 100 before converting it to either a decimal or a
percentage.
5 ✔︎ ✔︎ ✔︎
Scott (60%)
6 Huan (55%)
No
40
7
50 = 80%, so Tommy did better in the test.
Y6 – Spring – Block Block 4 – Step 6 – Order fractions, decimals and percentages Answers (continued)
Question Answer
a) multiple possible answers, e.g.
5
0.3 < 10 < 80%
There are four possible answers:
4 5 6 7
10, 10, 10, 10
b) multiple possible answers, e.g.
8 2
5 < 42% < 0.75
There are 13 possible answers:
42%, 43%, 46%, 47%
60%, 62%, 63%, 64%, 67%
70%, 72%, 73%, 74%
Y6 – Spring – Block 4 – Step 7 – Percentage of an amount – one step Answers
Question Answer
a) 312
b) 156
3
25% of 624 is half of 50% of 624
a) 1,710
b) 855
4
c) 342
a) 1,500
750
250
b) 750
375
125
c) 300
5 150
50
d) 30
15
5
The answers in part b) are half the answers in part a).
When the percentage stays the same and the number halves, the answer also halves.
Y6 – Spring – Block 4 – Step 7 – Percentage of an amount – one step Answers (continued)
Question Answer
a) 640
6 b) 1,024
7
Y6 – Spring – Block 4 – Step 8 – Percentage of an amount – multi-step Answers
Question Answer
a) 50
b) 20% of 500 = 100
90% of 500 = 450
30% of 500 = 150
1
70% of 500 = 350
60% of 500 = 300
100% of 500 = 500
5 = 10 ÷ 2, so 5% is half of 10%.
2
a) 2
b) 20
c) 200
d) 100
3 e) 300
f) 135
When the percentage stays at 5% and the number increases by a factor of 10, the answer
also increases by a factor of 10
a) 255
b) 255
4
children’s alternative methods, e.g. find 25% and subtract from the number
Multiple possible answers, e.g.
20% Divide by 5
90% Subtract 10% from the whole
60% Add 10% and 50%
5
15% Add 10% and 5%
55% Add 50% and 5%
40% Multiply 10% by 4
Y6 – Spring – Block 4 – Step 8 – Percentage of an amount – multi-step Answers (continued)
Question Answer
a) 200
110
8
b) 900
3,807
81
c) 600
240
58.8
6 d) 150
45
4.5
e) 550
2,420
4.4
f) 400
160
39.2
Yes
When the percentage doubles and the number stays the same, the answer doubles.
When the percentage stays the same and the number halves, the answer halves.
7
So doubling the percentage would double the answer and halving the number would
halve the answer. These cancel each other out, so the answer stays the same.
a) 20% of 40 = 8
40% of 20 = 8
25% of 60 = 15
60% of 25 = 15
When the numbers for the percentage and the number are swapped, the answer
8 stays the same.
b) multiple possible answers, e.g.
10% of 70 = 70% of 10 and 50% of 80 = 80% of 50
When the numbers for the percentage and the number are swapped, the answer
stays the same. This always happens.
Y6 – Spring – Block 4 – Step 9 – Percentages – missing values Answers
Question Answer
a) 1,368
b) 3,420
1 c) 684
d) 456
a) Tiny has found 10% of 200 instead of the number of which 10% is 200
b) ?
200
2
0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
c) 2,000
a) 470
3 b) 282
a) 20% of 150 = 30
20% of 300 = 60
b) 10% of 400 = 40
10% of 200 = 20
4 c) 25% of 400 = 100
75% of 300 = 225
d) 80% of 40 = 32
25% of 32 = 8
a)
224
20%
1,008
5
25% 560
100%
b) 448
c) 1,344
multiple possible answers, e.g.
10 2
6 100 20
500 100
The value of the triangle is always 5 times the value of the star.
