Number – fractions Questions with support 1
Write these numbers in order of size, starting with the smallest. 1.7
1.54
0.861
0.37
Smallest
Largest
Remember, to find the smallest number, you start before the decimal point. So first you need to find the numbers that start with 0. Then look after the decimal point. Which number is smaller? Now look at the numbers that start with 1. Which is the smaller of these numbers?
2
Samir says
1 4
is smaller than 0.4.
Explain why he is correct.
To explain why Samir is correct, you need to find the equivalent decimal or fraction. For example: A boy says
3 4
is smaller than 0.8.
Explain why he is correct. 3 4
= 0.75
0.75 is smaller than 0.8
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Ratio and proportion Questions with support 1
Two boys raise money for a charity by selling apples. They buy each apple for 20p and sell it for 30p. The boys sell the apples for £15. How much does it cost the boys altogether to buy the apples?
£
Remember that every, each, only and altogether are important words in ratio questions. For example: A girl planted some seeds. For every 3 seeds she planted, only 2 seeds grew. Altogether, 12 seeds grew. How many seeds did the girl plant? Seeds planted
3
Total planted
18
Seeds grew
2
Total grew
12
The ratio of seeds planted to seeds that grew is 3:2. 6 × 2 seeds (12 altogether) grew, so 6 × 3 seeds were planted.
2
Each time Chen’s mother gives him £5 he spends £3. So he saves 40%. Each time Maria’s mother gives her £5 she saves £1, so she saves % . Remember that each is an important word in ratio questions. For example: A horse sleeps for 9 hours each day. 37.5% of its life is spent asleep. A koala sleeps for 18 hours each day. What percentage of its life is spent asleep? Sleeping hours
% of the day sleeping
Horse
9
37.5%
Koala
18
75%
The ratio of sleeping hours is 9:18 or 1:2. So 2 × 37.5 is the percentage of the day for which the koala sleeps.
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3
Here are two similar rectangles. Write the ratio of side a to side b. b
a
a:b =
Example: Here are two similar right-angled triangles. Write the ratio of side a to side b.
a 1
b 2
1
2
3
4
Side a covers 2 columns and side b covers 4 columns, so the ratio is 2:4 or 1:2. Answer: a:b = 1:2
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