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SATs practice · Year 6Chapter 2 · Fractions and decimals reasoning
Year 6 · Chapter 2

Fractions and decimals reasoning

By the end of this chapter you will be able to

  • Say which of two fractions is larger and explain how you know
  • Simplify a fraction, and write an equivalent fraction
  • Add, subtract and multiply fractions and mixed numbers, and give the answer in simplest form
  • Move the digits of a decimal when multiplying or dividing by 10, 100 or 1000
  • Find a fraction, decimal or percentage of an amount, and say which is larger

You should already know

  • Equivalent fractions and simple fractions of amounts (Year 4 and Year 5 fractions)
  • Place value in decimals to two places and the four operations (Year 5 decimals)

Where this leads

  • Ratio and proportion reasoning (Chapter 3 of this book)

KS2 SATs practice for reasoning (Year 6). Original questions in the style of the national tests. Content: Compare and order fractions, including fractions greater than 1 (Year 5-6), Identify and use equivalent fractions, and simplify using common factors (Year 5-6), Add and subtract fractions with different denominators and mixed numbers (Year 6), Multiply and divide fractions by whole numbers, and multiply simple pairs of proper fractions (Year 5-6), Read, write and order decimals to thousandths, and multiply and divide by 10, 100 and 1000 (Year 5-6), Round decimals to a given degree of accuracy in context (Year 6), Recall equivalences between simple fractions, decimals and percentages, and find percentages of amounts (Year 5-6).

Exercise P  Do you remember?

Non-calculator
1
FWrite 6/8 in its simplest form.
2
FWork out 0.3 + 0.4.
3
FWhat is one half of 36?
4
FWhich fraction is larger: 3/4 or 2/3? Write the fraction.
5
FWhat is 25% of 20?
2.1

Comparing and ordering fractions

Year 6
Compare and order fractions, including fractions greater than 1 (Year 5-6)
Video lesson: Comparing and ordering fractionsComing soon
Practice material. Do this without a calculator. This is practice in the style of the Year 6 maths reasoning test. It is not the official test, and no official test item is used. Marks and timings are a practice guide only.
Story. At a school picnic, Jo ate 3/8 of a pizza and Sam ate 2/5 of an identical pizza. The class wants to know who ate more.

Rule

To compare fractions, write them with the same denominator. Then the fraction with the bigger numerator is bigger.

A fraction can be greater than 1, for example 7/3 = 2 1/3. For the full method, read Year 6 maths, chapter 4.

Key ideas

  • Equal denominators: compare the numerators.
  • A bigger denominator means smaller pieces: 1/8 is less than 1/4.
  • A fraction with the top bigger than the bottom is greater than 1.
Worked example 2.1.1
Which fraction is larger: 5/6 or 7/9? Write the fraction.

Method. Make the denominators the same, then compare the tops.

  1. Find a common denominator. The denominators are 6 and 9. Both divide into 18.
    common denominator 18
  2. Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 18 on the bottom.
    5/6 = 15/18 and 7/9 = 14/18
  3. Compare the tops. With the same bottom number, the bigger top number is the larger fraction.
    15 and 14
  4. Write the answer.
    5/6

Check. 15/18 and 14/18: the one with the bigger top is larger. ✓

Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.

Worked example 2.1.2
Which fraction is larger: 9/4 or 7/3? Write the fraction.

Method. Make the denominators the same, then compare the tops.

  1. Find a common denominator. The denominators are 4 and 3. Both divide into 12.
    common denominator 12
  2. Write both fractions with that denominator. Multiply the top and bottom of each fraction to make 12 on the bottom.
    9/4 = 27/12 and 7/3 = 28/12
  3. Compare the tops. With the same bottom number, the bigger top number is the larger fraction.
    27 and 28
  4. Write the answer.
    7/3

Check. 27/12 and 28/12: the one with the bigger top is larger. ✓

Watch out. A bigger bottom number makes smaller pieces, so 1/8 is less than 1/4.

Worked example 2.1.3
Put these in order, from smallest to largest: 3/4, 2/3, 5/6, 7/12.

Method. Use a common denominator, then order the tops.

  1. Find a common denominator. Use 12, which all the denominators divide into.
    12
  2. Write each fraction with the same bottom number. Then the order depends only on the tops.
    3/4 = 9/12, 2/3 = 8/12, 5/6 = 10/12, 7/12 = 7/12
  3. Order the tops and write the fractions. Smallest top first.
    7/12, 2/3, 3/4, 5/6
  4. Write the answer.
    7/12, 2/3, 3/4, 5/6

Check. Each fraction is less than the next. ✓

Watch out. Do not order by the bottom numbers alone: 1/2 is bigger than 1/3, even though 2 is less than 3.

Watch out

Watch out. 1/2 is bigger than 1/3, even though 2 is less than 3. Compare the pieces, not the bottom numbers.

Exam tip

Practice guide. Use a common denominator, then say which top number is bigger.

Exercise 2A  Practice: comparing and ordering fractions

Non-calculator
1
FWhich fraction is larger: 2/3 or 5/8? Write the fraction.
2
FWhich fraction is larger: 4/9 or 3/7? Write the fraction.
3
FWhich fraction is smaller: 7/10 or 3/4? Write the fraction.
4
FWhich fraction is larger: 11/6 or 9/5? Write the fraction.
5
FPut these in order, from smallest to largest: 1/2, 1/3, 2/5, 3/10.
6
FPut these in order, from smallest to largest: 5/4, 3/2, 7/8, 2/3.
7
FTick the fractions that are greater than a half. Options: 2/5 | 3/5 | 4/10 | 5/9 | 7/12 | 1/2. Write the options you would tick, in the order given.
8
PSRavi ran 5/8 of a race and Lena ran 3/5. Who ran further? Write the name.
9
PSWrite the fraction halfway between 1/4 and 3/4.
10
RAli says 1/8 is bigger than 1/4 because 8 is bigger than 4. Is he right? Explain.
11
RMaya says 7/4 is greater than 1 because the top is bigger than the bottom. Is she right? Explain.
12
FWhich fraction is larger: 1/3 or 3/8? Write the fraction.
13
FWhich fraction is larger: 6/7 or 5/6? Write the fraction.
14
PSPut these in order, from smallest to largest: 7/5, 4/3, 3/2, 5/4.
15
PSWhich fraction is the smallest: 3/5, 4/7 or 2/3? Write the fraction.
2.2

Equivalent fractions and simplifying

Year 6
Identify and use equivalent fractions, and simplify using common factors (Year 5-6)
Video lesson: Equivalent fractions and simplifyingComing soon
Story. The recipe card for a fruit cake says 3/5 of a cup of sugar for 20 slices, and Priya needs to make it for 40 slices. She wants to write the amount as a fraction she can measure with her cups.

Rule

An equivalent fraction has the same value. Multiply (or divide) the top and bottom by the same number.

To simplify, divide the top and bottom by their highest common factor (HCF). 18/24 = 3/4, because the HCF of 18 and 24 is 6.

Key ideas

  • Multiply or divide the top and bottom by the same number.
  • A fraction is in its simplest form when the top and bottom have no common factor except 1.
  • Equal fractions can be checked by cross-multiplying, for example 2/3 = 4/6 because 2 x 6 = 3 x 4.
Worked example 2.2.1
Write a fraction equal to 3/5 with the denominator 20.

Method. Multiply the top and the bottom by the same number.

  1. Find what the bottom was multiplied by. 5 x 4 = 20.
    x 4
  2. Do the same to the top. Multiply the top by 4 as well.
    3 x 4 = 12
  3. Write the fraction. Both parts are multiplied by the same number, so the value does not change.
    12/20
  4. Write the answer.
    12/20

Check. 3/5 = 12/20, because both are multiplied by 4. ✓

Worked example 2.2.2
Write 18/24 in its simplest form.

Method. Divide the top and bottom by the highest common factor.

  1. Find the highest common factor of the top and bottom. The biggest number that divides 18 and 24 is 6.
    HCF = 6
  2. Divide the top and bottom by it. 18 / 6 = 3 and 24 / 6 = 4.
    3/4
  3. Write the answer.
    3/4

Check. 3 and 4 have no common factor. ✓

Watch out. Dividing only the top, or only the bottom, changes the value of the fraction.

Worked example 2.2.3
Which fraction is equivalent to 2/3? Choose one: 4/6, 3/4 or 5/6.

Method. Equivalent fractions have the same value.

  1. Check 4/6. Multiply 2/3 by 2 on the top and the bottom: 4/6.
    2/3 = 4/6
  2. Check the others. 3/4 and 5/6 do not have the same value as 2/3.
    3/4 and 5/6 are not equal to 2/3
  3. Write the answer. Only 4/6 is equivalent.
    4/6
  4. Write the answer.
    4/6

Check. 4 x 3 = 6 x 2, so 4/6 = 2/3. ✓

Watch out

Watch out. When you simplify, divide the top and the bottom by the same number. Dividing only one of them changes the value.

Exam tip

Practice guide. Find the highest common factor first. It is quicker than dividing by 2 many times.

Exercise 2B  Practice: equivalent fractions and simplifying

Non-calculator
1
FWrite a fraction equal to 2/7 with the denominator 35.
2
FWrite a fraction equal to 5/8 with the denominator 24.
3
FWrite 45/60 in its simplest form.
4
FWrite 36/48 in its simplest form.
5
FWrite 28/42 in its simplest form.
6
FWrite 56/64 in its simplest form.
7
FFill in the missing number: 3/4 = __/20
8
FTick the fractions that are equal to 1/2. Options: 2/4 | 3/5 | 5/10 | 4/9 | 6/12. Write the options you would tick, in the order given.
9
FWrite 9/12 in its simplest form.
10
RIs 6/8 the same as 3/4? Explain how you know.
11
PSHalf of a tin of paint is used on the walls. Then 3/10 of the whole tin is used on the ceiling. What fraction of the tin is used altogether? Write it in simplest form.
12
PSWrite 84/108 in its simplest form.
13
RWrite two fractions equivalent to 5/6, with different bottom numbers.
14
RBen says 4/10 is equal to 2/5 because both have a 2 on the top or bottom. Is he right? Write yes or no.
15
PSWrite 0.6 as a fraction in its simplest form.
2.3

Adding, subtracting and mixed numbers

Year 6
Add and subtract fractions with different denominators and mixed numbers (Year 6)
Video lesson: Adding, subtracting and mixed numbersComing soon
Story. Tom walks 3/8 of a kilometre to the shop, then 1/4 of a kilometre to the park. Later, a jug holds 2 1/2 litres and the juice bottle has 1 3/4 litres in it, so the class must work out how much is left.

Rule

To add or subtract fractions, first write them with the same denominator. Add or subtract the numerators only.

For a mixed number, add or subtract the whole numbers and the fractions separately, then simplify.

Key ideas

  • Common denominator first, then add or subtract the tops.
  • Write the answer in simplest form.
  • If the fraction part adds to more than 1 whole, carry it into the whole numbers.
Worked example 2.3.1
Work out 1/4 + 1/6. Give your answer in its simplest form.

Method. Use a common denominator, add or subtract the tops, then simplify.

  1. Write both with the same bottom number. The bottoms are 4 and 6, so use 12.
    1/4 = 3/12 and 1/6 = 2/12
  2. Work out the tops. 3 + 2 = 5.
    5/12
  3. Simplify, or write as a mixed number. Divide the top and bottom by any common factor, or by the bottom if the top is bigger.
    5/12
  4. Write the answer.
    5/12

Check. 5/12 is the same as 5/12. ✓

Watch out. Add or subtract the tops only. The bottom number stays the same.

Worked example 2.3.2
Work out 5/6 - 2/3. Give your answer in its simplest form.

Method. Use a common denominator, add or subtract the tops, then simplify.

  1. Write both with the same bottom number. The bottoms are 6 and 3, so use 6.
    5/6 = 5/6 and 2/3 = 4/6
  2. Work out the tops. 5 - 4 = 1.
    1/6
  3. Simplify, or write as a mixed number. Divide the top and bottom by any common factor, or by the bottom if the top is bigger.
    1/6
  4. Write the answer.
    1/6

Check. 1/6 is the same as 1/6. ✓

Watch out. Add or subtract the tops only. The bottom number stays the same.

Worked example 2.3.3
Work out 3 1/2 + 2 2/3. Give your answer as a mixed number in its simplest form.

Method. Add the whole parts and the fraction parts, then simplify.

  1. Add the whole numbers. 3 + 2 = 5.
    5
  2. Add the fractions with a common denominator. Use 6 as the common bottom number.
    1/2 + 2/3 = 1 1/6
  3. Put the parts together. Add the whole number part to the whole part of the fraction total.
    6 1/6
  4. Write the answer.
    6 1/6

Check. 6 1/6 is the total. ✓

Watch out. When the fraction parts add to more than 1, carry the whole number into the front.

Watch out

Watch out. 1/3 + 1/4 is not 2/7. Find a common denominator (12) first.

Exam tip

Practice guide. Write the common denominator above both fractions before you do any adding.

Exercise 2C  Practice: adding and subtracting fractions

Non-calculator
1
FWork out 1/2 + 1/3. Give your answer in its simplest form.
2
FWork out 2/5 + 1/4. Give your answer in its simplest form.
3
FWork out 7/8 - 1/4. Give your answer in its simplest form.
4
FWork out 5/6 - 1/4. Give your answer in its simplest form.
5
PSWork out 3/8 + 1/4. Give your answer in its simplest form.
6
FWork out 2 1/4 + 3 1/2. Give your answer as a mixed number in its simplest form.
7
FWork out 1 2/3 + 2 1/6. Give your answer as a mixed number in its simplest form.
8
FWork out 3 1/2 - 1 2/3. Give your answer as a mixed number in its simplest form.
9
PSA jug holds 2 1/2 litres. It has 1 3/4 litres of juice in it. How many more litres does it need to be full? Write as a mixed number.
10
FWork out 1 1/4 + 2 3/8.
11
RBen says 3/4 + 1/8 = 4/12. Is he right? Write yes or no.
12
RAli says 1/3 + 1/4 = 2/7. Is he right? Write yes or no.
13
PSLena has 3/4 of a bag of sand. She uses 1/6 of a bag. How much sand is left? Give the fraction in its simplest form.
14
PSWork out 4/9 + 5/6. Give your answer in its simplest form.
15
PSWork out 4 3/4 + 1 1/2. Give your answer as a mixed number in its simplest form.
16
RExplain why 2/3 + 2/3 is more than 1 but 2/3 - 1/3 is less than 1.
2.4

Multiplying and dividing fractions

Year 6
Multiply and divide fractions by whole numbers, and multiply simple pairs of proper fractions (Year 5-6)
Video lesson: Multiplying and dividing fractionsComing soon
Story. Mrs Hale is making rice for a class party. Each child needs 3/4 of a cup, and she is making 6 portions. Later, a 3/4 metre length of ribbon is cut into 3 equal pieces for the tables.

Rule

To multiply a fraction by a whole number, multiply the top. 2/5 x 6 = 12/5 = 2 2/5.

To multiply two fractions, multiply the tops and multiply the bottoms. To divide by a whole number, multiply the bottom by it: 3/4 / 3 = 3/12 = 1/4.

Key ideas

  • Fraction x whole number: multiply the top only.
  • Fraction x fraction: multiply tops and bottoms, then simplify.
  • Fraction / whole number: multiply the bottom by the whole number.
Worked example 2.4.1
Work out 6 x 2/5. Give your answer in its simplest form.

Method. Multiply the whole number by the top of the fraction.

  1. Write the whole number as a fraction. 6 = 6/1.
    6/1
  2. Multiply the tops and the bottoms. 6 x 2 = 12, and 1 x 5 = 5.
    12/5
  3. Simplify and write as a mixed number. 12 divided by 5 gives the whole part.
    2 2/5
  4. Write the answer.
    2 2/5

Check. 6 lots of 2/5 is 2 2/5. ✓

Worked example 2.4.2
Work out 3/4 x 2/5. Give your answer in its simplest form.

Method. Multiply the tops, multiply the bottoms, then simplify.

  1. Multiply the tops. 3 x 2 = 6.
    6
  2. Multiply the bottoms. 4 x 5 = 20.
    20
  3. Simplify. Divide the top and bottom by any common factor.
    3/10
  4. Write the answer.
    3/10

Check. 6/20 simplifies to 3/10. ✓

Watch out. Simplify first when you can: cancel a factor from a top and a factor from a bottom.

Worked example 2.4.3
Work out 3/4 / 3. Give your answer in its simplest form.

Method. Dividing by a whole number makes the piece smaller.

  1. Multiply by the reciprocal of the whole number. Dividing by 3 is the same as multiplying by 1/3.
    3/4 x 1/3
  2. Multiply the bottoms. 4 x 3 = 12.
    3/12
  3. Simplify. Divide the top and bottom by their highest common factor.
    1/4
  4. Write the answer.
    1/4

Check. 1/4 x 3 = 3/4. ✓

Watch out. Dividing by 2 makes a fraction smaller, not bigger.

Watch out

Watch out. Dividing a fraction by 3 makes it smaller. It does not make it bigger.

Exam tip

Practice guide. Simplify before you multiply when a top and a bottom share a factor.

Exercise 2D  Practice: multiplying and dividing fractions

Non-calculator
1
FWork out 5 x 3/4. Give your answer in its simplest form.
2
FWork out 8 x 5/6. Give your answer in its simplest form.
3
FWork out 2/3 x 3/4. Give your answer in its simplest form.
4
FWork out 5/6 x 3/10. Give your answer in its simplest form.
5
FWork out 4/9 x 3/8. Give your answer in its simplest form.
6
FWork out 5/6 / 2. Give your answer in its simplest form.
7
FWork out 4/5 / 3. Give your answer in its simplest form.
8
PSMrs Hale makes 6 portions of rice. Each portion uses 3/4 of a cup. How many cups of rice does she use? Write as a mixed number.
9
PSA 3/4 metre ribbon is cut into 3 equal pieces. How long is each piece, in metres? Write as a fraction.
10
PSA shop sells 2/3 of a large cake and then 1/2 of what is left. What fraction of the whole cake is left?
11
FWork out 2/5 x 15. Write the answer in its simplest form.
12
RBen says that multiplying a fraction by 3 always makes it bigger. Is he right? Explain using 1/4.
13
RDara says that dividing a fraction by 3 always makes it smaller. Is he right? Explain using 3/4.
14
PSWork out 7/8 x 4/7. Give your answer in its simplest form.
15
RIs it true that 3/4 x 1/2 is less than 1/2? Write yes or no, and show the calculation.
16
PSWork out 3 x 2/9 x 3/4. Give the answer in simplest form.
2.5

Decimals: thousandths, multiplying and dividing, and rounding

Year 6
Read, write and order decimals to thousandths, and multiply and divide by 10, 100 and 1000 (Year 5-6), Round decimals to a given degree of accuracy in context (Year 6)
Video lesson: Decimals: thousandths, multiplying and dividing, and roundingComing soon
Story. A runner times her laps in a relay race. Her times are 12.3478 seconds, 12.0519 seconds and 12.35 seconds, and the coach needs to write them to two decimal places for the notice board.

Rule

Each place after the decimal point is a tenth, a hundredth, a thousandth. 0.047 has 4 hundredths and 7 thousandths.

When you multiply by 10, 100 or 1000, the digits move to the left. When you divide, they move to the right.

To round, look at the digit after the rounding place: 5 or more rounds up.

Key ideas

  • 0.047 = 47 thousandths, and 0.05 is bigger than 0.047.
  • x 100 moves the digits two places to the left, so 4.56 x 100 = 456.
  • Round to the place you are asked for, and look at the next digit.
Worked example 2.5.1
Work out 4.56 x 100.

Method. Multiply by 100 moves the digits 2 places.

  1. Decide which way the digits move. Multiplying by 100 moves each digit 2 places to the left; dividing moves them to the right.
    multiply by 100
  2. Move the digits. Move each digit 2 places left, and fill the gaps with zeros.
    4.56 becomes 456
  3. Write the answer. The decimal point ends in the new place.
    456
  4. Write the answer.
    456

Check. 456 / 100 = 4.56. ✓

Watch out. Dividing by 100 moves the digits two places to the right, not to the left.

Worked example 2.5.2
Work out 0.35 / 10.

Method. Divide by 10 moves the digits 1 place.

  1. Decide which way the digits move. Multiplying by 10 moves each digit 1 place to the left; dividing moves them to the right.
    divide by 10
  2. Move the digits. Move each digit 1 place right, and fill the gaps with zeros.
    0.35 becomes 0.035
  3. Write the answer. The decimal point ends in the new place.
    0.035
  4. Write the answer.
    0.035

Check. 0.035 x 10 = 0.35. ✓

Watch out. Dividing by 100 moves the digits two places to the right, not to the left.

Worked example 2.5.3
Round 12.3478 to the nearest hundredth.

Method. Look at the digit after the rounding place.

  1. Look at the digit after the hundredth place. This digit decides whether to round up or down.
    digit = 7
  2. Decide. 5 or more rounds up; 4 or less rounds down.
    7 is 5 or more, so round up
  3. Write the rounded number. Keep the digits up to the hundredth place.
    12.35
  4. Write the answer.
    12.35

Check. 12.35 is the closest value to 12.3478 at this accuracy. ✓

Watch out. 2.45 to one decimal place is 2.5, because the 5 rounds up.

Watch out

Watch out. 0.5 is bigger than 0.47, even though 47 is bigger than 5. Compare the place values, not the digits alone.

Exam tip

Practice guide. Line up the decimal points before you add, subtract or compare.

Exercise 2E  Practice: decimals to thousandths and rounding

Non-calculator
1
FWrite the value of the 7 in 3.047.
2
FWork out 6.25 x 10.
3
FWork out 80.5 / 100.
4
FWork out 0.8 x 1000.
5
FWork out 47.2 / 10.
6
FPut these decimals in order, from smallest to largest: 0.5, 0.047, 0.0625, 0.45.
7
FRound 12.3478 to the nearest hundredth.
8
FRound 12.0519 to the nearest hundredth.
9
PSRound 2.45 to the nearest tenth.
10
PSRound 7.6849 to the nearest whole number.
11
PSA pen costs 2.35 pounds. Work out the cost of 10 pens, in pounds, written with two decimal places.
12
PSA bag of flour has a mass of 1.275 kg. Round the mass to two decimal places, in kilograms.
13
RTick the decimals that are greater than 0.6. Options: 0.59 | 0.6 | 0.61 | 0.609 | 0.7 | 0.069. Write the options you would tick, in the order given.
14
RSam says that 0.5 is smaller than 0.47 because 5 is smaller than 47. Is he right? Explain.
15
PSA bottle holds 0.75 litres. How many millilitres is that? (1 litre = 1000 millilitres)
16
RWork out 0.6 x 0.1.
17
RExplain why 4.5 x 10 is 45, but 4.5 / 10 is 0.45.
2.6

Fractions, decimals and percentages

Year 6
Recall equivalences between simple fractions, decimals and percentages, and find percentages of amounts (Year 5-6)
Video lesson: Fractions, decimals and percentagesComing soon
Story. A class of 30 pupils is asked how they get to school. 40 per cent walk, and a quarter come by bus. The teacher writes each fraction, decimal and percentage on the board so that the class can compare them.

Rule

Some fractions, decimals and percentages are the same amount: 1/4 = 0.25 = 25%. Learn the common ones: 1/2, 1/4, 3/4, 1/5, 1/10.

To find a percentage of an amount, find 1% first (divide by 100), then multiply. 40% of 30 = 0.3 x 40 = 12.

Key ideas

  • 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/10 = 0.1 = 10%.
  • To find 1%, divide by 100. To find 10%, divide by 10.
  • A fraction of an amount: divide by the bottom, then multiply by the top.
Worked example 2.6.1
What is 40% of 30?

Method. Find 1% first, then multiply.

  1. Find one per cent. Divide 30 by 100.
    30 / 100 = 0.3
  2. Multiply by the number of per cent. Multiply the answer by 40.
    0.3 x 40 = 12
  3. Write the answer. 40% of 30 is 12.
    12
  4. Write the answer.
    12

Check. 1% of 30 is 0.3, so 40% is 12. ✓

Worked example 2.6.2
What is 3/5 of 90?

Method. Divide by the bottom, then multiply by the top.

  1. Divide by 5. 90 / 5 = 18.
    18
  2. Multiply by 3. 18 x 3 = 54.
    54
  3. Write the answer.
    54

Check. 54 / 3 = 18 and 18 x 5 = 90. ✓

Worked example 2.6.3
What is 15% of 240?

Method. Find 1% first, then multiply.

  1. Find one per cent. Divide 240 by 100.
    240 / 100 = 2.4
  2. Multiply by the number of per cent. Multiply the answer by 15.
    2.4 x 15 = 36
  3. Write the answer. 15% of 240 is 36.
    36
  4. Write the answer.
    36

Check. 1% of 240 is 2.4, so 15% is 36. ✓

Watch out

Watch out. 25% is the same as 1/4, not 1/25. Think of 25 out of 100.

Exam tip

Practice guide. Learn the common equivalences first. Then percentages and fractions of amounts get much easier.

Exercise 2F  Practice: fractions, decimals and percentages

Non-calculator
1
FWrite 3/4 as a decimal.
2
FWrite 0.2 as a percentage.
3
FWrite 3/5 as a percentage.
4
FWhat is 25% of 84?
5
FWhat is 7% of 300?
6
FWhat is 35% of 60?
7
FWhat is 1/10 of 350?
8
FWhat is 3/4 of 48?
9
RTick the options that are equal to 25%. Options: 0.25 | 1/4 | 2.5 | 25/100 | 1/5. Write the options you would tick, in the order given.
10
RAli says 0.6 is less than 3/5 because 0.6 has a decimal point. Is he right? Write yes or no.
11
PSIn a class of 30 pupils, 40% walk to school. How many pupils walk to school?
12
PSA class of 30 pupils: 1/5 come by car, and 1/3 come by bus. How many pupils come by car or by bus altogether?
13
RWhich is more: 60% of 80 or 3/4 of 60? Show your working.
14
RWrite one fraction, one decimal and one percentage that are all equal to 0.4.
15
PSA school has 240 pupils, and 15% of them are left-handed. How many pupils are left-handed?
16
PSA sweater costs 45 pounds. It is reduced by 1/5. How much is the reduction, in pounds?

Chapter summary

SkillMethod
Comparing fractionsUse a common denominator, then compare the tops.
Equivalent fractionsMultiply or divide the top and bottom by the same number.
SimplifyingDivide the top and bottom by the highest common factor.
Adding and subtractingCommon denominator, then add or subtract the tops.
MultiplyingMultiply the tops, multiply the bottoms, then simplify.
Dividing by a whole numberMultiply the bottom by the whole number.
Decimals x or / 10, 100, 1000x moves the digits left; / moves them right.
PercentagesFind 1% (divide by 100), then multiply by the percentage.

Can you…?

  • I can compare and order fractions, including fractions greater than 1
  • I can simplify a fraction and write an equivalent fraction
  • I can add and subtract fractions and mixed numbers
  • I can multiply and divide fractions, and give the answer in simplest form
  • I can move the digits of a decimal when multiplying or dividing by 10, 100 or 1000
  • I can round a decimal and find a percentage of an amount

Key terms

equivalent fraction
a fraction with the same value, such as 1/2 and 2/4
simplest form
a fraction where the top and bottom have no common factor except 1
common denominator
the same bottom number for two or more fractions
mixed number
a whole number with a fraction, such as 2 1/3
thousandths
places after the decimal point: 0.001 is one thousandth
percentage
a number out of 100, shown with the % sign

Exercise 2Z  Check-up

Non-calculator
1
Which fraction is larger: 5/9 or 4/7? Write the fraction.
2
Write a fraction equal to 3/7 with the denominator 28.
3
Write 48/72 in its simplest form.
4
Work out 2/3 + 3/8. Give your answer in its simplest form.
5
Work out 2 3/4 + 1 1/6. Give your answer as a mixed number in its simplest form.
6
Work out 3/5 x 10/9. Give your answer in its simplest form.
7
Work out 7/8 / 2. Give your answer in its simplest form.
8
Work out 0.46 x 100.
9
Round 5.6478 to the nearest hundredth.
10
What is 15% of 60?

Total 20 marks. Allow about 20 minutes.

Exercise 2X  Practice test questions

Non-calculator
1
FWork out 3/4 - 1/8. Give your answer in its simplest form.[1 mark]
2
FWhich fraction is larger: 4/5 or 7/9? Write the fraction.[1 mark]
3
FRound 3.4961 to the nearest tenth.[1 mark]
4
FWrite 0.125 as a fraction in its simplest form.[2 marks]
5
PSWork out 4 x 5/6. Give your answer in its simplest form.[2 marks]
6
PSA bottle holds 2.5 litres. Work out how many 0.05 litre cups can be filled from it.[2 marks]
7
PSRavi has 2 1/2 metres of rope and uses 1 3/4 metres. How much rope is left? Write as a mixed number.[2 marks]
8
RExplain how you know that 5/8 is greater than 1/2.[2 marks]
9
FWhat is 35% of 200?[2 marks]
10
PSTick the fractions that are less than 2/3. Options: 1/2 | 3/4 | 5/9 | 4/6 | 7/12. Write the options you would tick, in the order given.[2 marks]
11
RMaya says 4 x 3/5 = 12/5 = 2 2/5. Explain whether she is right.[3 marks]
← Chapter 1: Number reasoningChapter 3: Ratio and proportion reasoning →

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