Halves and quarters
By the end of this chapter you will be able to
- Recognise a half and a quarter of a shape
- Find a half and a quarter of a number or set
- Write 1/2, 1/4 and 3/4
- Say that 2/4 and 1/2 are the same
- Recognise unit fractions
You should already know
- Sharing equally (Do you remember?)
- Multiplication and division facts (chapter 7)
Where this leads
- Measuring length and mass (chapter 9)
Step-by-step practice: maths (Level 3). Small steps, repeated until fluent. Content: Recognise, find, name and write 1/2 and 1/4 of a shape, a length, a set of objects or a quantity, Write simple fractions, for example 1/2 of 8 = 4, and 1/4 of 12 = 3, Recognise that 2/4 and 1/2 are equivalent, and that 3/4 is three of four equal parts, Recognise unit fractions, and find 3/4 of an amount by finding 1/4 and taking three.
Exercise P Do you remember?
Non-calculatorMethod. Share the sweets equally, so each person gets the same number.
- Share the sweets into equal groups. There are 2 people, so there are 2 equal groups.12 ÷ 2
- Count what each person gets. Each equal group is one share.12 ÷ 2 = 6
- Write the answer. This is what each person gets.6
Check. Check: 2 people get 6 each, which is 12 sweets.
Watch out. Check the total: each share times the number of people gives the total.
Method. Share the sweets equally, so each person gets the same number.
- Share the sweets into equal groups. There are 3 people, so there are 3 equal groups.15 ÷ 3
- Count what each person gets. Each equal group is one share.15 ÷ 3 = 5
- Write the answer. This is what each person gets.5
Check. Check: 3 people get 5 each, which is 15 sweets.
Watch out. Check the total: each share times the number of people gives the total.
Method. Share the sweets equally, so each person gets the same number.
- Share the sweets into equal groups. There are 6 people, so there are 6 equal groups.18 ÷ 6
- Count what each person gets. Each equal group is one share.18 ÷ 6 = 3
- Write the answer. This is what each person gets.3
Check. Check: 6 people get 3 each, which is 18 sweets.
Watch out. Check the total: each share times the number of people gives the total.
Method. Share the sweets equally, so each person gets the same number.
- Share the sweets into equal groups. There are 4 people, so there are 4 equal groups.20 ÷ 4
- Count what each person gets. Each equal group is one share.20 ÷ 4 = 5
- Write the answer. This is what each person gets.5
Check. Check: 4 people get 5 each, which is 20 sweets.
Watch out. Check the total: each share times the number of people gives the total.
Method. Share the sweets equally, so each person gets the same number.
- Share the sweets into equal groups. There are 2 people, so there are 2 equal groups.14 ÷ 2
- Count what each person gets. Each equal group is one share.14 ÷ 2 = 7
- Write the answer. This is what each person gets.7
Check. Check: 2 people get 7 each, which is 14 sweets.
Watch out. Check the total: each share times the number of people gives the total.
Halves of shapes and amounts
A half is one of two equal parts. The shape must be split into two parts that are the same size.
To find a half of a number, share it into two equal groups and take one group.
Key ideas
- A half is one of two equal parts.
- Equal parts must be the same size.
- To find a half, divide by 2.
Method. Count the equal parts for the bottom number, and the shaded parts for the top number.
- Count the equal parts. The shape is split into 2 equal parts.2 equal parts
- Count the shaded parts. 1 of the 2 parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.1/2
Check. Check: 1 shaded parts out of 2 equal parts.
Watch out. The bottom number counts all the equal parts, shaded or not.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 12 into 2 equal groups. Each group is one part of the whole.12 ÷ 2 = 6
- Take 1 of the groups. 1/2 means 1 of the 2 equal parts.1 × 6 = 6
- Write the answer. This is the amount for the fraction.6
Check. Check: 6 is 1 of the 2 equal groups of 6.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Watch out
Watch out. A half needs two equal parts. Parts of different sizes are not halves.
Exam tip
Grown-up tip. Fold a piece of paper in half and check both sides match. Share sweets between two people and ask: “Is it fair?”
Exercise 8A Practice: halves
Non-calculatorMethod. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Count the equal parts for the bottom number, and the shaded parts for the top number.
- Count the equal parts. The shape is split into 2 equal parts.2 equal parts
- Count the shaded parts. 1 of the 2 parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.1/2
Check. Check: 1 shaded parts out of 2 equal parts.
Watch out. The bottom number counts all the equal parts, shaded or not.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Count the equal parts for the bottom number, and the shaded parts for the top number.
- Count the equal parts. The shape is split into 2 equal parts.2 equal parts
- Count the shaded parts. 1 of the 2 parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.1/2
Check. Check: 1 shaded parts out of 2 equal parts.
Watch out. The bottom number counts all the equal parts, shaded or not.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are equal
- Write the answer. There are 2 parts and they are all the same size.yes
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are equal
- Write the answer. There are 2 parts and they are all the same size.yes
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Quarters of shapes and amounts
A quarter is one of four equal parts. Four quarters make one whole.
To find a quarter of a number, share it into four equal groups and take one group.
Key ideas
- A quarter is one of four equal parts.
- Four quarters make a whole.
- To find a quarter, divide by 4.
Method. A shape is split into quarters only when there are 4 equal parts.
- Count the parts. We need 4 equal parts to be quarters.4 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are equal
- Write the answer. There are 4 parts and they are all the same size.yes
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 20 into 4 equal groups. Each group is one part of the whole.20 ÷ 4 = 5
- Take 1 of the groups. 1/4 means 1 of the 4 equal parts.1 × 5 = 5
- Write the answer. This is the amount for the fraction.5
Check. Check: 5 is 1 of the 4 equal groups of 5.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 24 into 4 equal groups. Each group is one part of the whole.24 ÷ 4 = 6
- Take 1 of the groups. 1/4 means 1 of the 4 equal parts.1 × 6 = 6
- Write the answer. This is the amount for the fraction.6
Check. Check: 6 is 1 of the 4 equal groups of 6.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Watch out
Watch out. A quarter is one of FOUR equal parts, not one of two. 1/4 of 20 is 5, not 10.
Exam tip
Grown-up tip. Fold paper in half, then in half again. Count the four parts, then colour one.
Exercise 8B Practice: quarters
Non-calculatorMethod. A shape is split into quarters only when there are 4 equal parts.
- Count the parts. We need 4 equal parts to be quarters.4 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are equal
- Write the answer. There are 4 parts and they are all the same size.yes
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into quarters only when there are 4 equal parts.
- Count the parts. We need 4 equal parts to be quarters.4 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are equal
- Write the answer. There are 4 parts and they are all the same size.yes
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Count the equal parts for the bottom number, and the shaded parts for the top number.
- Count the equal parts. The shape is split into 4 equal parts.4 equal parts
- Count the shaded parts. 1 of the 4 parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.1/4
Check. Check: 1 shaded parts out of 4 equal parts.
Watch out. The bottom number counts all the equal parts, shaded or not.
Method. A shape is split into quarters only when there are 4 equal parts.
- Count the parts. We need 4 equal parts to be quarters.4 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A shape is split into quarters only when there are 4 equal parts.
- Count the parts. We need 4 equal parts to be quarters.4 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Count the equal parts for the bottom number, and the shaded parts for the top number.
- Count the equal parts. The shape is split into 4 equal parts.4 equal parts
- Count the shaded parts. 3 of the 4 parts are shaded.3 shaded
- Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.3/4
Check. Check: 3 shaded parts out of 4 equal parts.
Watch out. The bottom number counts all the equal parts, shaded or not.
Method. A shape is split into quarters only when there are 4 equal parts.
- Count the parts. We need 4 equal parts to be quarters.4 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Count the equal parts for the bottom number, and the shaded parts for the top number.
- Count the equal parts. The shape is split into 4 equal parts.4 equal parts
- Count the shaded parts. 1 of the 4 parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.1/4
Check. Check: 1 shaded parts out of 4 equal parts.
Watch out. The bottom number counts all the equal parts, shaded or not.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 44 sweets into 4 equal groups. Each group is one part of the whole.44 ÷ 4 = 11
- Take 1 of the groups for the box. 1/4 is 1 of the 4 equal parts.1 × 11 = 11
- Write the answer. This is the number in the box.11
Check. Check: 11 is 1 of the 4 equal groups of 11.
Watch out. Work out one part first, then take the number of parts.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 44 sweets into 4 equal groups. Each group is one part of the whole.44 ÷ 4 = 11
- Take 1 of the groups for the box. 1/4 is 1 of the 4 equal parts.1 × 11 = 11
- Write the answer. This is the number in the box.11
Check. Check: 11 is 1 of the 4 equal groups of 11.
Watch out. Work out one part first, then take the number of parts.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 36 into 4 equal groups. Each group is one part of the whole.36 ÷ 4 = 9
- Take 1 of the groups. 1/4 means 1 of the 4 equal parts.1 × 9 = 9
- Write the answer. This is the amount for the fraction.9
Check. Check: 9 is 1 of the 4 equal groups of 9.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 20 into 4 equal groups. Each group is one part of the whole.20 ÷ 4 = 5
- Take 1 of the groups. 1/4 means 1 of the 4 equal parts.1 × 5 = 5
- Write the answer. This is the amount for the fraction.5
Check. Check: 5 is 1 of the 4 equal groups of 5.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 16 into 4 equal groups. Each group is one part of the whole.16 ÷ 4 = 4
- Take 1 of the groups. 1/4 means 1 of the 4 equal parts.1 × 4 = 4
- Write the answer. This is the amount for the fraction.4
Check. Check: 4 is 1 of the 4 equal groups of 4.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 8 into 4 equal groups. Each group is one part of the whole.8 ÷ 4 = 2
- Take 1 of the groups. 1/4 means 1 of the 4 equal parts.1 × 2 = 2
- Write the answer. This is the amount for the fraction.2
Check. Check: 2 is 1 of the 4 equal groups of 2.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 20 sweets into 4 equal groups. Each group is one part of the whole.20 ÷ 4 = 5
- Take 1 of the groups for the box. 1/4 is 1 of the 4 equal parts.1 × 5 = 5
- Write the answer. This is the number in the box.5
Check. Check: 5 is 1 of the 4 equal groups of 5.
Watch out. Work out one part first, then take the number of parts.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 36 stickers into 4 equal groups. Each group is one part of the whole.36 ÷ 4 = 9
- Take 1 of the groups for the box. 1/4 is 1 of the 4 equal parts.1 × 9 = 9
- Write the answer. This is the number in the box.9
Check. Check: 9 is 1 of the 4 equal groups of 9.
Watch out. Work out one part first, then take the number of parts.
Three quarters, and 3/4 of an amount
3/4 means three of four equal parts. The bottom number says how many equal parts there are. The top number says how many we take.
To find 3/4 of an amount, first find 1/4, then take three of those parts.
Key ideas
- 3/4 is three of four equal parts.
- Find 1/4 first, then take three.
- The top number is how many we take.
Method. Count the equal parts for the bottom number, and the shaded parts for the top number.
- Count the equal parts. The shape is split into 4 equal parts.4 equal parts
- Count the shaded parts. 3 of the 4 parts are shaded.3 shaded
- Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.3/4
Check. Check: 3 shaded parts out of 4 equal parts.
Watch out. The bottom number counts all the equal parts, shaded or not.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 12 into 4 equal groups. Each group is one part of the whole.12 ÷ 4 = 3
- Take 3 of the groups. 3/4 means 3 of the 4 equal parts.3 × 3 = 9
- Write the answer. This is the amount for the fraction.9
Check. Check: 9 is 3 of the 4 equal groups of 3.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 16 stickers into 4 equal groups. Each group is one part of the whole.16 ÷ 4 = 4
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 4 = 12
- Write the answer. This is the number in the box.12
Check. Check: 12 is 3 of the 4 equal groups of 4.
Watch out. Work out one part first, then take the number of parts.
Watch out
Watch out. 3/4 of 12 is 9, not 3. Take three of the four equal groups, not one.
Exam tip
Grown-up tip. Ask: “How many equal parts? How many do we take? Find one part first.”
Exercise 8C Practice: three quarters
Non-calculatorMethod. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 12 into 4 equal groups. Each group is one part of the whole.12 ÷ 4 = 3
- Take 3 of the groups. 3/4 means 3 of the 4 equal parts.3 × 3 = 9
- Write the answer. This is the amount for the fraction.9
Check. Check: 9 is 3 of the 4 equal groups of 3.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 48 sweets into 4 equal groups. Each group is one part of the whole.48 ÷ 4 = 12
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 12 = 36
- Write the answer. This is the number in the box.36
Check. Check: 36 is 3 of the 4 equal groups of 12.
Watch out. Work out one part first, then take the number of parts.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 16 stickers into 4 equal groups. Each group is one part of the whole.16 ÷ 4 = 4
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 4 = 12
- Write the answer. This is the number in the box.12
Check. Check: 12 is 3 of the 4 equal groups of 4.
Watch out. Work out one part first, then take the number of parts.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 16 into 4 equal groups. Each group is one part of the whole.16 ÷ 4 = 4
- Take 3 of the groups. 3/4 means 3 of the 4 equal parts.3 × 4 = 12
- Write the answer. This is the amount for the fraction.12
Check. Check: 12 is 3 of the 4 equal groups of 4.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 48 into 4 equal groups. Each group is one part of the whole.48 ÷ 4 = 12
- Take 3 of the groups. 3/4 means 3 of the 4 equal parts.3 × 12 = 36
- Write the answer. This is the amount for the fraction.36
Check. Check: 36 is 3 of the 4 equal groups of 12.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 8 beads into 4 equal groups. Each group is one part of the whole.8 ÷ 4 = 2
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 2 = 6
- Write the answer. This is the number in the box.6
Check. Check: 6 is 3 of the 4 equal groups of 2.
Watch out. Work out one part first, then take the number of parts.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 40 stickers into 4 equal groups. Each group is one part of the whole.40 ÷ 4 = 10
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 10 = 30
- Write the answer. This is the number in the box.30
Check. Check: 30 is 3 of the 4 equal groups of 10.
Watch out. Work out one part first, then take the number of parts.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 36 into 4 equal groups. Each group is one part of the whole.36 ÷ 4 = 9
- Take 3 of the groups. 3/4 means 3 of the 4 equal parts.3 × 9 = 27
- Write the answer. This is the amount for the fraction.27
Check. Check: 27 is 3 of the 4 equal groups of 9.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 40 into 4 equal groups. Each group is one part of the whole.40 ÷ 4 = 10
- Take 3 of the groups. 3/4 means 3 of the 4 equal parts.3 × 10 = 30
- Write the answer. This is the amount for the fraction.30
Check. Check: 30 is 3 of the 4 equal groups of 10.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 32 beads into 4 equal groups. Each group is one part of the whole.32 ÷ 4 = 8
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 8 = 24
- Write the answer. This is the number in the box.24
Check. Check: 24 is 3 of the 4 equal groups of 8.
Watch out. Work out one part first, then take the number of parts.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 44 into 4 equal groups. Each group is one part of the whole.44 ÷ 4 = 11
- Take 3 of the groups. 3/4 means 3 of the 4 equal parts.3 × 11 = 33
- Write the answer. This is the amount for the fraction.33
Check. Check: 33 is 3 of the 4 equal groups of 11.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 32 beads into 4 equal groups. Each group is one part of the whole.32 ÷ 4 = 8
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 8 = 24
- Write the answer. This is the number in the box.24
Check. Check: 24 is 3 of the 4 equal groups of 8.
Watch out. Work out one part first, then take the number of parts.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 48 sweets into 4 equal groups. Each group is one part of the whole.48 ÷ 4 = 12
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 12 = 36
- Write the answer. This is the number in the box.36
Check. Check: 36 is 3 of the 4 equal groups of 12.
Watch out. Work out one part first, then take the number of parts.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 12 sweets into 4 equal groups. Each group is one part of the whole.12 ÷ 4 = 3
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 3 = 9
- Write the answer. This is the number in the box.9
Check. Check: 9 is 3 of the 4 equal groups of 3.
Watch out. Work out one part first, then take the number of parts.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 40 stickers into 4 equal groups. Each group is one part of the whole.40 ÷ 4 = 10
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 10 = 30
- Write the answer. This is the number in the box.30
Check. Check: 30 is 3 of the 4 equal groups of 10.
Watch out. Work out one part first, then take the number of parts.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 28 stickers into 4 equal groups. Each group is one part of the whole.28 ÷ 4 = 7
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 7 = 21
- Write the answer. This is the number in the box.21
Check. Check: 21 is 3 of the 4 equal groups of 7.
Watch out. Work out one part first, then take the number of parts.
Fractions that are the same
Some fractions look different but cover the same part of a shape. 2/4 and 1/2 are the same.
Two equal parts out of four cover the same part of a shape as one part out of two.
Key ideas
- 2/4 and 1/2 are the same.
- Different fractions can name the same part.
- Check by shading both shapes.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 1/2. We want a fraction with the same value.1/2
- Compare each option with the target. 2/4 covers the same part of a shape as 1/2.2/4
- Write the answer. This fraction is the same as the target.2/4
Check. Shade 1/2 and 2/4 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 1/4. We want a fraction with the same value.1/4
- Compare each option with the target. 2/8 covers the same part of a shape as 1/4.2/8
- Write the answer. This fraction is the same as the target.2/8
Check. Shade 1/4 and 2/8 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 1/3. We want a fraction with the same value.1/3
- Compare each option with the target. 2/6 covers the same part of a shape as 1/3.2/6
- Write the answer. This fraction is the same as the target.2/6
Check. Shade 1/3 and 2/6 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Watch out
Watch out. 2/4 is the same as 1/2, but 3/4 is not. Check the shaded parts carefully.
Exam tip
Grown-up tip. Use paper strips: fold one into halves and another into quarters, and lay them on top of each other.
Exercise 8D Practice: fractions that are the same
Non-calculatorMethod. Two fractions are the same when they cover the same part of a shape.
- Look at 2/3. We want a fraction with the same value.2/3
- Compare each option with the target. 4/6 covers the same part of a shape as 2/3.4/6
- Write the answer. This fraction is the same as the target.4/6
Check. Shade 2/3 and 4/6 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 1/2. We want a fraction with the same value.1/2
- Compare each option with the target. 2/4 covers the same part of a shape as 1/2.2/4
- Write the answer. This fraction is the same as the target.2/4
Check. Shade 1/2 and 2/4 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 1/3. We want a fraction with the same value.1/3
- Compare each option with the target. 3/9 covers the same part of a shape as 1/3.3/9
- Write the answer. This fraction is the same as the target.3/9
Check. Shade 1/3 and 3/9 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 3/4. We want a fraction with the same value.3/4
- Compare each option with the target. 9/12 covers the same part of a shape as 3/4.9/12
- Write the answer. This fraction is the same as the target.9/12
Check. Shade 3/4 and 9/12 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 2/3. We want a fraction with the same value.2/3
- Compare each option with the target. 6/9 covers the same part of a shape as 2/3.6/9
- Write the answer. This fraction is the same as the target.6/9
Check. Shade 2/3 and 6/9 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 3/4. We want a fraction with the same value.3/4
- Compare each option with the target. 9/12 covers the same part of a shape as 3/4.9/12
- Write the answer. This fraction is the same as the target.9/12
Check. Shade 3/4 and 9/12 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 3/4. We want a fraction with the same value.3/4
- Compare each option with the target. 9/12 covers the same part of a shape as 3/4.9/12
- Write the answer. This fraction is the same as the target.9/12
Check. Shade 3/4 and 9/12 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 2/3. We want a fraction with the same value.2/3
- Compare each option with the target. 8/12 covers the same part of a shape as 2/3.8/12
- Write the answer. This fraction is the same as the target.8/12
Check. Shade 2/3 and 8/12 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 1/2. We want a fraction with the same value.1/2
- Compare each option with the target. 2/4 covers the same part of a shape as 1/2.2/4
- Write the answer. This fraction is the same as the target.2/4
Check. Shade 1/2 and 2/4 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 1/3. We want a fraction with the same value.1/3
- Compare each option with the target. 4/12 covers the same part of a shape as 1/3.4/12
- Write the answer. This fraction is the same as the target.4/12
Check. Shade 1/3 and 4/12 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 1/5. We want a fraction with the same value.1/5
- Compare each option with the target. 2/10 covers the same part of a shape as 1/5.2/10
- Write the answer. This fraction is the same as the target.2/10
Check. Shade 1/5 and 2/10 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 2/3. We want a fraction with the same value.2/3
- Compare each option with the target. 8/12 covers the same part of a shape as 2/3.8/12
- Write the answer. This fraction is the same as the target.8/12
Check. Shade 2/3 and 8/12 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 3/4. We want a fraction with the same value.3/4
- Compare each option with the target. 6/8 covers the same part of a shape as 3/4.6/8
- Write the answer. This fraction is the same as the target.6/8
Check. Shade 3/4 and 6/8 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 1/3. We want a fraction with the same value.1/3
- Compare each option with the target. 4/12 covers the same part of a shape as 1/3.4/12
- Write the answer. This fraction is the same as the target.4/12
Check. Shade 1/3 and 4/12 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 3/4. We want a fraction with the same value.3/4
- Compare each option with the target. 9/12 covers the same part of a shape as 3/4.9/12
- Write the answer. This fraction is the same as the target.9/12
Check. Shade 3/4 and 9/12 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Method. Two fractions are the same when they cover the same part of a shape.
- Look at 3/4. We want a fraction with the same value.3/4
- Compare each option with the target. 9/12 covers the same part of a shape as 3/4.9/12
- Write the answer. This fraction is the same as the target.9/12
Check. Shade 3/4 and 9/12 on two shapes. They cover the same part.
Watch out. 2/4 and 1/2 are the same. Both mean the shape is split into halves.
Unit fractions
A unit fraction has 1 on top. For example, 1/4 is one of four equal parts.
The bottom number tells you how many equal parts the whole is split into.
Key ideas
- A unit fraction has 1 on top.
- The bottom number is the number of equal parts.
- 1/2, 1/3 and 1/4 are unit fractions.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.4 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 4
- Write the fraction. The top number is 1 for one part.1/4
Check. Check: 4 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.6 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 6
- Write the fraction. The top number is 1 for one part.1/6
Check. Check: 6 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top.
- Look at the top number of each fraction. A unit fraction has 1 on top.2/4 has 2 on top, 3/4 has 3 on top, 1/4 has 1 on top
- Find the one with 1 on top. Only one of them has a 1 on top.1/4
- Write the answer. This is the unit fraction.1/4
Check. 1/4 is one of equal parts. The others take more than one part.
Watch out. The top number is the number of parts we take. A unit fraction takes just one.
Watch out
Watch out. 2/4 is not a unit fraction, because it has 2 on top. A unit fraction has 1 on top.
Exam tip
Grown-up tip. Ask: “How many equal parts is the shape split into? How many parts are we talking about?”
Exercise 8E Practice: unit fractions
Non-calculatorMethod. A unit fraction has a 1 on top.
- Look at the top number of each fraction. A unit fraction has 1 on top.1/2 has 1 on top, 4/6 has 4 on top, 2/10 has 2 on top
- Find the one with 1 on top. Only one of them has a 1 on top.1/2
- Write the answer. This is the unit fraction.1/2
Check. 1/2 is one of equal parts. The others take more than one part.
Watch out. The top number is the number of parts we take. A unit fraction takes just one.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.5 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 5
- Write the fraction. The top number is 1 for one part.1/5
Check. Check: 5 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top.
- Look at the top number of each fraction. A unit fraction has 1 on top.1/9 has 1 on top, 4/5 has 4 on top, 3/7 has 3 on top
- Find the one with 1 on top. Only one of them has a 1 on top.1/9
- Write the answer. This is the unit fraction.1/9
Check. 1/9 is one of equal parts. The others take more than one part.
Watch out. The top number is the number of parts we take. A unit fraction takes just one.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.2 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 2
- Write the fraction. The top number is 1 for one part.1/2
Check. Check: 2 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.6 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 6
- Write the fraction. The top number is 1 for one part.1/6
Check. Check: 6 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.4 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 4
- Write the fraction. The top number is 1 for one part.1/4
Check. Check: 4 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.9 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 9
- Write the fraction. The top number is 1 for one part.1/9
Check. Check: 9 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top.
- Look at the top number of each fraction. A unit fraction has 1 on top.1/5 has 1 on top, 4/6 has 4 on top, 5/9 has 5 on top
- Find the one with 1 on top. Only one of them has a 1 on top.1/5
- Write the answer. This is the unit fraction.1/5
Check. 1/5 is one of equal parts. The others take more than one part.
Watch out. The top number is the number of parts we take. A unit fraction takes just one.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.10 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 10
- Write the fraction. The top number is 1 for one part.1/10
Check. Check: 10 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top.
- Look at the top number of each fraction. A unit fraction has 1 on top.1/2 has 1 on top, 3/5 has 3 on top, 2/6 has 2 on top
- Find the one with 1 on top. Only one of them has a 1 on top.1/2
- Write the answer. This is the unit fraction.1/2
Check. 1/2 is one of equal parts. The others take more than one part.
Watch out. The top number is the number of parts we take. A unit fraction takes just one.
Method. A unit fraction has a 1 on top.
- Look at the top number of each fraction. A unit fraction has 1 on top.1/3 has 1 on top, 2/8 has 2 on top, 5/9 has 5 on top
- Find the one with 1 on top. Only one of them has a 1 on top.1/3
- Write the answer. This is the unit fraction.1/3
Check. 1/3 is one of equal parts. The others take more than one part.
Watch out. The top number is the number of parts we take. A unit fraction takes just one.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.8 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 8
- Write the fraction. The top number is 1 for one part.1/8
Check. Check: 8 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.7 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 7
- Write the fraction. The top number is 1 for one part.1/7
Check. Check: 7 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top.
- Look at the top number of each fraction. A unit fraction has 1 on top.1/9 has 1 on top, 3/8 has 3 on top, 5/10 has 5 on top
- Find the one with 1 on top. Only one of them has a 1 on top.1/9
- Write the answer. This is the unit fraction.1/9
Check. 1/9 is one of equal parts. The others take more than one part.
Watch out. The top number is the number of parts we take. A unit fraction takes just one.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.3 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 3
- Write the fraction. The top number is 1 for one part.1/3
Check. Check: 3 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top.
- Look at the top number of each fraction. A unit fraction has 1 on top.1/4 has 1 on top, 4/8 has 4 on top, 3/6 has 3 on top
- Find the one with 1 on top. Only one of them has a 1 on top.1/4
- Write the answer. This is the unit fraction.1/4
Check. 1/4 is one of equal parts. The others take more than one part.
Watch out. The top number is the number of parts we take. A unit fraction takes just one.
Chapter summary
| Skill | Method |
|---|---|
| Halves | Two equal parts; find a half by dividing by 2 |
| Quarters | Four equal parts; find a quarter by dividing by 4 |
| Three quarters | Find 1/4, then take three of those parts |
| Same fractions | Fractions such as 2/4 and 1/2 cover the same part of a shape |
| Unit fractions | One part of equal parts, with 1 on top |
Can you…?
- I can recognise a half and a quarter of a shape
- I can find a half and a quarter of a number or a set
- I can write 1/2, 1/4 and 3/4
- I can say that 2/4 and 1/2 are the same
- I can find 3/4 of an amount
Key terms
- half
- one of two equal parts; written 1/2
- quarter
- one of four equal parts; written 1/4
- numerator
- the top number of a fraction, the number of parts we take
- equivalent
- fractions that have the same value, such as 2/4 and 1/2
Exercise 8Z Check-up
Non-calculatorMethod. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 24 into 4 equal groups. Each group is one part of the whole.24 ÷ 4 = 6
- Take 1 of the groups. 1/4 means 1 of the 4 equal parts.1 × 6 = 6
- Write the answer. This is the amount for the fraction.6
Check. Check: 6 is 1 of the 4 equal groups of 6.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are equal
- Write the answer. There are 2 parts and they are all the same size.yes
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 16 into 2 equal groups. Each group is one part of the whole.16 ÷ 2 = 8
- Take 1 of the groups. 1/2 means 1 of the 2 equal parts.1 × 8 = 8
- Write the answer. This is the amount for the fraction.8
Check. Check: 8 is 1 of the 2 equal groups of 8.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.9 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 9
- Write the fraction. The top number is 1 for one part.1/9
Check. Check: 9 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. Count the equal parts for the bottom number, and the shaded parts for the top number.
- Count the equal parts. The shape is split into 2 equal parts.2 equal parts
- Count the shaded parts. 1 of the 2 parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.1/2
Check. Check: 1 shaded parts out of 2 equal parts.
Watch out. The bottom number counts all the equal parts, shaded or not.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 48 into 4 equal groups. Each group is one part of the whole.48 ÷ 4 = 12
- Take 3 of the groups. 3/4 means 3 of the 4 equal parts.3 × 12 = 36
- Write the answer. This is the amount for the fraction.36
Check. Check: 36 is 3 of the 4 equal groups of 12.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.5 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 5
- Write the fraction. The top number is 1 for one part.1/5
Check. Check: 5 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A shape is split into quarters only when there are 4 equal parts.
- Count the parts. We need 4 equal parts to be quarters.4 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Total 19 marks. Allow about 19 minutes.
Exercise 8X Practice test questions
Non-calculatorMethod. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 28 into 4 equal groups. Each group is one part of the whole.28 ÷ 4 = 7
- Take 1 of the groups. 1/4 means 1 of the 4 equal parts.1 × 7 = 7
- Write the answer. This is the amount for the fraction.7
Check. Check: 7 is 1 of the 4 equal groups of 7.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. Count the equal parts for the bottom number, and the shaded parts for the top number.
- Count the equal parts. The shape is split into 4 equal parts.4 equal parts
- Count the shaded parts. 2 of the 4 parts are shaded.2 shaded
- Write the fraction. The shaded parts go on top. The number of equal parts goes underneath.2/4
Check. Check: 2 shaded parts out of 4 equal parts.
Watch out. The bottom number counts all the equal parts, shaded or not.
Method. A unit fraction has a 1 on top.
- Look at the top number of each fraction. A unit fraction has 1 on top.1/9 has 1 on top, 4/6 has 4 on top, 4/8 has 4 on top
- Find the one with 1 on top. Only one of them has a 1 on top.1/9
- Write the answer. This is the unit fraction.1/9
Check. 1/9 is one of equal parts. The others take more than one part.
Watch out. The top number is the number of parts we take. A unit fraction takes just one.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.3 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 3
- Write the fraction. The top number is 1 for one part.1/3
Check. Check: 3 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. A unit fraction has a 1 on top. The bottom number is the number of equal parts.
- Count the equal parts. The bottom number is the number of equal parts.6 equal parts
- One part is 1 of them. A unit fraction has 1 on top.1 part out of 6
- Write the fraction. The top number is 1 for one part.1/6
Check. Check: 6 of these parts make the whole.
Watch out. One part of a shape split into four is 1/4.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 16 beads into 4 equal groups. Each group is one part of the whole.16 ÷ 4 = 4
- Take 1 of the groups for the box. 1/4 is 1 of the 4 equal parts.1 × 4 = 4
- Write the answer. This is the number in the box.4
Check. Check: 4 is 1 of the 4 equal groups of 4.
Watch out. Work out one part first, then take the number of parts.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are not equal
- Write the answer. The parts are not all the same size, so it is not split into equal parts.no
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Divide the number into equal parts, then take the number of parts the fraction says.
- Split 8 into 4 equal groups. Each group is one part of the whole.8 ÷ 4 = 2
- Take 1 of the groups. 1/4 means 1 of the 4 equal parts.1 × 2 = 2
- Write the answer. This is the amount for the fraction.2
Check. Check: 2 is 1 of the 4 equal groups of 2.
Watch out. The bottom number tells you how many equal groups to split into. The top number tells you how many to take.
Method. A shape is split into halves only when there are 2 equal parts.
- Count the parts. We need 2 equal parts to be halves.2 parts
- Check the parts are the same size. Equal parts must be the same size.the parts are equal
- Write the answer. There are 2 parts and they are all the same size.yes
Check. Check the size of each part by eye: all must match.
Watch out. Equal parts are the same size. Count the parts and check each one.
Method. Split the amount into equal parts, then take the parts the fraction asks for.
- Split the 8 beads into 4 equal groups. Each group is one part of the whole.8 ÷ 4 = 2
- Take 3 of the groups for the box. 3/4 is 3 of the 4 equal parts.3 × 2 = 6
- Write the answer. This is the number in the box.6
Check. Check: 6 is 3 of the 4 equal groups of 2.
Watch out. Work out one part first, then take the number of parts.