Fractions
By the end of this chapter you will be able to
- Say what the top and bottom numbers of a fraction mean
- Find and name one third and one quarter of a shape
- Find and name two quarters and three quarters of a shape
- Find one third, one quarter and three quarters of a length
- Find a fraction of a group by sharing it into equal groups
- Write a fraction of a number, for example 1/2 of 6 = 3
- Know that 2/4 and 1/2 are the same amount
You should already know
- Halves and quarters of shapes and groups (Year 1, Chapter 10)
- Sharing into equal groups (Chapter 3)
- Counting in 2s, 5s and 10s (Chapter 3)
Where this leads
- Measuring lengths in cm (Chapter 5)
- Fractions of an amount of money (Chapter 6)
National Curriculum for England, Key Stage 1 mathematics, Year 2. Content: Recognise, find and name 1/3, 1/4, 2/4 and 3/4 of a length, shape, set of objects or quantity, Write simple fractions, for example 1/2 of 6 = 3, Recognise that 2/4 and 1/2 are equivalent.
Exercise P Do you remember?
Non-calculatorKey words. One half means 1 of the 2 equal parts.
Method. Share into 2 equal plates, then take the ones you need.
- Share the 8 counters into 2 equal plates. Every plate needs the same number.8 ÷ 2 = 4
- Find what is in one plate. Each plate has 4 counters.4 in one plate
- Take one plate. One plate is one half of the whole.4
Check. Put the plates back together: 4 + 4 = 8. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Method. Four equal quarters make one whole shape.
- Count the equal parts. Each part is one quarter.4 quarters
- Put them together. All four quarters make the whole square.1 + 1 + 1 + 1 = 4 quarters
- Write the answer. 4
Check. Count them again: 1, 2, 3, 4. ✓
Watch out. Count all the equal parts, not only the shaded ones.
Method. Count in 2s. Each jump is 2.
- Start at 2. Count in jumps of 2.2, 4, 6
- Count on to the gap. The next jump after 6 is 8.2, 4, 6, 8
- Write the answer. 8
Check. Count back in 2s from 8: 6, 4, 2. ✓
Watch out. Every jump is the same size, which is 2.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.2 parts
- Compare the sizes. Equal parts are the same size.The parts are not the same size.
- Decide. No. The parts are not equal.
Check. Measure the parts with a ruler. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Make groups of 2, then count the groups.
- Make groups of 2. Each plate has 2 socks.2 + 2 + 2 = 6
- Count the groups. There are 3 plates.3 plates
- Write the answer. 3
Check. Count in 2s: 2, 4, 6. ✓
Watch out. Count the plates, not the socks.
Thirds and quarters of a shape
A fraction tells us about equal parts.
A third is one of three equal parts. We write it as 1/3.
A quarter is one of four equal parts. We write it as 1/4.
The bottom number tells how many equal parts there are.
Key ideas
- The bottom number is how many equal parts there are.
- The top number is how many parts are shaded.
- A third is one of three equal parts: 1/3.
- A quarter is one of four equal parts: 1/4.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 3.3 equal parts
- Count the shaded parts. 1 of the 3 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one third.1/3
Check. Say it in words: one third. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 1 of the 4 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one quarter.1/4
Check. Say it in words: one quarter. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Count the equal parts before you name the fraction.
- Count the equal parts. The shape has 3 equal parts, not 4.3 equal parts
- Count the shaded parts. One of the 3 parts is shaded.1 shaded
- Write the fraction. One of three equal parts is one third, not one quarter.1/3
Check. Three equal parts, one shaded: one third. ✓
Watch out. Count the equal parts first. Four parts would make a quarter.
Watch out
Watch out: the bottom number counts all the equal parts.
It does not count only the shaded parts.
Exam tip
Grown-up tip. Fold a paper circle or square into equal parts. Ask: “How many equal parts? How many are shaded?”
Exercise 4A Thirds and quarters of a shape
Non-calculatorKey words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 3.3 equal parts
- Count the shaded parts. 1 of the 3 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one third.1/3
Check. Say it in words: one third. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 1 of the 4 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one quarter.1/4
Check. Say it in words: one quarter. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 3.3 equal parts
- Count the shaded parts. 1 of the 3 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one third.1/3
Check. Say it in words: one third. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 1 of the 4 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one quarter.1/4
Check. Say it in words: one quarter. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.3 parts
- Compare the sizes. Equal parts are the same size.The parts are not the same size.
- Decide. No. The parts are not equal.
Check. Measure the parts with a ruler. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Equal parts are the same size. Compare the parts to decide.
- Look at each part. Compare the parts side by side.3 parts
- Compare the sizes. Equal parts are the same size.The parts are the same size.
- Decide. Yes. The parts are equal.
Check. Measure the parts with a ruler. The same length means equal. ✓
Watch out. A line that looks like it is in the middle may not be. Check before you decide.
Method. Look at each picture and find the one with one third shaded.
- Look at A. Count the equal parts and the shaded parts.A: 4 equal parts, 1 shaded
- Look at B. Count the equal parts and the shaded parts.B: 3 equal parts, 1 shaded
- Look at C. Count the equal parts and the shaded parts.C: 4 equal parts, 2 shaded
- Find the picture that matches. We want the picture with one third shaded.Matches: B
- Write the answer. B
Check. A and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 1 of the 4 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one quarter.1/4
Check. Say it in words: one quarter. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 3.3 equal parts
- Count the shaded parts. 1 of the 3 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one third.1/3
Check. Say it in words: one third. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Count the equal parts before you decide.
- Count the equal parts. The circle has 3 equal parts, not 4.3 equal parts
- Count the shaded parts. One of the 3 parts is shaded.1 shaded
- Decide. One of three equal parts is one third, not one quarter.No. It is one third.
Check. Count the parts again: 1, 2, 3. ✓
Watch out. Count the equal parts first.
Method. Look at each picture and find the one with 4 equal parts.
- Look at A. Count the equal parts and the shaded parts.A: 3 equal parts, 0 shaded
- Look at B. Count the equal parts and the shaded parts.B: 4 equal parts, 0 shaded
- Find the picture that matches. We want the picture with 4 equal parts.Matches: B
- Write the answer. B
Check. A do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. Compare the two shaded parts.
- Look at Ella. Her square has 4 equal parts. One part is a quarter.1/4
- Look at Sam. His circle has 3 equal parts. One part is a third.1/3
- Compare them. Fewer equal parts means each part is bigger. A third is bigger than a quarter.1/3 is bigger than 1/4
- Write the answer. Sam. One third is bigger than one quarter.
Check. Four quarters make one whole, and so do three thirds. Thirds are bigger. ✓
Watch out. More equal parts means each part is smaller.
Method. Compare the sizes of the parts.
- Look at a third. One third is one of three equal parts.Three parts
- Look at a quarter. One quarter is one of four equal parts.Four parts
- Compare. Fewer parts means bigger parts, so a third is bigger.No. A third is bigger than a quarter.
Check. Three equal parts fill a circle, and four equal parts fill it too. ✓
Watch out. More equal parts means each part is smaller.
Thirds and quarters of a length
A length can be shared into equal parts, just like a shape.
This ribbon is 12 cm long. We cut it into 3 equal pieces. Each piece is one third of the ribbon.
To find one third, share 12 into 3 equal parts: 12 ÷ 3 = 4. So one third of 12 cm is 4 cm.
Key ideas
- Share the whole length into equal pieces first.
- One third is one of three equal pieces.
- One quarter is one of four equal pieces.
- Write the answer in cm.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 12 cm into 3 equal pieces. Every piece needs the same number.12 ÷ 3 = 4
- Find what is in one piece. Each piece has 4 cm.4 in one piece
- Take one piece. One piece is one third of the whole.4
Check. Put the pieces back together: 4 + 4 + 4 = 12. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 8 cm into 4 equal pieces. Every piece needs the same number.8 ÷ 4 = 2
- Find what is in one piece. Each piece has 2 cm.2 in one piece
- Take one piece. One piece is one quarter of the whole.2
Check. Put the pieces back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 9 cm into 3 equal pieces. Every piece needs the same number.9 ÷ 3 = 3
- Find what is in one piece. Each piece has 3 cm.3 in one piece
- Take one piece. One piece is one third of the whole.3
Check. Put the pieces back together: 3 + 3 + 3 = 9. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Watch out
Watch out: share the whole length first.
Then count the length of one piece.
Exam tip
Grown-up tip. Use a strip of paper or ribbon. Fold it into three or four equal pieces. Ask: “How long is one piece?”
Exercise 4B Thirds and quarters of a length
Non-calculatorKey words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 6 cm into 3 equal pieces. Every piece needs the same number.6 ÷ 3 = 2
- Find what is in one piece. Each piece has 2 cm.2 in one piece
- Take one piece. One piece is one third of the whole.2
Check. Put the pieces back together: 2 + 2 + 2 = 6. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 12 cm into 4 equal pieces. Every piece needs the same number.12 ÷ 4 = 3
- Find what is in one piece. Each piece has 3 cm.3 in one piece
- Take one piece. One piece is one quarter of the whole.3
Check. Put the pieces back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 15 cm into 3 equal pieces. Every piece needs the same number.15 ÷ 3 = 5
- Find what is in one piece. Each piece has 5 cm.5 in one piece
- Take one piece. One piece is one third of the whole.5
Check. Put the pieces back together: 5 + 5 + 5 = 15. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 16 cm into 4 equal pieces. Every piece needs the same number.16 ÷ 4 = 4
- Find what is in one piece. Each piece has 4 cm.4 in one piece
- Take one piece. One piece is one quarter of the whole.4
Check. Put the pieces back together: 4 + 4 + 4 + 4 = 16. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 8 cm into 4 equal pieces. Every piece needs the same number.8 ÷ 4 = 2
- Find what is in one piece. Each piece has 2 cm.2 in one piece
- Take one piece. One piece is one quarter of the whole.2
Check. Put the pieces back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 18 cm into 3 equal pieces. Every piece needs the same number.18 ÷ 3 = 6
- Find what is in one piece. Each piece has 6 cm.6 in one piece
- Take one piece. One piece is one third of the whole.6
Check. Put the pieces back together: 6 + 6 + 6 = 18. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 9 cm into 3 equal pieces. Every piece needs the same number.9 ÷ 3 = 3
- Find what is in one piece. Each piece has 3 cm.3 in one piece
- Take one piece. One piece is one third of the whole.3
Check. Put the pieces back together: 3 + 3 + 3 = 9. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 20 cm into 4 equal pieces. Every piece needs the same number.20 ÷ 4 = 5
- Find what is in one piece. Each piece has 5 cm.5 in one piece
- Take one piece. One piece is one quarter of the whole.5
Check. Put the pieces back together: 5 + 5 + 5 + 5 = 20. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal pieces, then take the ones you need.
- Share the 15 cm into 3 equal pieces. Every piece needs the same number.15 ÷ 3 = 5
- Find what is in one piece. Each piece has 5 cm.5 in one piece
- Take one piece. One piece is one third of the whole.5
Check. Put the pieces back together: 5 + 5 + 5 = 15. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 8 cm into 4 equal pieces. Every piece needs the same number.8 ÷ 4 = 2
- Find what is in one piece. Each piece has 2 cm.2 in one piece
- Take one piece. One piece is one quarter of the whole.2
Check. Put the pieces back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Method. Share the 12 cm into 4 equal pieces, then check one piece.
- Share the ribbon. Share 12 cm into 4 equal pieces.12 ÷ 4 = 3
- Check one piece. Each piece is 3 cm, not 4 cm.3 cm in one piece
- Decide. Ben is not right. One quarter of 12 cm is 3 cm.No. One quarter of 12 cm is 3 cm.
Check. Four pieces of 3 cm make 12 cm: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Count the pieces, then share the length.
Method. Work out one piece of each ribbon, then compare.
- Ruby’s piece. Share 12 cm into 3 equal pieces.12 ÷ 3 = 4 cm
- Ali’s piece. Share 8 cm into 4 equal pieces.8 ÷ 4 = 2 cm
- Compare. 4 cm is more than 2 cm.4 > 2
- Write the answer. Ruby. Her piece is longer.
Check. Ruby’s piece is 4 cm and Ali’s is 2 cm. ✓
Watch out. Compare the pieces, not the whole ribbons.
Two quarters and three quarters
A quarter is one of four equal parts. Two quarters are shaded here. We write two quarters as 2/4.
Three quarters means three of the four equal parts. We write it as 3/4.
The top number counts the parts we have. The bottom number counts all the equal parts.
Key ideas
- A quarter is one of four equal parts.
- Two quarters is 2/4.
- Three quarters is 3/4.
- The top number is the number of parts we have.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 2 of the 4 equal parts are shaded.2 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is two quarters.2/4
Check. Say it in words: two quarters. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 3 of the 4 equal parts are shaded.3 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is three quarters.3/4
Check. Say it in words: three quarters. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 2 of the 4 equal parts are shaded.2 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is two quarters.2/4
Check. Say it in words: two quarters. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Watch out
Watch out: the top number is the shaded parts, so three quarters is 3/4.
It is not 4/3.
Exam tip
Grown-up tip. Cut a sandwich into four equal pieces. Ask: “How many pieces do we have? How many pieces make the whole sandwich?”
Exercise 4C Two quarters and three quarters
Non-calculatorKey words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 2 of the 4 equal parts are shaded.2 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is two quarters.2/4
Check. Say it in words: two quarters. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 3 of the 4 equal parts are shaded.3 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is three quarters.3/4
Check. Say it in words: three quarters. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 1 of the 4 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one quarter.1/4
Check. Say it in words: one quarter. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 3 of the 4 equal parts are shaded.3 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is three quarters.3/4
Check. Say it in words: three quarters. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Look at each picture and find the one with three quarters shaded.
- Look at A. Count the equal parts and the shaded parts.A: 4 equal parts, 2 shaded
- Look at B. Count the equal parts and the shaded parts.B: 4 equal parts, 3 shaded
- Look at C. Count the equal parts and the shaded parts.C: 4 equal parts, 1 shaded
- Find the picture that matches. We want the picture with three quarters shaded.Matches: B
- Write the answer. B
Check. A and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Key words. Two quarters means 2 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 8 cm into 4 equal pieces. Every piece needs the same number.8 ÷ 4 = 2
- Find what is in one piece. Each piece has 2 cm.2 in one piece
- Take 2 pieces. two quarters means 2 of the 4 equal pieces.2 × 2 = 4
- Write the answer. 4
Check. Put the pieces back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. Three quarters means 3 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 12 cm into 4 equal pieces. Every piece needs the same number.12 ÷ 4 = 3
- Find what is in one piece. Each piece has 3 cm.3 in one piece
- Take 3 pieces. three quarters means 3 of the 4 equal pieces.3 × 3 = 9
- Write the answer. 9
Check. Put the pieces back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Method. Count the slices. Find the slice that is left.
- Count the equal slices. The toast is cut into 4 equal slices.4 slices
- Find the slices eaten. Mo eats 3 slices, so 1 slice is left.4 − 3 = 1
- Write the fraction. One slice of four equal slices is one quarter.1/4
Check. Three slices eaten and one left: 3 + 1 = 4. ✓
Watch out. The shaded slice is the one left, so it is one quarter.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 2 of the 4 equal parts are shaded.2 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is two quarters.2/4
Check. Say it in words: two quarters. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Method. Compare the two bars. Count the shaded parts in each.
- Count bar A. Two of the four equal parts are shaded.2/4
- Count bar B. Three of the four equal parts are shaded.3/4
- Compare. Three shaded parts is more than two shaded parts.3 > 2
- Write the answer. 3/4
Check. Three quarters has one more quarter than two quarters. ✓
Watch out. Count the shaded parts, not the bars.
Method. Compare the number of shaded parts.
- Count the shaded parts in 2/4. Two of the four parts are shaded.2 shaded
- Count the shaded parts in 3/4. Three of the four parts are shaded.3 shaded
- Compare. Two and three are different numbers.2 ≠ 3
- Decide. No. 3/4 has more shaded parts than 2/4.
Check. Three shaded parts is more than two shaded parts. ✓
Watch out. Shaded parts that are not the same number are not the same amount.
Fractions of a set and a quantity
We can find a fraction of a group too. Share the group into equal groups. Then count the groups we need.
Here are 9 balls on 3 plates. Each plate has 3 balls. So one third of 9 is 3.
The same idea works for lengths and amounts too.
Key ideas
- Share the group into equal plates first.
- Count how many are on one plate.
- Three quarters means three of four equal plates.
- Check: the plates put together make the whole.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal plates, then take the ones you need.
- Share the 9 balls into 3 equal plates. Every plate needs the same number.9 ÷ 3 = 3
- Find what is in one plate. Each plate has 3 balls.3 in one plate
- Take one plate. One plate is one third of the whole.3
Check. Put the plates back together: 3 + 3 + 3 = 9. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. Three quarters means 3 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 12 sweets into 4 equal plates. Every plate needs the same number.12 ÷ 4 = 3
- Find what is in one plate. Each plate has 3 sweets.3 in one plate
- Take 3 plates. three quarters means 3 of the 4 equal plates.3 × 3 = 9
- Write the answer. 9
Check. Put the plates back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 20 stars into 4 equal plates. Every plate needs the same number.20 ÷ 4 = 5
- Find what is in one plate. Each plate has 5 stars.5 in one plate
- Take one plate. One plate is one quarter of the whole.5
Check. Put the plates back together: 5 + 5 + 5 + 5 = 20. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Watch out
Watch out: 3/4 of 12 means three of the four equal plates.
Count the three plates, not the one left over.
Exam tip
Grown-up tip. Use four cups and some buttons. Share them out one at a time. Ask: “How many are in one cup?”
Exercise 4D Fractions of a set and a quantity
Non-calculatorKey words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal plates, then take the ones you need.
- Share the 6 apples into 3 equal plates. Every plate needs the same number.6 ÷ 3 = 2
- Find what is in one plate. Each plate has 2 apples.2 in one plate
- Take one plate. One plate is one third of the whole.2
Check. Put the plates back together: 2 + 2 + 2 = 6. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 8 cubes into 4 equal plates. Every plate needs the same number.8 ÷ 4 = 2
- Find what is in one plate. Each plate has 2 cubes.2 in one plate
- Take one plate. One plate is one quarter of the whole.2
Check. Put the plates back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. Two quarters means 2 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 8 sweets into 4 equal plates. Every plate needs the same number.8 ÷ 4 = 2
- Find what is in one plate. Each plate has 2 sweets.2 in one plate
- Take 2 plates. two quarters means 2 of the 4 equal plates.2 × 2 = 4
- Write the answer. 4
Check. Put the plates back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. Three quarters means 3 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 12 cakes into 4 equal plates. Every plate needs the same number.12 ÷ 4 = 3
- Find what is in one plate. Each plate has 3 cakes.3 in one plate
- Take 3 plates. three quarters means 3 of the 4 equal plates.3 × 3 = 9
- Write the answer. 9
Check. Put the plates back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal plates, then take the ones you need.
- Share the 15 pens into 3 equal plates. Every plate needs the same number.15 ÷ 3 = 5
- Find what is in one plate. Each plate has 5 pens.5 in one plate
- Take one plate. One plate is one third of the whole.5
Check. Put the plates back together: 5 + 5 + 5 = 15. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 20 grapes into 4 equal plates. Every plate needs the same number.20 ÷ 4 = 5
- Find what is in one plate. Each plate has 5 grapes.5 in one plate
- Take one plate. One plate is one quarter of the whole.5
Check. Put the plates back together: 5 + 5 + 5 + 5 = 20. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. Three quarters means 3 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 16 counters into 4 equal plates. Every plate needs the same number.16 ÷ 4 = 4
- Find what is in one plate. Each plate has 4 counters.4 in one plate
- Take 3 plates. three quarters means 3 of the 4 equal plates.4 × 3 = 12
- Write the answer. 12
Check. Put the plates back together: 4 + 4 + 4 + 4 = 16. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 16 stars into 4 equal plates. Every plate needs the same number.16 ÷ 4 = 4
- Find what is in one plate. Each plate has 4 stars.4 in one plate
- Take one plate. One plate is one quarter of the whole.4
Check. Put the plates back together: 4 + 4 + 4 + 4 = 16. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. Three quarters means 3 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 16 stars into 4 equal plates. Every plate needs the same number.16 ÷ 4 = 4
- Find what is in one plate. Each plate has 4 stars.4 in one plate
- Take 3 plates. three quarters means 3 of the 4 equal plates.4 × 3 = 12
- Write the answer. 12
Check. Put the plates back together: 4 + 4 + 4 + 4 = 16. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 12 marbles into 4 equal plates. Every plate needs the same number.12 ÷ 4 = 3
- Find what is in one plate. Each plate has 3 marbles.3 in one plate
- Take one plate. One plate is one quarter of the whole.3
Check. Put the plates back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Method. Share the stickers into 4 equal plates. Give away the plate that is left.
- Share the stickers. Share 12 into 4 equal plates.12 ÷ 4 = 3
- Find the amount kept. Mo keeps 3 plates, which is 3 + 3 + 3 = 9 stickers.9 kept
- Find the amount given away. The plate that is left is 1/4 of the stickers.12 − 9 = 3
- Write the answer. 3
Check. 9 kept and 3 given away make 12: 9 + 3 = 12. ✓
Watch out. The part given away is the one plate that is left.
Method. Share 12 into 4 equal plates, not 3.
- Share into 4 plates. Four plates need the number to divide by 4.12 ÷ 4 = 3
- Check one plate. Each plate has 3, not 4.3 on one plate
- Decide. Ella divided by the wrong number.No. 1/4 of 12 is 3.
Check. Four plates of 3 make 12: 3 + 3 + 3 + 3 = 12. ✓
Watch out. The bottom number tells you how many equal groups to make.
Method. Find 1/3 of 12 and 1/4 of 12. Then compare them.
- Find 1/3 of 12. Share 12 into 3 equal plates. Each plate has 4.12 ÷ 3 = 4
- Find 1/4 of 12. Share 12 into 4 equal plates. Each plate has 3.12 ÷ 4 = 3
- Compare. The bigger share is 4, and 4 is more than 3.4 > 3
- Write the answer. 1/3
Check. Three plates of 4 make 12, and four plates of 3 make 12. ✓
Watch out. More equal plates means each plate is smaller.
Writing simple fractions of a number
We can write a fraction of a number with the word of. 1/2 of 6 means one half of 6.
Share 6 into 2 equal groups. Each group has 3. So 1/2 of 6 = 3.
We can write 1/4 of 12 in the same way: 1/4 of 12 = 3.
Key ideas
- The bottom number says how many equal groups to make.
- The top number says how many groups to take.
- The word of means: share the number first.
- Write the sentence in the same order: 1/2 of 6 = 3.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/2 means one half.1/2 of 6
- Share the number into equal groups. Share 6 into 2 equal groups. Each group has 3.6 ÷ 2 = 3
- Take the groups we need. We need 1 of the 2 groups.3
- Write the sentence. 1/2 of 6 = 3
Check. Share 6 into 2 equal groups, then add 1 of them: 3. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/4 means one quarter.1/4 of 12
- Share the number into equal groups. Share 12 into 4 equal groups. Each group has 3.12 ÷ 4 = 3
- Take the groups we need. We need 1 of the 4 groups.3
- Write the sentence. 1/4 of 12 = 3
Check. Share 12 into 4 equal groups, then add 1 of them: 3. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 3/4 means three quarters.3/4 of 8
- Share the number into equal groups. Share 8 into 4 equal groups. Each group has 2.8 ÷ 4 = 2
- Take the groups we need. We need 3 of the 4 groups.2 × 3 = 6
- Write the sentence. 3/4 of 8 = 6
Check. Share 8 into 4 equal groups, then add 3 of them: 6. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Watch out
Watch out: 1/2 of 6 is 3, not 2.
Share 6 into 2 equal groups, then count one group.
Exam tip
Grown-up tip. Put 6 buttons on the table. Ask: “Can we share them into 2 equal piles?” Then ask: “How many are in one pile?”
Exercise 4E Writing simple fractions of a number
Non-calculatorKey words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/2 means one half.1/2 of 6
- Share the number into equal groups. Share 6 into 2 equal groups. Each group has 3.6 ÷ 2 = 3
- Take the groups we need. We need 1 of the 2 groups.3
- Write the sentence. 1/2 of 6 = 3
Check. Share 6 into 2 equal groups, then add 1 of them: 3. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/2 means one half.1/2 of 8
- Share the number into equal groups. Share 8 into 2 equal groups. Each group has 4.8 ÷ 2 = 4
- Take the groups we need. We need 1 of the 2 groups.4
- Write the sentence. 1/2 of 8 = 4
Check. Share 8 into 2 equal groups, then add 1 of them: 4. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/4 means one quarter.1/4 of 8
- Share the number into equal groups. Share 8 into 4 equal groups. Each group has 2.8 ÷ 4 = 2
- Take the groups we need. We need 1 of the 4 groups.2
- Write the sentence. 1/4 of 8 = 2
Check. Share 8 into 4 equal groups, then add 1 of them: 2. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/3 means one third.1/3 of 9
- Share the number into equal groups. Share 9 into 3 equal groups. Each group has 3.9 ÷ 3 = 3
- Take the groups we need. We need 1 of the 3 groups.3
- Write the sentence. 1/3 of 9 = 3
Check. Share 9 into 3 equal groups, then add 1 of them: 3. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/4 means one quarter.1/4 of 12
- Share the number into equal groups. Share 12 into 4 equal groups. Each group has 3.12 ÷ 4 = 3
- Take the groups we need. We need 1 of the 4 groups.3
- Write the sentence. 1/4 of 12 = 3
Check. Share 12 into 4 equal groups, then add 1 of them: 3. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 3/4 means three quarters.3/4 of 12
- Share the number into equal groups. Share 12 into 4 equal groups. Each group has 3.12 ÷ 4 = 3
- Take the groups we need. We need 3 of the 4 groups.3 × 3 = 9
- Write the sentence. 3/4 of 12 = 9
Check. Share 12 into 4 equal groups, then add 3 of them: 9. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 2/4 means two quarters.2/4 of 8
- Share the number into equal groups. Share 8 into 4 equal groups. Each group has 2.8 ÷ 4 = 2
- Take the groups we need. We need 2 of the 4 groups.2 × 2 = 4
- Write the sentence. 2/4 of 8 = 4
Check. Share 8 into 4 equal groups, then add 2 of them: 4. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/2 means one half.1/2 of 4
- Share the number into equal groups. Share 4 into 2 equal groups. Each group has 2.4 ÷ 2 = 2
- Take the groups we need. We need 1 of the 2 groups.2
- Write the sentence. 1/2 of 4 = 2
Check. Share 4 into 2 equal groups, then add 1 of them: 2. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/4 means one quarter.1/4 of 16
- Share the number into equal groups. Share 16 into 4 equal groups. Each group has 4.16 ÷ 4 = 4
- Take the groups we need. We need 1 of the 4 groups.4
- Write the sentence. 1/4 of 16 = 4
Check. Share 16 into 4 equal groups, then add 1 of them: 4. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 8 buns into 4 equal plates. Every plate needs the same number.8 ÷ 4 = 2
- Find what is in one plate. Each plate has 2 buns.2 in one plate
- Take one plate. One plate is one quarter of the whole.2
Check. Put the plates back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal plates, then take the ones you need.
- Share the 12 pencils into 3 equal plates. Every plate needs the same number.12 ÷ 3 = 4
- Find what is in one plate. Each plate has 4 pencils.4 in one plate
- Take one plate. One plate is one third of the whole.4
Check. Put the plates back together: 4 + 4 + 4 = 12. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Method. Share 10 into 2 equal groups. Check one group.
- Share the 10 apples. Share 10 into 2 equal groups.10 ÷ 2 = 5
- Check one group. Each group has 5, not 4.5 in one group
- Decide. Tom did not share the number correctly.No. 1/2 of 10 is 5.
Check. Two groups of 5 make 10: 5 + 5 = 10. ✓
Watch out. Count the things in one group, not the number of groups.
Method. One third is one of three equal plates. Find all three plates.
- Look at one third. One third is one plate, and it has 4 stars.4 stars
- Find all three thirds. The whole has three plates of 4.4 + 4 + 4 = 12
- Write the missing number. 1/3 of 12 is 4, so the whole is 12.12
Check. Check: 1/3 of 12 = 4, because 12 ÷ 3 = 4. ✓
Watch out. The whole is three times the one-third plate.
Two quarters are the same as one half
Look at the two shapes. Both have the same amount shaded.
Two quarters are the same as one half. So 2/4 and 1/2 are equal.
Two out of four equal parts is half of the shape.
Key ideas
- Two halves make one whole.
- Four quarters make one whole.
- Two quarters are the same as one half: 2/4 = 1/2.
- More parts does not always mean a bigger amount.
Method. Compare the amounts. If the shaded amounts are the same, the fractions are equal.
- Look at 2/4. 2 of the 4 equal parts is two quarters.2/4
- Look at 1/2. 1 of the 2 equal parts is one half.1/2
- Compare the amounts. The same amount shaded means the fractions are equal.2/4 = 1/2
- Decide. Yes. 2/4 is the same as 1/2.
Check. Make both amounts with equal parts and compare them side by side. ✓
Watch out. More parts does not always mean a bigger amount. Compare the shaded amounts.
Method. Work out both shaded parts. If they are the same length, the fractions are equal.
- Work out 1/2 of 8. Share 8 cm into 2 equal pieces.8 ÷ 2 = 4 cm
- Work out 2/4 of 8. Share 8 cm into 4 equal pieces, then take 2 of them.2 × 2 = 4 cm
- Compare. Both shaded parts are the same length.4 cm = 4 cm
- Write the answer. So 2/4 is the same as 1/2.4
Check. Two pieces of 4 cm make 8 cm, and so do two pieces of 4 cm. ✓
Watch out. Look at the length of the shaded part, not the number of pieces.
Method. Count the equal parts. Two of the four equal parts make half the pizza.
- Count the equal parts. The pizza has 4 equal parts.4 equal parts
- Count the shaded parts. Two of the four parts are shaded.2 shaded
- Write the fraction. Two quarters are the same as one half.1/2
Check. Two halves make one whole pizza, and two quarters make one half. ✓
Watch out. Two out of four equal parts is half.
Watch out
Watch out: 4 is more than 2, but 2/4 is the same as 1/2.
Exam tip
Grown-up tip. Fold a strip of paper in half, then in half again. Shade two quarters. Ask: “Is it the same as one half?”
Exercise 4F Two quarters are the same as one half
Non-calculatorMethod. Compare the amounts. If the shaded amounts are the same, the fractions are equal.
- Look at 1/2. 1 of the 2 equal parts is one half.1/2
- Look at 2/4. 2 of the 4 equal parts is two quarters.2/4
- Compare the amounts. The same amount shaded means the fractions are equal.1/2 = 2/4
- Decide. Yes. 1/2 is the same as 2/4.
Check. Make both amounts with equal parts and compare them side by side. ✓
Watch out. More parts does not always mean a bigger amount. Compare the shaded amounts.
Method. Two quarters make one half, so the two shaded amounts match.
- Look at the shading. Two of the four equal parts are shaded.2/4 shaded
- Find the matching half. Two quarters are the same as one half.2/4 = 1/2
- Write the answer. 1/2
Check. Two quarters and one half fill the same space. ✓
Watch out. Look for the fraction that is the same amount.
Method. Compare the amounts. If the shaded amounts are the same, the fractions are equal.
- Look at 3/4. 3 of the 4 equal parts is three quarters.3/4
- Look at 1/2. 1 of the 2 equal parts is one half.1/2
- Compare the amounts. The same amount shaded means the fractions are equal.3/4 ≠ 1/2
- Decide. No. 3/4 is not the same as 1/2.
Check. Make both amounts with equal parts and compare them side by side. ✓
Watch out. More parts does not always mean a bigger amount. Compare the shaded amounts.
Method. Count the quarters that make one half.
- Count the quarters. One half needs 2 quarters.2 quarters
- Put two quarters together. Two quarters fill half of the bar.1/4 + 1/4 = 2/4
- Write the answer. 1/2
Check. 2/4 and 1/2 are the same amount. ✓
Watch out. Two quarters make one half.
Key words. Two quarters means 2 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 12 sweets into 4 equal plates. Every plate needs the same number.12 ÷ 4 = 3
- Find what is in one plate. Each plate has 3 sweets.3 in one plate
- Take 2 plates. two quarters means 2 of the 4 equal plates.3 × 2 = 6
- Write the answer. 6
Check. Put the plates back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. One half means 1 of the 2 equal parts.
Method. Share into 2 equal plates, then take the ones you need.
- Share the 12 sweets into 2 equal plates. Every plate needs the same number.12 ÷ 2 = 6
- Find what is in one plate. Each plate has 6 sweets.6 in one plate
- Take one plate. One plate is one half of the whole.6
Check. Put the plates back together: 6 + 6 = 12. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Method. Work out both amounts. Compare them.
- Work out 2/4 of 12. Share 12 into 4 equal plates. Take 2 plates: 3 + 3 = 6.2/4 of 12 = 6
- Work out 1/2 of 12. Share 12 into 2 equal plates. Each plate has 6.1/2 of 12 = 6
- Compare. Both amounts are 6.6 = 6
- Decide. No. 2/4 of 12 and 1/2 of 12 are both 6.
Check. Two groups of 6 make 12, and so do four groups of 3. ✓
Watch out. Equal amounts can be found in different ways.
Key words. One half means 1 of the 2 equal parts.
Method. Share into 2 equal pieces, then take the ones you need.
- Share the 10 cm into 2 equal pieces. Every piece needs the same number.10 ÷ 2 = 5
- Find what is in one piece. Each piece has 5 cm.5 in one piece
- Take one piece. One piece is one half of the whole.5
Check. Put the pieces back together: 5 + 5 = 10. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Method. Look at each picture and find the one with two quarters shaded.
- Look at A. Count the equal parts and the shaded parts.A: 4 equal parts, 2 shaded
- Look at B. Count the equal parts and the shaded parts.B: 4 equal parts, 1 shaded
- Look at C. Count the equal parts and the shaded parts.C: 4 equal parts, 3 shaded
- Find the picture that matches. We want the picture with two quarters shaded.Matches: A
- Write the answer. A
Check. B and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. Compare the amounts. If the shaded amounts are the same, the fractions are equal.
- Look at 2/4. 2 of the 4 equal parts is two quarters.2/4
- Look at 1/2. 1 of the 2 equal parts is one half.1/2
- Compare the amounts. The same amount shaded means the fractions are equal.2/4 = 1/2
- Decide. Yes. 2/4 is the same as 1/2.
Check. Make both amounts with equal parts and compare them side by side. ✓
Watch out. More parts does not always mean a bigger amount. Compare the shaded amounts.
Method. Compare the shaded amounts, not the bottom numbers.
- Look at 1/2. One half is one of two equal parts.1 of 2 parts
- Look at 2/4. Two quarters fill the same amount as one half.2 of 4 parts
- Compare. The two shaded amounts are the same.2/4 = 1/2
- Decide. No. 2/4 and 1/2 are the same amount.
Check. Two quarters make one half, so they are equal. ✓
Watch out. A bigger bottom number does not mean a bigger amount.
Method. Compare the shaded parts.
- Look at Ruby. Ruby eats one half of the pizza.1/2
- Look at Sam. Sam eats two quarters of the pizza.2/4
- Compare. Two quarters make one half.2/4 = 1/2
- Decide. Same. One half and two quarters are equal.
Check. Two quarters are the same amount as one half. ✓
Watch out. Compare the shaded amounts, not the number of parts.
Chapter summary
| Skill | Method |
|---|---|
| Fraction | The bottom number is how many equal parts. The top number is how many parts are shaded. |
| Thirds and quarters | One third is one of three equal parts (1/3). One quarter is one of four equal parts (1/4). |
| Two and three quarters | Two quarters is 2/4. Three quarters is 3/4. |
| Fraction of a group | Share the group into equal groups. Then take the number of groups the fraction asks for. |
| Writing 1/2 of 6 | Share 6 into 2 equal groups. Each group has 3, so 1/2 of 6 = 3. |
| Equal fractions | Two quarters make one half. So 2/4 and 1/2 are the same amount. |
Can you…?
- I can say what the top and bottom numbers of a fraction mean
- I can name one third and one quarter of a shape
- I can name two quarters and three quarters of a shape
- I can find one third, one quarter and three quarters of a length
- I can find a fraction of a group by sharing it into equal groups
- I can write a fraction of a number, such as 1/2 of 6 = 3
- I know that 2/4 and 1/2 are the same amount
Key terms
- fraction
- a part of a whole, written with a top number and a bottom number
- equal parts
- parts that are the same size
- third
- one of three equal parts; written 1/3
- quarter
- one of four equal parts; written 1/4
- half
- one of two equal parts; written 1/2
- top number
- the number of parts we have, or the number that are shaded
- bottom number
- the number of equal parts in the whole
- of
- a word that tells us which amount to share, as in 1/2 of 6
- equivalent
- the same amount, written in a different way, such as 2/4 and 1/2
Exercise 4Z Check-up
Non-calculatorKey words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 3 of the 4 equal parts are shaded.3 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is three quarters.3/4
Check. Say it in words: three quarters. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 3.3 equal parts
- Count the shaded parts. 1 of the 3 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one third.1/3
Check. Say it in words: one third. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 12 cm into 4 equal pieces. Every piece needs the same number.12 ÷ 4 = 3
- Find what is in one piece. Each piece has 3 cm.3 in one piece
- Take one piece. One piece is one quarter of the whole.3
Check. Put the pieces back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal plates, then take the ones you need.
- Share the 9 balls into 3 equal plates. Every plate needs the same number.9 ÷ 3 = 3
- Find what is in one plate. Each plate has 3 balls.3 in one plate
- Take one plate. One plate is one third of the whole.3
Check. Put the plates back together: 3 + 3 + 3 = 9. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. Two quarters means 2 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 8 sweets into 4 equal plates. Every plate needs the same number.8 ÷ 4 = 2
- Find what is in one plate. Each plate has 2 sweets.2 in one plate
- Take 2 plates. two quarters means 2 of the 4 equal plates.2 × 2 = 4
- Write the answer. 4
Check. Put the plates back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/2 means one half.1/2 of 6
- Share the number into equal groups. Share 6 into 2 equal groups. Each group has 3.6 ÷ 2 = 3
- Take the groups we need. We need 1 of the 2 groups.3
- Write the sentence. 1/2 of 6 = 3
Check. Share 6 into 2 equal groups, then add 1 of them: 3. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Method. Compare the amounts. If the shaded amounts are the same, the fractions are equal.
- Look at 2/4. 2 of the 4 equal parts is two quarters.2/4
- Look at 1/2. 1 of the 2 equal parts is one half.1/2
- Compare the amounts. The same amount shaded means the fractions are equal.2/4 = 1/2
- Decide. Yes. 2/4 is the same as 1/2.
Check. Make both amounts with equal parts and compare them side by side. ✓
Watch out. More parts does not always mean a bigger amount. Compare the shaded amounts.
Method. Look at each picture and find the one with one quarter shaded.
- Look at A. Count the equal parts and the shaded parts.A: 4 equal parts, 2 shaded
- Look at B. Count the equal parts and the shaded parts.B: 4 equal parts, 1 shaded
- Look at C. Count the equal parts and the shaded parts.C: 3 equal parts, 1 shaded
- Find the picture that matches. We want the picture with one quarter shaded.Matches: B
- Write the answer. B
Check. A and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Key words. Three quarters means 3 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 20 cubes into 4 equal plates. Every plate needs the same number.20 ÷ 4 = 5
- Find what is in one plate. Each plate has 5 cubes.5 in one plate
- Take 3 plates. three quarters means 3 of the 4 equal plates.5 × 3 = 15
- Write the answer. 15
Check. Put the plates back together: 5 + 5 + 5 + 5 = 20. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Method. Share 12 into 4 equal plates. Each plate is one quarter.
- Share the 12 pears. Share 12 into 4 equal plates.12 ÷ 4 = 3
- Check one plate. Each plate has 3, not 6.3 in one plate
- Decide. Ali has shared into the wrong number of plates.No. 1/4 of 12 is 3.
Check. Four plates of 3 make 12: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Four equal plates are needed for a quarter.
Total 15 marks. Allow about 15 minutes.
Exercise 4X End-of-chapter quiz
Non-calculatorKey words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 3.3 equal parts
- Count the shaded parts. 1 of the 3 equal parts are shaded.1 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is one third.1/3
Check. Say it in words: one third. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. The bottom number is how many equal parts there are. The top number is how many parts are shaded.
Method. Count the equal parts underneath. Count the shaded parts on top.
- Count the equal parts. All the parts are the same size. There are 4.4 equal parts
- Count the shaded parts. 2 of the 4 equal parts are shaded.2 shaded
- Write the fraction. The shaded parts go on top. All the equal parts go underneath. That is two quarters.2/4
Check. Say it in words: two quarters. ✓
Watch out. The bottom number counts all the equal parts. The top number counts only the shaded parts.
Key words. One quarter means 1 of the 4 equal parts.
Method. Share into 4 equal plates, then take the ones you need.
- Share the 8 apples into 4 equal plates. Every plate needs the same number.8 ÷ 4 = 2
- Find what is in one plate. Each plate has 2 apples.2 in one plate
- Take one plate. One plate is one quarter of the whole.2
Check. Put the plates back together: 2 + 2 + 2 + 2 = 8. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. One third means 1 of the 3 equal parts.
Method. Share into 3 equal plates, then take the ones you need.
- Share the 6 cherries into 3 equal plates. Every plate needs the same number.6 ÷ 3 = 2
- Find what is in one plate. Each plate has 2 cherries.2 in one plate
- Take one plate. One plate is one third of the whole.2
Check. Put the plates back together: 2 + 2 + 2 = 6. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.
Key words. The word of tells us which amount to share.
Method. Share the number into equal groups. Then take the groups the fraction asks for.
- Read the fraction. 1/2 means one half.1/2 of 10
- Share the number into equal groups. Share 10 into 2 equal groups. Each group has 5.10 ÷ 2 = 5
- Take the groups we need. We need 1 of the 2 groups.5
- Write the sentence. 1/2 of 10 = 5
Check. Share 10 into 2 equal groups, then add 1 of them: 5. ✓
Watch out. The bottom number says how many equal groups to make. The top number says how many to take.
Key words. Three quarters means 3 of the 4 equal parts.
Method. Share into 4 equal pieces, then take the ones you need.
- Share the 12 cm into 4 equal pieces. Every piece needs the same number.12 ÷ 4 = 3
- Find what is in one piece. Each piece has 3 cm.3 in one piece
- Take 3 pieces. three quarters means 3 of the 4 equal pieces.3 × 3 = 9
- Write the answer. 9
Check. Put the pieces back together: 3 + 3 + 3 + 3 = 12. ✓
Watch out. Make every piece the same size before you count. Then count the pieces you need.
Method. Look at each picture and find the one with three quarters shaded.
- Look at A. Count the equal parts and the shaded parts.A: 4 equal parts, 3 shaded
- Look at B. Count the equal parts and the shaded parts.B: 4 equal parts, 2 shaded
- Look at C. Count the equal parts and the shaded parts.C: 3 equal parts, 1 shaded
- Find the picture that matches. We want the picture with three quarters shaded.Matches: A
- Write the answer. A
Check. B and C do not match. ✓
Watch out. Count the equal parts first, then the shaded parts.
Method. Compare the shaded amounts.
- Look at 2/4. Two of the four parts are shaded.2 shaded
- Look at 1/4. One of the four parts is shaded.1 shaded
- Compare. Two parts is more than one part.2 ≠ 1
- Decide. No. 2/4 is more than 1/4.
Check. Two quarters are more than one quarter. ✓
Watch out. The top number tells how many parts are shaded.
Method. Work out 1/4 of 12 and 1/3 of 12. Then compare them.
- Work out 1/4 of 12. Share 12 into 4 equal plates. Each plate has 3.12 ÷ 4 = 3
- Work out 1/3 of 12. Share 12 into 3 equal plates. Each plate has 4.12 ÷ 3 = 4
- Compare. Four is more than three.4 > 3
- Write the answer. Ruby. One third of 12 is more than one quarter.
Check. Mo has 3 cakes and Ruby has 4 cakes. ✓
Watch out. The smaller the number of equal parts, the bigger each part.
Key words. One half means 1 of the 2 equal parts.
Method. Share into 2 equal plates, then take the ones you need.
- Share the 14 pencils into 2 equal plates. Every plate needs the same number.14 ÷ 2 = 7
- Find what is in one plate. Each plate has 7 pencils.7 in one plate
- Take one plate. One plate is one half of the whole.7
Check. Put the plates back together: 7 + 7 = 14. ✓
Watch out. Make every plate the same size before you count. Then count the plates you need.