Primary 5 Four Operations of Fractions Study Guide
Primary 5 fractions in six short steps: mixed numbers, multiplying, then the word problems where each fraction has its own whole. Every step has a bar or a set to work with and a question to try.
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How do you calculate with mixed numbers and fractions in Primary 5?
Give the numbers parts of the same size, and know which whole each fraction is of.
A mixed number such as 1 3/4 is the same amount as 7 quarters, 7/4. Once the parts are one size, fractions can be added, subtracted and multiplied. In the word problems a fraction may be of the whole amount, of what is left, or of a different group, so your child first says which whole it belongs to.
Your child uses this all through the chapter to:
- add and subtract mixed numbers, opening a whole when the parts run short;
- multiply fractions, because "of" means multiply;
- multiply a mixed number by a whole number;
- find a fraction of a set, and then a fraction of the remainder;
- compare two amounts drawn in units of one size;
- work backwards from what is left to the amount at first.
Step 1
Adding and subtracting mixed numbers
Make the parts the same size, then open a whole if you need more. Find a number both bottom numbers go into and rewrite both fractions in those parts. When the fraction you subtract is bigger than the one you have, open one whole into the same parts. The amount does not change, only the way it is written.
A rope is 3 1/3 m long. Ali cuts off 1 1/2 m. How long is the rope that is left?
Follow the three steps
Find 2 1/2 + 1 3/4.
Step 2
Multiplying fractions
"Of" means multiply, so a fraction of a fraction is a product. Multiply the tops, and multiply the bottoms. If a top number and a bottom number share a common factor, cancel it first: the numbers stay small and the answer comes out in its simplest form. Improper fractions multiply in exactly the same way.
Pick one, then fold across
Work out 9/4 × 2/3. Give your answer as a mixed number.
Step 3
Multiplying a mixed number by a whole number
Turn the mixed number into one fraction, then multiply. For 2 1/4, the top number is 2 × 4 + 1, all over 4, which gives 9/4. Multiply the numerator by the whole number and keep the denominator. Then write the total as a mixed number and simplify its fraction.
Pick one, then cut and count
3 jugs, each holding 2 1/4 litres
A jug holds 1 2/5 litres of juice. How much juice is there in 4 of these jugs?
Step 4
Fraction of a set and fraction of the remainder
The bottom number makes the equal groups; the top number says how many to take. For a fraction of the remainder, first find what is left. That remainder is the new, smaller whole, and the next fraction makes its equal groups from it.
A tray holds 24 cupcakes. 1/3 of them are chocolate. 3/4 of the remainder are vanilla. The rest are strawberry.
Follow the four steps
A baker made 40 buns. She sold 3/8 of them in the morning and 2/5 of the remainder in the afternoon. How many buns were left?
Step 5
Fraction remainder questions with equal units
Cut the whole bar into units of one size so different parts can be compared. When the second fraction is of the remainder, carry its cuts across the whole bar. The same idea works for two groups: if 1/2 of one group is equal to 1/3 of another, that shared amount is 1 unit, so the groups are 2 units and 3 units.
A shelf has fiction, science and history books. 1/3 of them are fiction. 1/4 of the remainder are science. The rest are history. There are 30 more history books than science books. How many books are on the shelf?
Follow the four steps
Jun had some cards. He gave 1/2 of them to Ben and 1/3 of the remainder to Raj. Raj got 10 cards. How many cards did Jun have at first?
Step 6
Working backwards in fraction word problems
Undo the last thing first. Draw the bar forwards, then go backwards: put the fixed amount back before anything else. What you have then is the fraction left, so divide to find one part and multiply to get the whole.
Ravi had some marbles. He gave away 1/3 of them, then 8 more. He had 22 marbles left. How many marbles did he have at first?
Undo it one step at a time
Aisha had some money. She spent 1/4 of it, then $6 more. She had $30 left. How much money did she have at first?
Primary 5 fractions questions, worked step by stepCover the working and try each one on paper. Open the hint if you are stuck, then check one line at a time.
Find 5 1/6 − 2 3/4. Give your answer as a mixed number.
- 5 1
/6 − 2 3/4 = 5 2/12 − 2 9/12 - 2
/12 is less than 9/12, so open one whole: 5 2/12 = 4 14/12 - 4 14
/12 − 2 9/12 = 2 5/12
Find 5/6 × 9/10. Give your answer in its simplest form.
- Cancel 5 and 10 by 5: 1
/6 × 9/2 - Cancel 9 and 6 by 3: 1
/2 × 3/2 - 1
/2 × 3/2 = 3/4
A box of tiles has a mass of 3 2/5 kg. What is the total mass of 8 such boxes? Give your answer as a mixed number.
- 3 2
/5 = (3 × 5 + 2)/5 = 17/5 - 8 × 17
/5 = 136/5 - 136
/5 = 27 1/5
2/5 of Farid's stamps is equal to 1/2 of Gopal's stamps. They have 81 stamps altogether. How many stamps does Gopal have?
- 2
/5 of Farid's = 1/2 of Gopal's = 2 units - Farid = 5 units, Gopal = 4 units
- 9 units = 81, so 1 unit = 81 ÷ 9 = 9
- Gopal = 4 × 9 = 36
Mr Tan had some eggs. He used 1/3 of them, then 4 more for a cake. Next, he used 1/2 of the eggs left for breakfast. He then had 10 eggs. How many eggs did he have at first?
- 10 eggs are the other half, so before breakfast: 10 × 2 = 20
- Put the 4 back: 20 + 4 = 24
- 24 eggs are 2 of 3 parts, so 1 part = 24 ÷ 2 = 12
- At first = 3 × 12 = 36
Step 7
Check yourself
Five quick questions across the chapter. Nothing is saved, and every reply points to the page to practise next.
Work out 7 × 1 3/4.
What is 2/3 of 9/10? Give the answer in its simplest form.
There are 48 marbles in a bag. 5/8 of them are glass. How many marbles are not glass?
1/4 of the apples in a crate is equal to 1/3 of the pears. There are 63 apples and pears altogether. How many pears are there?
Lina had some stickers. She gave away 2/5 of them, then 3 more. She had 15 stickers left. How many stickers did she have at first?
How to use this guide. Steps 1 to 3 are calculation: ask your child to say what size the parts are before they tap, quarters or sixths, because every method here needs parts of one size. If adding or subtracting mixed numbers feels shaky, spend longer on Step 1 before moving on.
Steps 4 to 6 are word problems. Before each tap, ask "a fraction of what?" and let your child point to that whole on the bar. Then let them try the worked examples alone on paper and use the working only to compare, a line at a time.
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P5 Four Operations of Fractions lessons and practice
8 lesson videos and 31 questions across eight subtopics, from Basic to Challenge, each with a worked solution.
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