Skip to main content

PSLE Mathematics · Primary 5 and 6

Fractions

Fractions run through the whole of primary Mathematics. In Primary 5 and 6 you link fractions to division, multiply and divide fractions, and solve word problems where a fraction is taken of a remainder. These skills feed straight into ratio, percentage and speed, so a firm grip on fractions makes much of the PSLE paper easier. This guide explains each operation, shows a full worked example using the unit method, and ends with three practice questions.

What the syllabus expects

  • Express the result of dividing one whole number by another as a fraction, such as 3 ÷ 4 = 3/4
  • Add and subtract fractions and mixed numbers with different denominators
  • Multiply a fraction by a whole number and by another fraction, including mixed numbers
  • Divide a proper fraction by a whole number, and a whole number or proper fraction by a proper fraction
  • Find a fraction of a quantity, and find the whole when a fraction of it is known
  • Solve multi-step word problems involving a fraction of a remainder

Fractions as division and equivalent fractions

A fraction is a division waiting to happen. 3/4 means 3 ÷ 4, so 3 ÷ 4 = 3/4 = 0.75. When the numerator is bigger than the denominator you get an improper fraction, for example 7 ÷ 3 = 7/3 = 2 1/3. Equivalent fractions name the same amount. Multiply or divide the numerator and the denominator by the same number, so 2/3 = 8/12 and 15/20 = 3/4. To add or subtract fractions with different denominators, rename them with a common denominator, usually the lowest common multiple of the denominators. For 3/4 + 1/6, the lowest common multiple of 4 and 6 is 12, so the sum is 9/12 + 2/12 = 11/12. For mixed numbers, either add the wholes and the parts separately, or change both into improper fractions first. Always give the final answer in its simplest form.

Multiplying fractions

To multiply two fractions, multiply the numerators together and the denominators together: 2/3 × 3/5 = 6/15 = 2/5. Cancelling common factors before you multiply keeps the numbers small. In 4/9 × 3/8, the 4 and the 8 share a factor of 4, and the 3 and the 9 share a factor of 3, which leaves 1/3 × 1/2 = 1/6. The word 'of' means multiply, so 2/5 of 30 = 2/5 × 30 = 12. Mixed numbers must be changed into improper fractions before multiplying: 1 1/2 × 1 1/2 = 3/2 × 3/2 = 9/4 = 2 1/4. A quick check is that multiplying by a proper fraction always gives an answer smaller than the number you started with.

Dividing fractions

Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of 3/4 is 4/3, and the reciprocal of 5 is 1/5. So 2/3 ÷ 4 = 2/3 × 1/4 = 2/12 = 1/6, and 6 ÷ 2/3 = 6 × 3/2 = 9. You can picture 6 ÷ 2/3 as asking how many two-thirds fit into 6. Each whole holds 1 1/2 of them, so 6 wholes hold 9. Dividing by a proper fraction makes the answer bigger, which is a fast way to catch a wrong answer. In word problems, division appears as sharing or as grouping. Sharing: 3/4 kg of rice shared equally among 3 bags gives 3/4 ÷ 3 = 1/4 kg in each bag. Grouping: the number of 1/8 litre cups that can be filled from 3/4 litre is 3/4 ÷ 1/8 = 3/4 × 8 = 6 cups.

Fraction of a remainder

Many PSLE questions take a fraction of the whole, then a fraction of what is left. Ask yourself 'a fraction of what?' every time. Suppose Ali spends 1/3 of his money on a book and 1/4 of the remainder on a pen. The remainder is 2/3 of his money, so the pen costs 1/4 of 2/3, which is 1/6 of his money, not 1/4 of it. A model makes this clear. Draw one bar for all his money and cut it into 3 equal units. Shade 1 unit for the book. The other 2 units must be cut into 4 equal parts, so change every unit into 4 smaller units, giving 12 small units in all. Now the book is 4 units, the pen is 2 units and 6 units are left. With equal units you can compare every part directly, and once you know the value of one unit, every other amount follows by multiplying.

Worked example

Mrs Tan had some flour. She used 2/5 of it to bake bread and 1/3 of the remainder to bake cookies. She had 840 g of flour left. How much flour did she have at first?

  1. Draw a bar for all the flour and cut it into 5 equal units, because the first fraction is in fifths.
  2. Bread uses 2/5, which is 2 units, so the remainder is 5 − 2 = 3 units.
  3. Cookies use 1/3 of the remainder, which is 1/3 × 3 units = 1 unit.
  4. Flour left = 3 − 1 = 2 units, and this is 840 g.
  5. 1 unit = 840 ÷ 2 = 420 g.
  6. Flour at first = 5 units = 5 × 420 = 2100 g.
  7. Check: bread uses 2/5 × 2100 = 840 g, leaving 1260 g. Cookies use 1/3 × 1260 = 420 g, leaving 840 g, which matches the question.

Answer: She had 2100 g (2.1 kg) of flour at first.

Common mistakes

  • Taking a fraction of the whole when the question says 'of the remainder'. In the worked example, 1/3 of all the flour would be wrong. Find the remainder first, then take the fraction of it.
  • Adding numerators and denominators, such as 1/2 + 1/3 = 2/5. Rename with a common denominator instead: 3/6 + 2/6 = 5/6.
  • Multiplying mixed numbers part by part, such as 1 1/2 × 1 1/2 = 1 1/4. Change them into improper fractions first: 3/2 × 3/2 = 9/4 = 2 1/4.
  • Flipping the wrong fraction when dividing. Only the divisor (the fraction after the ÷ sign) is replaced by its reciprocal: 3/5 ÷ 3/10 = 3/5 × 10/3 = 2.
  • Comparing fractions of different wholes as if they were the same. 1/4 of Ali's money and 1/4 of his remainder are different amounts, so convert both into units of the same bar before comparing.
  • Leaving an answer as 12/16 or 9/4 when the question asks for the simplest form or a mixed number. Simplify to 3/4 or write 2 1/4.

Exam tips

  • In every multi-step fraction problem, write 'of what?' next to each fraction and label the remainder on your model before you take the next fraction.
  • Choose the number of units so that every fraction gives a whole number of units, for example 12 units when you need thirds and then quarters of the remainder.
  • Check reasonableness: dividing by a proper fraction should give a bigger answer, and multiplying by one should give a smaller answer.

Practice questions

1. Easy: Find the value of 3/4 ÷ 6, giving your answer in its simplest form.

Show answer

1/8. Working: 3/4 ÷ 6 = 3/4 × 1/6 = 3/24 = 1/8.

2. Medium: A ribbon 4 1/2 m long is cut into pieces, each 3/8 m long. How many pieces are there?

Show answer

12 pieces. Working: 4 1/2 ÷ 3/8 = 9/2 × 8/3 = 72/6 = 12.

3. Harder: Jun Wei had some stickers. He gave 1/4 of them to his sister and 2/3 of the remainder to his friend. He gave his friend 60 more stickers than his sister. How many stickers did he have at first?

Show answer

240 stickers. Working: let all the stickers be 4 units. Sister gets 1 unit, the remainder is 3 units, and the friend gets 2/3 × 3 = 2 units. The difference is 2 − 1 = 1 unit = 60, so 4 units = 240. Check: sister 60, remainder 180, friend 120, and 120 − 60 = 60.

Related topics

Want a tutor for PSLE Math?

Shortlist on WhatsApp within 16 hours. You choose the tutor. About Primary Math tuition

Get matched with a tutor

Or ask on WhatsApp