How many fit

Primary 6 Fractions study guide: the whole chapter, step by step

About this subtopic

In the lesson. That's what two divided by one half means.

Lesson video, with the working

Dividing by a fraction

2 min 57 s

The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.

Watch on its own page

Today's question

A jug holds 3 litres of water. It's poured out into cups, and each cup holds 1/4 litre. How many cups can we fill?

12 cups can be filled.

Ans: 12

Example 1

A different jug holds 2 litres, and this time the cups hold 1/2 litre each. How many cups can we fill?

4 cups can be filled.

Ans: 4

How to solve it

Draw the whole amount, 3 litres. Each cup is one quarter of a litre, so cut every litre into 4.
Count the cups along the bar: each litre holds 4 cups, so 3 litres hold 3 times 4, which is 12 cups.
Write the count as a division: 3 divided by one quarter.
To divide by a fraction, turn it upside down and multiply: one quarter becomes 4 over 1, so 3 times 4 is 12.
Check the answer is more than 3, not less, because lots of small cups fill a big jug.

Count how many of that fraction fit. 4 one-half-litre cups fit in 2 litres. That's what 2 divided by one half means.

Practice questions with worked solutions

Question 1 is free to try. The other 6 open in the free trial, each with its full working.

Basic

1Free 2

Intermediate

Challenge

Working

dividing by 1/2 is the same as multiplying by 2
number of bottles = 5 ÷ 1/2 = 5 × 2
5 × 2 = 10 bottles

Answer: 10 bottles

For parents

How do you solve dividing by a fraction questions in P6?

Dividing by a fraction is the second new fraction outcome in Primary 6.

What your child learns here

Dividing by a fraction is the second new fraction outcome in Primary 6. The page starts from 'how many fit?' and then introduces the reciprocal, turning the fraction upside down and multiplying, so the shortcut has a meaning.

Divide a whole number by a proper fraction without a calculator.
Divide a proper fraction by a proper fraction.
Take the reciprocal of the divisor (turn it upside down) and multiply.
Decide whether a fractional remainder counts in a word problem.

Does the answer make sense?

Before rounding down, dividing metres or litres by a fraction smaller than 1 must give your child a number bigger than the amount started with, since each piece or bottle is less than a whole one. Only whole pieces count, so a leftover bit of ribbon shorter than one piece never rounds the answer up.

How to practise these questions

Basic questions train dividing by a fraction as asking how many pieces of that size fit, counting only whole pieces. The Intermediate question cuts two separate lengths, so your child counts the whole pieces from each length before adding them. If how many fit is unclear, read the written step-by-step solution together.

Questions parents ask

What does 'reciprocal' mean? The reciprocal of a fraction is the fraction turned upside down: the reciprocal of 2 over 5 is 5 over 2. Dividing by a fraction is the same as multiplying by its reciprocal.

Is dividing by a fraction in the PSLE syllabus? Yes. 'Dividing a whole number/proper fraction by a proper fraction without calculator' is outcome 1.2 of the Primary 6 Fractions sub-strand.

Why is the answer bigger when you divide by a fraction? Because the question asks how many of the fraction fit. Pieces smaller than one whole fit more times than there are wholes, so 4 ÷ one half is 8.