Fraction Word Problems

In short: In a fraction word problem, always ask "a fraction of what?": the whole amount, or what is left. Bar models help you see it, and if you know what a fraction of the total is, divide to find one part, then multiply.

Before you start

Adding, subtracting, multiplying and dividing fractions (the earlier chapters in this unit).
Finding a fraction of an amount: divide by the bottom, multiply by the top.
If $\frac{1}{4}$ of a number is 5, the number is $5 \times 4 = 20$ .

Operation words

Words	Means
sum of	add
difference between	subtract the smaller from the bigger
product of	multiply
quotient of $a$ and $b$	$a \div b$
increase by	add
decrease by	subtract
square of $\frac{1}{4}$	$\frac{1}{4} \times \frac{1}{4} = \frac{1}{16}$

"Of the whole" or "of the remainder"?

Bar models for the remainder

Jeremy's pocket money as 4 equal parts. Two parts are saved.

Working backwards

When you know the end and want the start, undo each step in reverse.

Fraction word problems

Operation words

Sum, difference
Product, quotient
Increase, decrease

Of what?

Of the whole
Of the remainder

Bar models

Split the whole
Split the leftover

Work backwards

Start from the end
Undo each step

Check

Put the answer back in

Quick summary

Learn the words: sum, difference, product, quotient, increase, decrease, square.
Always ask "a fraction of what?": the whole, or the remainder.
A fraction of the remainder is a fraction of a fraction: $\frac{1}{8}$ of $\frac{2}{3}$ is $\frac{1}{12}$ .
Bar models make these problems visual.
If a fraction of the total is known, divide to find one part, then multiply.
Check your answer by running the story forwards.

Quiz

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Try 3 questions now

What is the sum of $\frac{2}{3}$ , $\frac{3}{4}$ and $\frac{1}{12}$ ?
1. A $\frac{6}{19}$
2. B $1 \frac{1}{4}$
3. C $1 \frac{1}{2}$
4. D $\frac{17}{12}$
Show answer
C: $1 \frac{1}{2}$
In twelfths: $\frac{8}{12} + \frac{9}{12} + \frac{1}{12} = \frac{18}{12} = 1 \frac{1}{2}$ .
Increase the difference between $\frac{5}{6}$ and $\frac{2}{3}$ by $\frac{1}{6}$ .
1. A $\frac{1}{3}$
2. B $\frac{1}{6}$
3. C $\frac{2}{3}$
4. D $\frac{1}{2}$
Show answer
A: $\frac{1}{3}$
Difference: $\frac{5}{6} - \frac{4}{6} = \frac{1}{6}$ . Add $\frac{1}{6}$ : $\frac{2}{6} = \frac{1}{3}$ .
Nicole had 90 dollars. She spent $\frac{2}{5}$ of it on a dress and $\frac{1}{6}$ of it on a book. How much was left?
1. A 51 dollars
2. B 39 dollars
3. C 45 dollars
4. D 30 dollars
Show answer
B: 39 dollars
Dress 36, book 15. $90 - 51 = 39$ .

Before you start

Operation words

"Of the whole" or "of the remainder"?

Bar models for the remainder

Working backwards

Quick summary

Quiz

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Maths Preparation for Selective School Exam chapters