Fraction Word Problems

Using bar models to solve fraction word problems

10 problems covering addition, subtraction, and multiplication

Problem-Solving Strategy

READ

Identify what you know and what you need to find

DRAW

Draw a bar model to visualise the relationship

SOLVE

Write the number sentence and calculate (find a common denominator if needed)

CHECK

Verify your answer makes sense and include units

Part A: Addition & Subtraction Problems

5 problems

Example 1: Orange Syrup Drink

Easy

Problem: A jug contained $\frac{1}{8}$ litre of orange syrup. Mary mixed $\frac{9}{10}$ litre of water with the orange syrup to make a drink. What was the volume of the drink? Give your answer as a mixed number.

ShowHide solution

Step 1: Draw the Bar Model

Step 2: Solve

Find a common denominator of 8 and 10

$8 \times 5 = 40$ and $10 \times 4 = 40$ , so the common denominator is 40

Convert fractions

$\frac{1}{8} = \frac{5}{40}$ and $\frac{9}{10} = \frac{36}{40}$

Add the fractions

$\frac{5}{40} + \frac{36}{40} = \frac{41}{40}$

Convert to mixed number

$\frac{41}{40}$ litres = $1\frac{1}{40}$ litres

Answer: The volume of the drink was $1\frac{1}{40}$ litres.

Tip: Remember to express your answer as a mixed number when asked!

Example 2: Comparing Pole Lengths

Medium

Problem: Pole A is $\frac{3}{4}$ m long. It is $\frac{1}{5}$ m longer than Pole B. What is the length of Pole B?

ShowHide solution

Step 1: Draw the Bar Model

Step 2: Solve

Understand the relationship

Pole B is $\frac{1}{5}$ m shorter than Pole A, so length of Pole B = $\frac{3}{4}$ m − $\frac{1}{5}$ m

Find a common denominator of 4 and 5

$4 \times 5 = 20$ and $5 \times 4 = 20$ , so the common denominator is 20

Convert fractions

$\frac{3}{4} = \frac{15}{20}$ and $\frac{1}{5} = \frac{4}{20}$

Subtract

$\frac{15}{20} - \frac{4}{20} = \frac{11}{20}$ m

Answer: The length of Pole B is $\frac{11}{20}$ m.

Tip: Draw the bar model to see that "A is longer than B" means A = B + difference, so B = A − difference.

Example 3: Sharing Potatoes

Medium

Problem: Mrs Toh bought 1 kg of potatoes. She used $\frac{2}{5}$ kg of potatoes to cook chicken curry. She gave her neighbour $\frac{1}{10}$ kg of potatoes. What was the mass of potatoes she had left? Express your answer in its simplest form.

ShowHide solution

Step 1: Draw the Bar Model

Step 2: Solve

Find the total used and given away

Add $\frac{2}{5}$ kg and $\frac{1}{10}$ kg. The common denominator of 5 and 10 is 10.

Convert and add

$\frac{2}{5} + \frac{1}{10} = \frac{4}{10} + \frac{1}{10} = \frac{5}{10} = \frac{1}{2}$ , so $\frac{1}{2}$ kg was used or given away

Subtract from total

$1 - \frac{1}{2} = \frac{1}{2}$ kg left

Answer: She had $\frac{1}{2}$ kg of potatoes left.

Tip: You can also solve this in two steps: $1 - \frac{2}{5} = \frac{3}{5}$ , then $\frac{3}{5} - \frac{1}{10} = \frac{6}{10} - \frac{1}{10} = \frac{5}{10} = \frac{1}{2}$ .

Example 4: Three Boxes

Hard

Problem: The mass of Box X is $8\frac{1}{2}$ kg. The mass of Box X is $2\frac{2}{5}$ kg less than the mass of Box Y. The mass of Box Y is $1\frac{1}{4}$ kg more than the mass of Box Z. What is the mass of Box Z?

ShowHide solution

Step 1: Draw the Bar Model

Step 2: Solve

Find mass of Box Y

$8\frac{1}{2} + 2\frac{2}{5} = 8\frac{5}{10} + 2\frac{4}{10} = 10\frac{9}{10}$ kg

Find mass of Box Z

$10\frac{9}{10} - 1\frac{1}{4} = 10\frac{18}{20} - 1\frac{5}{20}$ (common denominator 20)

Calculate

$10\frac{18}{20} - 1\frac{5}{20} = 9\frac{13}{20}$ kg

Answer: The mass of Box Z is $9\frac{13}{20}$ kg.

Tip: Work step by step: first find Y from X, then find Z from Y.

Example 5: Flask of Water

Hard

Problem: A flask contained some water. Leila drank $1\frac{3}{8}$ litres of the water. She then poured $1\frac{3}{4}$ litres of water into the flask. There were then 4 litres of water in the flask. How much water was in the flask at first?

ShowHide solution

Step 1: Draw the Bar Model

Step 2: Solve

Work backwards from the 4 litres at the end. First take away the water that was poured in. This is the water left after drinking.

$4 - 1\frac{3}{4} = 3\frac{4}{4} - 1\frac{3}{4} = 2\frac{1}{4}$ litres

Then add back the water that Leila drank. This is the water in the flask at first.

$2\frac{1}{4} + 1\frac{3}{8} = 2\frac{2}{8} + 1\frac{3}{8} = 3\frac{5}{8}$ litres

Check by going forwards: drink, then pour in

$3\frac{5}{8} - 1\frac{3}{8} = 2\frac{2}{8} = 2\frac{1}{4}$ litres, then $2\frac{1}{4} + 1\frac{3}{4} = 3\frac{4}{4} = 4$ litres ✓

Answer: There were $3\frac{5}{8}$ litres of water in the flask at first.

Tip: In before-after problems, work backwards from the final amount: take away what was added, then add back what was taken away.

Part B: Multiplication Problems

5 problems

Example 1: Concert Attendees

Easy

Problem: There are 150 people at a concert. $\frac{2}{3}$ of them are adults and the rest are children. (a) How many adults are there? (b) How many children are there?

ShowHide solution

Step 1: Draw the Bar Model

Step 2: Solve

(a) Find number of adults

$\frac{2}{3} \times 150 = 100$ adults

(b) Find number of children

$150 - 100 = 50$ children

Answer: (a) There are 100 adults. (b) There are 50 children.

Tip: Alternative for (b): $\frac{1}{3} \times 150 = 50$ children (since $1 - \frac{2}{3} = \frac{1}{3}$ are children)

Example 2: Flour for Baking

Medium

Problem: Mrs Tan had $\frac{3}{4}$ kg of flour. She used $\frac{1}{3}$ of the flour to bake a cake. (a) How much flour did she use? (b) How much flour was left? Give your answers as fractions in the simplest form.

ShowHide solution

Step 1: Draw the Bar Model

Step 2: Solve

(a) Find flour used

$\frac{1}{3} \times \frac{3}{4} = \frac{3}{12} = \frac{1}{4}$ kg

(b) Find flour left

$\frac{3}{4} - \frac{1}{4} = \frac{2}{4} = \frac{1}{2}$ kg

Answer: (a) Mrs Tan used $\frac{1}{4}$ kg of flour. (b) $\frac{1}{2}$ kg of flour was left.

Tip: Remember: " $\frac{1}{3}$ OF $\frac{3}{4}$ " means multiply: $\frac{1}{3} \times \frac{3}{4}$

Example 3: Students with Glasses

Medium

Problem: There are 480 students in a hall. $\frac{3}{5}$ of the students are girls. $\frac{1}{4}$ of the girls wear glasses. How many girls wear glasses?

ShowHide solution

Step 1: Draw the Bar Model

Step 2: Solve

Find the number of girls first

$\frac{3}{5} \times 480 = 288$ girls

Then find the number of girls with glasses

$\frac{1}{4} \times 288 = 72$ girls

Another way: multiply the fractions first

$\frac{1}{4} \times \frac{3}{5} \times 480 = \frac{3}{20} \times 480 = 72$ girls

Answer: 72 girls wear glasses.

Tip: You can multiply the fractions first ( $\frac{1}{4} \times \frac{3}{5} = \frac{3}{20}$ ), then multiply by the total.

Example 4: Coloured Buttons

Hard

Problem: Mrs Tay had a box of red, blue, green and white buttons. $\frac{1}{4}$ of the buttons were red and $\frac{1}{3}$ of the buttons were blue. $\frac{1}{5}$ of the remaining buttons were green. The rest of the buttons were white. There were 36 more white buttons than green buttons. (a) What fraction of the buttons were green? (b) How many buttons did Mrs Tay have altogether?

ShowHide solution

Step 1: Draw the Bar Model

Step 2: Solve

Find the remaining fraction

$1 - \frac{1}{4} - \frac{1}{3} = \frac{12}{12} - \frac{3}{12} - \frac{4}{12} = \frac{5}{12}$ of the buttons

(a) Find the green fraction

$\frac{1}{5} \times \frac{5}{12} = \frac{5}{60} = \frac{1}{12}$ of the buttons

Find the white fraction

$\frac{5}{12} - \frac{1}{12} = \frac{4}{12} = \frac{1}{3}$ of the buttons

Difference (white − green)

$\frac{1}{3} - \frac{1}{12} = \frac{4}{12} - \frac{1}{12} = \frac{3}{12} = \frac{1}{4}$ of the buttons

(b) Find the total

$\frac{1}{4}$ of the buttons = 36 buttons, so total = $36 \times 4 = 144$ buttons

Answer: (a) $\frac{1}{12}$ of the buttons were green. (b) Mrs Tay had 144 buttons altogether.

Tip: Work step by step: First find remaining, then green, then white, then use the difference to find total.

Example 5: Fruits in a Crate

Hard

Problem: There were some fruits in a crate. $\frac{3}{7}$ of them were apples and $\frac{5}{8}$ of the remainder were pears. The rest of them were oranges. There were 42 more pears than oranges. How many fruits were there in the crate?

ShowHide solution

Step 1: Draw the Bar Model

Step 2: Solve

Find remainder (not apples)

$1 - \frac{3}{7} = \frac{4}{7}$ of the fruits

Find pears fraction

$\frac{5}{8} \times \frac{4}{7} = \frac{20}{56} = \frac{5}{14}$ of the fruits

Find oranges fraction

Oranges are $1 - \frac{5}{8} = \frac{3}{8}$ of the remainder, and $\frac{3}{8} \times \frac{4}{7} = \frac{12}{56} = \frac{3}{14}$ of the fruits

Find difference

$\frac{5}{14} - \frac{3}{14} = \frac{2}{14} = \frac{1}{7}$ of the fruits

Find total

$\frac{1}{7}$ of the fruits = 42 fruits, so total = $42 \times 7 = 294$ fruits

Answer: There were 294 fruits in the crate.

Tip: Always express each quantity as a fraction of the TOTAL, then use the given difference to find the actual total.

Key Takeaways

Addition & Subtraction

If A is more than B: B = A − difference
If A is less than B: B = A + difference
Always find a common denominator before adding/subtracting
For before-after: work backwards from the final amount

Multiplication

"OF" means multiply: 2/3 of 150 = 2/3 × 150
Fraction of fraction: Multiply together
Remainder = 1 − fraction taken
Express ALL parts as fractions of the SAME total

Remember: Bar models help visualise relationships. Always include units and simplify your final answer!