# Fractions of a Quantity

> Find a fraction of an amount of money, time, mass or angle, and write one amount as a fraction of another.

From Selective School Maths on WhizzNotes, free study notes for NSW students: https://whizznotes.com/selective-school-maths/fractions-of-a-quantity/. Updated 3 November 2026.
Year 11 and Year 12 boxes go deeper than the Year 10 text around them.

### Story time: Sharing the lolly jar
Coach Daniels has a jar of 36 lollies for the netball team. She says, "Three quarters of the jar is for the players, and the rest is for the umpires."

How many do the players get? First find one quarter: $36 \div 4 = 9$. Three quarters is three of those: $9 \times 3 = 27$ lollies.

**Divide by the bottom, multiply by the top.** That one rule finds a fraction of anything: money, minutes, kilograms or degrees.

**In short:** To find a fraction of an amount, divide by the bottom number, then multiply by the top number. So $\frac{3}{4}$ of 20 is $20 \div 4 \times 3 = 15$, because "of" means multiply.

## Before you start

- Simplifying fractions to lowest terms.
- Times tables and short division.
- Unit facts: 1 hour $= 60$ minutes, 1 kg $= 1000$ g, 1 L $= 1000$ mL, 1 km $= 1000$ m, 1 m $= 100$ cm, 1 year $= 52$ weeks, a full turn $= 360^\circ$, a right angle $= 90^\circ$, a fortnight $= 14$ days.

## A fraction of an amount

### Key idea: Divide by the bottom, multiply by the top
$$\frac{3}{4} \text{ of } 36 = 36 \div 4 \times 3 = 9 \times 3 = 27$$

The word **of** means multiply, so this is also $\frac{3}{4} \times 36$.

### Worked example: Whole numbers
$\frac{4}{5}$ of 45: $45 \div 5 = 9$, then $9 \times 4 = 36$.

$\frac{4}{7}$ of 56: $56 \div 7 = 8$, then $8 \times 4 = 32$.

### Worked example: Money
$\frac{1}{3}$ of 381.60 dollars: $381.60 \div 3 = 127.20$ dollars.

$\frac{7}{12}$ of 288 dollars: $288 \div 12 = 24$, then $24 \times 7 = 168$ dollars.

$\frac{3}{4}$ of 298 dollars: $298 \div 4 = 74.50$, then $74.50 \times 3 = 223.50$ dollars.

## Mixed units: convert first

Change to a smaller unit so the division comes out evenly.

### Worked example: Time
$\frac{3}{10}$ of $1\frac{1}{2}$ hours. $1\frac{1}{2}$ hours $= 90$ minutes. $90 \div 10 \times 3 = 27$ minutes.

$\frac{5}{12}$ of 2 hours 48 minutes. That is 168 minutes. $168 \div 12 = 14$, and $14 \times 5 = 70$ minutes.

### Worked example: Mass and capacity
$\frac{3}{20}$ of 1.5 kg $= \frac{3}{20}$ of 1500 g $= 75 \times 3 = 225$ g.

$\frac{3}{5}$ of 1.75 L $= \frac{3}{5}$ of 1750 mL $= 350 \times 3 = 1050$ mL $= 1.05$ L.

## One amount as a fraction of another

### Key idea: Part over whole, same units
$$\text{fraction} = \frac{\text{part}}{\text{whole}}$$

Both amounts must be in the **same unit**. Then simplify.

### Worked example: What fraction of $1\frac{1}{2}$ metres is 6 cm?
$1\frac{1}{2}$ m $= 150$ cm.

$\frac{6}{150} = \frac{1}{25}$

### Worked example: More practice
A fortnight as a fraction of 42 days: $\frac{14}{42} = \frac{1}{3}$.

$76$ cents of 4 dollars: $\frac{76}{400} = \frac{19}{100}$.

$15^\circ$ of a right angle: $\frac{15}{90} = \frac{1}{6}$.

### Watch out: Mixing units
$45$ cm of $1.5$ m is not $\frac{45}{1.5}$. Change 1.5 m to 150 cm first: $\frac{45}{150} = \frac{3}{10}$.

## Angles as a fraction of a turn

A full turn (a **revolution**) is $360^\circ$. So $270^\circ$ is $\frac{270}{360} = \frac{3}{4}$ of a turn, and $18^\circ$ is $\frac{18}{360} = \frac{1}{20}$ of a turn.

### Challenge: Selective level: tricky units
$\frac{7}{13}$ of a year in weeks: a year has 52 weeks. $52 \div 13 = 4$ and $4 \times 7 = 28$ weeks.

$240$ square metres as a fraction of 1 hectare: a hectare is $10\,000$ square metres. $\frac{240}{10\,000} = \frac{24}{1000} = \frac{3}{125}$.

$75$ mL as a fraction of 2 L: $\frac{75}{2000} = \frac{3}{80}$.

**Mind map**

```text
Fractions of a quantity
  Fraction of an amount
    Divide by the bottom
    Multiply by the top
  Convert first
    Hours to minutes
    kg to g, L to mL
  Part of a whole
    Part over whole
    Same units
    Simplify
  Angles
    Full turn 360°
    Right angle 90°
```

## Quick summary

- To find a fraction of an amount: divide by the denominator, then multiply by the numerator.
- "Of" means multiply.
- Change awkward units to smaller ones first (hours to minutes, kg to g).
- To write one amount as a fraction of another: part over whole, in the same units, then simplify.
- A full turn is $360^\circ$, so an angle as a fraction of a turn is $\frac{\text{angle}}{360}$.

## Quiz

Try these questions from the chapter quiz.

1. $\frac{3}{4}$ of 36 $=$
   - A. 9
   - B. 27
   - C. 48
   - D. 12
   - Answer: B. 27. $36 \div 4 = 9$, then $9 \times 3 = 27$.

2. $\frac{2}{9}$ of 27 $=$
   - A. 3
   - B. 6
   - C. 9
   - D. 18
   - Answer: B. 6. $27 \div 9 = 3$, then $3 \times 2 = 6$.

3. $\frac{5}{8}$ of 48 $=$
   - A. 30
   - B. 6
   - C. 40
   - D. 24
   - Answer: A. 30. $48 \div 8 = 6$, then $6 \times 5 = 30$.

The whole chapter quiz is on the page, for signed-in students: https://whizznotes.com/selective-school-maths/fractions-of-a-quantity/#quiz