Find a fraction of a quantity - Non-unit fraction
Theory
To find a non-unit fraction of a quantity, divide by the denominator to find one part, then multiply by the numerator. So \(\dfrac{3}{4}\) of a quantity is (quantity \(\div 4)\times 3\).
A non-unit fraction has a numerator larger than \(1\), such as \(\dfrac{3}{4}\) or \(\dfrac{2}{3}\).
Divide the quantity by the denominator to find one equal part.
Then multiply by the numerator to count how many of those parts are wanted.
Every non-unit fraction of a quantity uses the same two steps: divide, then multiply.
| Fraction | Divide | Multiply | Result |
|---|---|---|---|
| \(\dfrac{3}{4}\) of \(20\) | \(20\div 4=5\) | \(5\times 3\) | \(15\) |
| \(\dfrac{2}{3}\) of \(18\) | \(18\div 3=6\) | \(6\times 2\) | \(12\) |
| \(\dfrac{5}{6}\) of \(18\) | \(18\div 6=3\) | \(3\times 5\) | \(15\) |
| \(\dfrac{3}{8}\) of \(40\) | \(40\div 8=5\) | \(5\times 3\) | \(15\) |
How to find a non-unit fraction of a quantity
- Divide the quantity by the denominator to find one part.
- Multiply that part by the numerator.
- Write the result with its unit if it has one.
Divide by \(4\), then multiply by \(3\).
| \(\dfrac{3}{4}\text{ of }20\) | \(=\) | \((20\div 4)\times 3=15\) |
| \(\dfrac{2}{3}\text{ of }18\) | \(=\) | \((18\div 3)\times 2=12\) |
| \(\dfrac{5}{6}\text{ of }18\) | \(=\) | \((18\div 6)\times 5=15\) |
| \(\dfrac{3}{8}\text{ of }40\) | \(=\) | \((40\div 8)\times 3=15\) |
The saving is $15.
Common pitfalls
Frequently asked questions
How do you find a non-unit fraction of a quantity?
Divide the quantity by the denominator, then multiply by the numerator. For \(\dfrac{3}{4}\) of \(20\), work out \((20\div 4)\times 3=15\).
Why divide before multiplying?
Dividing finds the size of one equal part, and multiplying counts how many of those parts the fraction asks for.
What is the difference from a unit fraction?
A unit fraction needs only the divide step. A non-unit fraction has a numerator above \(1\), so it also needs the multiply step.
Can I multiply first instead?
Yes, the answer is the same, but dividing first keeps the numbers small and easier to handle.