Multiplying Mixed Numerals
Multiplying Mixed Numerals extends fraction multiplication to numbers such as \(2\frac{1}{4} \times 3\frac{1}{2}\) in NSW Year 7 maths (NESA outcome MA4‑FRC‑C‑01). Change each mixed numeral to an improper fraction, cancel, multiply, then write the answer back as a mixed numeral.
You will estimate first by rounding to whole numbers, use an area model to see all four parts of a product, and learn why multiplying the wholes and the fractions separately gives the wrong answer. Garden bed areas, scaling up a pancake recipe and distance from speed and time are everyday uses. It is part of Year 7 Fractions.
Every question with a fully worked solution.
- Multiplying Mixed Numerals - Video - Multiplying Mixed Numbers | Step by Step Watch
Theory
To multiply mixed numerals, change each one to an improper fraction, cancel, multiply, then change the answer back to a mixed numeral. This Year 7 maths page shows each step, an area model that explains why, and how to estimate and check.
Step 1. Change each mixed numeral to an improper fraction: \(2\dfrac{3}{10} = \dfrac{2 \times 10 + 3}{10} = \dfrac{23}{10}\). A whole number goes over \(1\).
Step 2. Cancel common factors (a top with a bottom).
Step 3. Multiply the tops and multiply the bottoms.
Step 4. Change the answer back to a mixed numeral: \(23 \div 4\) is \(5\) remainder \(3\), so \(\dfrac{23}{4} = 5\dfrac{3}{4}\).
Change, cancel, multiply, change back:
How to multiply mixed numerals
- Estimate by rounding to whole numbers.
- Change each mixed numeral to an improper fraction.
- Cancel, then multiply tops and bottoms.
- Change back to a mixed numeral and compare with the estimate.
| \(1\dfrac{1}{4} \times 1\dfrac{1}{2}\) | \(=\) | \(\dfrac{5}{4} \times \dfrac{3}{2}\) |
| \(\) | \(=\) | \(\dfrac{15}{8} = 1\dfrac{7}{8}\) |
\(1\dfrac{7}{8}\)
| \(3\dfrac{2}{3} \times 1\dfrac{1}{3}\) | \(=\) | \(\dfrac{11}{3} \times \dfrac{4}{3}\) |
| \(\) | \(=\) | \(\dfrac{44}{9} = 4\dfrac{8}{9}\) |
Estimate \(4 \times 1 = 4\). The answer is \(4\dfrac{8}{9}\).
(i) \(3 \times 1\dfrac{2}{3}\)
(ii) \(\dfrac{1}{2} \times 3\dfrac{1}{3}\)
| \(\dfrac{3}{1} \times \dfrac{5}{3}\) | \(=\) | \(5\) |
| \(\dfrac{1}{2} \times \dfrac{10}{3}\) | \(=\) | \(\dfrac{5}{3} = 1\dfrac{2}{3}\) |
(i) \(5\)
(ii) \(1\dfrac{2}{3}\)
| \(\dfrac{15}{8} \times \dfrac{12}{5}\) | \(=\) | \(\dfrac{3}{2} \times \dfrac{3}{1}\) |
| \(\) | \(=\) | \(\dfrac{9}{2} = 4\dfrac{1}{2}\) |
\(15\) and \(5\) share \(5\); \(12\) and \(8\) share \(4\). The answer is \(4\dfrac{1}{2}\).
| \(\dfrac{10}{3} \times \dfrac{6}{5}\) | \(=\) | \(\dfrac{2}{1} \times \dfrac{2}{1}\) |
| \(\) | \(=\) | \(4\) |
Lily jogs \(4\) km.
| \(\dfrac{15}{4} \times \dfrac{20}{9}\) | \(=\) | \(\dfrac{5}{1} \times \dfrac{5}{3}\) |
| \(\) | \(=\) | \(\dfrac{25}{3} = 8\dfrac{1}{3}\) |
Estimate \(4 \times 2 = 8\). The answer \(8\dfrac{1}{3}\) is close.
Common pitfalls
Frequently asked questions
How do you multiply mixed numerals?
Change them to improper fractions, cancel, multiply tops and bottoms, then change back.
Can you multiply the whole numbers and fractions separately?
No. That misses parts of the product. Use improper fractions.
How do you change a mixed numeral to an improper fraction?
Whole number times denominator, plus numerator, over the denominator. \(1\dfrac{7}{8} = \dfrac{15}{8}\).
How do you estimate the answer?
Round each mixed numeral to the nearest whole number. \(3\dfrac{3}{4} \times 2\dfrac{2}{9} \approx 4 \times 2\).
Why cancel before multiplying?
It keeps the numbers small, so the answer is already in simplest form.