Multiplying and dividing fractions

I can multiply a fraction by a whole number or by a fraction, and divide a fraction by a whole number.

For grown-ups: this lesson in words

Years 5 and 6 · Maths

A pizza is cut into 4 equal slices. Here they are. Each slice is 1/4 of the pizza.
Ring 1 slice, then another, then another. That is 3 lots of 1/4: 3 of the 4 slices.
3 × 1/4 = 3/4
Picture: A set of 4 slices of pizza with 3 of them ringed. It is labelled 3/4.
A circle is cut into 4 equal parts. Each part is 1/4.
Shade 1/4, then another 1/4, then another 1/4. That is 3 lots of 1/4.
3 × 1/4 = 3/4
Multiplying a fraction by a whole number means adding it that many times: 1/4 + 1/4 + 1/4 = 3/4
Picture: A circle cut into 4 equal parts, with 3 parts shaded. It is labelled 3/4.
Now 3 × 2/5. These 2 bars are cut into fifths. 6 fifths are shaded: 2 and 2 and 2, so 3 lots of 2/5.
3 × 2/5 = 6/5
Multiply the top number only: 3 × 2 = 6. The bottom stays 5, because the parts are still fifths.
6/5 is more than 1 whole: 1 whole bar and 1 more fifth. 6/5 = 1 1/5
Picture: Two bars, each cut into 5 equal parts, with 6 parts shaded. It is labelled 6/5.
Your turn: A circle is cut into 3 equal parts, with 2 parts shaded. Each part is 1/3. What is 2 × 1/3?
Picture: A circle cut into 3 equal parts, with 2 parts shaded.
Choose one:
- 2/6
- 2/3
- 3/3
Answer
The answer: 2/3
2 × 1/3 = 2/3. On top, 2 × 1 = 2. The bottom stays 3, because the parts are still thirds.
Picture: A circle cut into 3 equal parts, with 2 parts shaded. It is labelled 2/3.

numerator:: The top number of a fraction: how many parts we have.
denominator:: The bottom number of a fraction: how many equal parts the whole is cut into.
mixed number:: A whole number and a fraction together, like 1 1/3.
simplest form:: A fraction written with the smallest numbers it can have: 2/6 in its simplest form is 1/3.

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