Multiplying fractions using number lines – a math worksheet for practice.

Let's solve each of the multiplication problems using the number line method. The goal is to draw hops on the number line and find the product of each whole number and fraction.

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1) $ 6 \times \frac{1}{11} $

- We are multiplying 6 by $ \frac{1}{11} $.
- This means we make 6 hops of size $ \frac{1}{11} $ on the number line.
- Each hop goes from one tick mark to the next (since the number line is marked in elevenths).
- Starting at 0:
- 1st hop: $ \frac{1}{11} $
- 2nd hop: $ \frac{2}{11} $
- ...
- 6th hop: $ \frac{6}{11} $

✔ Answer: $ \frac{6}{11} $

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2) $ 8 \times \frac{2}{5} $

- We're making 8 hops, each of size $ \frac{2}{5} $.
- But the number line shows fifths, so we can count in increments of $ \frac{2}{5} $.
- Start at 0:
- 1st hop: $ \frac{2}{5} $
- 2nd hop: $ \frac{4}{5} $
- 3rd hop: $ \frac{6}{5} = 1\frac{1}{5} $
- 4th hop: $ \frac{8}{5} = 1\frac{3}{5} $
- 5th hop: $ \frac{10}{5} = 2 $
- 6th hop: $ \frac{12}{5} = 2\frac{2}{5} $
- 7th hop: $ \frac{14}{5} = 2\frac{4}{5} $
- 8th hop: $ \frac{16}{5} = 3\frac{1}{5} $

✔ Answer: $ \frac{16}{5} $ or $ 3\frac{1}{5} $

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3) $ 3 \times \frac{5}{6} $

- Make 3 hops of $ \frac{5}{6} $ each.
- Number line is marked in sixths.
- Start at 0:
- 1st hop: $ \frac{5}{6} $
- 2nd hop: $ \frac{10}{6} = 1\frac{4}{6} = 1\frac{2}{3} $
- 3rd hop: $ \frac{15}{6} = 2\frac{3}{6} = 2\frac{1}{2} $

✔ Answer: $ \frac{15}{6} $ or $ 2\frac{1}{2} $

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4) $ 9 \times \frac{1}{14} $

- Make 9 hops of $ \frac{1}{14} $.
- Number line shows fourteenths.
- After 9 hops: $ \frac{9}{14} $

✔ Answer: $ \frac{9}{14} $

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5) $ 2 \times \frac{8}{7} $

- Make 2 hops of $ \frac{8}{7} $.
- $ \frac{8}{7} = 1\frac{1}{7} $
- Start at 0:
- 1st hop: $ \frac{8}{7} $
- 2nd hop: $ \frac{16}{7} = 2\frac{2}{7} $

✔ Answer: $ \frac{16}{7} $ or $ 2\frac{2}{7} $

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✔ Final Answers:

1) $ \frac{6}{11} $
2) $ \frac{16}{5} $ or $ 3\frac{1}{5} $
3) $ \frac{15}{6} $ or $ 2\frac{1}{2} $
4) $ \frac{9}{14} $
5) $ \frac{16}{7} $ or $ 2\frac{2}{7} $

> Note: You can draw the hops on the number lines as follows:
> - For each problem, start at 0 and make jumps equal to the fraction, repeating the number of times indicated by the whole number.
> - The final landing point is the answer.

Let me know if you'd like a visual guide for drawing the hops!