Fractional distances on a number line worksheet - Free Printable

Let's solve each problem step by step using the number lines provided.

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Left Number Line:

- Points:
- $ M = 2 $
- $ J = 18 $

So, the distance from $ M $ to $ J $ is:
$$
J - M = 18 - 2 = 16
$$

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#### Problem 1:
Find the coordinate of point B that is $ \frac{1}{4} $ of the distance from M to J.

We calculate:
$$
\text{Distance} = \frac{1}{4} \times 16 = 4
$$
Now add this to $ M $:
$$
B = M + 4 = 2 + 4 = 6
$$
✔ Answer: $ B = 6 $

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#### Problem 2:
Find the coordinate of point C that is $ \frac{7}{8} $ of the distance from M to J.

$$
\frac{7}{8} \times 16 = 14
$$
Add to $ M $:
$$
C = 2 + 14 = 16
$$
✔ Answer: $ C = 16 $

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#### Problem 3:
Find the coordinate of point D that is $ \frac{7}{16} $ of the distance from M to J.

$$
\frac{7}{16} \times 16 = 7
$$
Add to $ M $:
$$
D = 2 + 7 = 9
$$
✔ Answer: $ D = 9 $

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Right Number Line:

Points given:
- $ A = -7 $
- $ B = -5 $
- $ C = -4 $
- $ D = 0 $
- $ E = 2 $
- $ F = 5 $

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#### Problem 4:
Find the coordinate of point G that is $ \frac{2}{3} $ of the distance from B to D.

First, find distance from $ B $ to $ D $:
$$
D - B = 0 - (-5) = 5
$$
Now:
$$
\frac{2}{3} \times 5 = \frac{10}{3} \approx 3.333
$$
Add to $ B $:
$$
G = B + \frac{10}{3} = -5 + \frac{10}{3} = \frac{-15 + 10}{3} = \frac{-5}{3} \approx -1.666...
$$
But we need to express it as a coordinate on the number line.

Wait — let’s double-check: Is this a fraction or decimal?

We can leave it as a fraction:
$$
G = -\frac{5}{3}
$$
But let's verify:

From $ B = -5 $ to $ D = 0 $, total distance = 5 units.

$ \frac{2}{3} $ of that is $ \frac{10}{3} \approx 3.333 $ units from $ B $ toward $ D $.

So:
$$
G = -5 + \frac{10}{3} = \frac{-15 + 10}{3} = \frac{-5}{3} = -1\frac{2}{3}
$$

✔ Answer: $ G = -\frac{5}{3} $ or $ -1\frac{2}{3} $

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#### Problem 5:
Find the coordinate of point H that is $ \frac{1}{5} $ of the distance from C to F.

$ C = -4 $, $ F = 5 $

Distance:
$$
F - C = 5 - (-4) = 9
$$
$ \frac{1}{5} $ of that:
$$
\frac{1}{5} \times 9 = \frac{9}{5} = 1.8
$$
Add to $ C $:
$$
H = -4 + 1.8 = -2.2
$$
Or as a fraction:
$$
-4 + \frac{9}{5} = \frac{-20 + 9}{5} = \frac{-11}{5} = -2.2
$$

✔ Answer: $ H = -\frac{11}{5} $ or $ -2.2 $

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#### Problem 6:
Find the coordinate of point J that is $ \frac{1}{6} $ of the distance from A to E.

$ A = -7 $, $ E = 2 $

Distance:
$$
E - A = 2 - (-7) = 9
$$
$ \frac{1}{6} $ of that:
$$
\frac{1}{6} \times 9 = 1.5
$$
Add to $ A $:
$$
J = -7 + 1.5 = -5.5
$$
Or as a fraction:
$$
-7 + \frac{3}{2} = \frac{-14 + 3}{2} = \frac{-11}{2} = -5.5
$$

✔ Answer: $ J = -\frac{11}{2} $ or $ -5.5 $

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✔ Final Answers:

1. $ B = 6 $
2. $ C = 16 $
3. $ D = 9 $
4. $ G = -\frac{5}{3} $ (or $ -1\frac{2}{3} $)
5. $ H = -\frac{11}{5} $ (or $ -2.2 $)
6. $ J = -\frac{11}{2} $ (or $ -5.5 $)

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Let me know if you'd like these plotted or visualized!