Grade 6 Fraction Word Problems Worksheet with five math exercises on adding fractions, comparing distances, calculating remaining space, total weight, and comparing table widths.

Let's solve each of the fraction word problems step by step.

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1. Stella goes for a long walk and walks $ \frac{2}{10} $ mile. She rested for some time and walked $ \frac{4}{10} $ mile. How much did Stella walk in total?

Step 1: Add the two distances:
$$
\frac{2}{10} + \frac{4}{10} = \frac{6}{10}
$$

Step 2: Simplify the fraction:
$$
\frac{6}{10} = \frac{3}{5}
$$

✔ Answer: Stella walked $ \frac{3}{5} $ mile in total.

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2. Amelia walks $ \frac{8}{10} $ of a mile to her school. Ava walks $ \frac{7}{10} $ of a mile to school. Who walks more and by what distance?

Step 1: Compare the fractions:
- $ \frac{8}{10} > \frac{7}{10} $

So, Amelia walks more.

Step 2: Find the difference:
$$
\frac{8}{10} - \frac{7}{10} = \frac{1}{10}
$$

✔ Answer: Amelia walks more by $ \frac{1}{10} $ mile.

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3. The new playground had $ \frac{1}{5} $th of its space for football ground, $ \frac{3}{5} $th space for track and field activities. How much space is left after this now?

Step 1: Add the used space:
$$
\frac{1}{5} + \frac{3}{5} = \frac{4}{5}
$$

Step 2: Subtract from the whole (1 whole = $ \frac{5}{5} $):
$$
\frac{5}{5} - \frac{4}{5} = \frac{1}{5}
$$

✔ Answer: $ \frac{1}{5} $ of the space is left.

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4. An empty box weighs $ 3\frac{1}{2} $ kg. It is then filled with $ 14\frac{1}{3} $ kg of fruit. What is the weight of the box when it is full?

Step 1: Convert mixed numbers to improper fractions.

- $ 3\frac{1}{2} = \frac{7}{2} $
- $ 14\frac{1}{3} = \frac{43}{3} $

Step 2: Add the weights:
$$
\frac{7}{2} + \frac{43}{3}
$$

Find a common denominator: LCM of 2 and 3 is 6.

$$
\frac{7}{2} = \frac{21}{6}, \quad \frac{43}{3} = \frac{86}{6}
$$

Now add:
$$
\frac{21}{6} + \frac{86}{6} = \frac{107}{6}
$$

Step 3: Convert to mixed number:
$$
\frac{107}{6} = 17\frac{5}{6}
$$

✔ Answer: The full box weighs $ 17\frac{5}{6} $ kg.

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5. A black table has a width of $ \frac{1}{3} $ meter, a brown table has a width of $ \frac{2}{5} $ meter, and the white table has a width of $ \frac{4}{5} $ meter. Which table has the longest width?

We need to compare:
- $ \frac{1}{3} $
- $ \frac{2}{5} $
- $ \frac{4}{5} $

Step 1: Compare $ \frac{2}{5} $ and $ \frac{4}{5} $: clearly $ \frac{4}{5} > \frac{2}{5} $

Step 2: Compare $ \frac{4}{5} $ and $ \frac{1}{3} $. Use common denominator (LCM of 5 and 3 is 15):

- $ \frac{4}{5} = \frac{12}{15} $
- $ \frac{1}{3} = \frac{5}{15} $

Since $ \frac{12}{15} > \frac{5}{15} $, $ \frac{4}{5} > \frac{1}{3} $

✔ Answer: The white table has the longest width.

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✔ Final Answers:

1. $ \frac{3}{5} $ mile
2. Amelia walks more by $ \frac{1}{10} $ mile
3. $ \frac{1}{5} $ of the space is left
4. $ 17\frac{5}{6} $ kg
5. The white table has the longest width

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