Adding and Subtracting Unlike Fractions Word Problems worksheet ... - Free Printable

Let's solve each of these adding and subtracting unlike fractions word problems step by step. We'll find common denominators, perform the operations, and simplify where needed.

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Problem 1:

> Bo, Ryan, and Zach walked $ \frac{1}{4} $ miles from school to Bo’s house. Then they walked $ \frac{4}{6} $ miles from Bo’s house to the park. What is the total distance?

We need to add:
$$
\frac{1}{4} + \frac{4}{6}
$$

First, simplify $ \frac{4}{6} = \frac{2}{3} $

Now add $ \frac{1}{4} + \frac{2}{3} $

Find the least common denominator (LCD) of 4 and 3 → 12

Convert:
- $ \frac{1}{4} = \frac{3}{12} $
- $ \frac{2}{3} = \frac{8}{12} $

Add:
$$
\frac{3}{12} + \frac{8}{12} = \frac{11}{12}
$$

✔ Answer: $ \boxed{\frac{11}{12}} $

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Problem 2:

> Hannah ate $ \frac{2}{6} $ of the pizza, Bella ate $ \frac{1}{4} $. How much did they eat together?

Add:
$$
\frac{2}{6} + \frac{1}{4}
$$

Simplify $ \frac{2}{6} = \frac{1}{3} $

Now add $ \frac{1}{3} + \frac{1}{4} $

LCD of 3 and 4 → 12

Convert:
- $ \frac{1}{3} = \frac{4}{12} $
- $ \frac{1}{4} = \frac{3}{12} $

Add:
$$
\frac{4}{12} + \frac{3}{12} = \frac{7}{12}
$$

✔ Answer: $ \boxed{\frac{7}{12}} $

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Problem 3:

> Faith walks $ \frac{7}{10} $ of a mile, Holly walks $ \frac{2}{5} $. How much farther does Faith walk?

Subtract:
$$
\frac{7}{10} - \frac{2}{5}
$$

LCD of 10 and 5 → 10

Convert $ \frac{2}{5} = \frac{4}{10} $

Now:
$$
\frac{7}{10} - \frac{4}{10} = \frac{3}{10}
$$

✔ Answer: $ \boxed{\frac{3}{10}} $

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Problem 4:

> Christian ate $ \frac{3}{9} $, Gabriel ate $ \frac{1}{3} $. What fraction of cookies were left?

First, simplify $ \frac{3}{9} = \frac{1}{3} $

Total eaten:
$$
\frac{1}{3} + \frac{1}{3} = \frac{2}{3}
$$

So, fraction left:
$$
1 - \frac{2}{3} = \frac{1}{3}
$$

✔ Answer: $ \boxed{\frac{1}{3}} $

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Problem 5:

> $ \frac{2}{4} $ went Monday, $ \frac{1}{5} $ went Tuesday. What fraction went altogether?

Add:
$$
\frac{2}{4} + \frac{1}{5}
$$

Simplify $ \frac{2}{4} = \frac{1}{2} $

Now add $ \frac{1}{2} + \frac{1}{5} $

LCD of 2 and 5 → 10

Convert:
- $ \frac{1}{2} = \frac{5}{10} $
- $ \frac{1}{5} = \frac{2}{10} $

Add:
$$
\frac{5}{10} + \frac{2}{10} = \frac{7}{10}
$$

✔ Answer: $ \boxed{\frac{7}{10}} $

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✔ Final Answers:

1. $ \boxed{\frac{11}{12}} $
2. $ \boxed{\frac{7}{12}} $
3. $ \boxed{\frac{3}{10}} $
4. $ \boxed{\frac{1}{3}} $
5. $ \boxed{\frac{7}{10}} $

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