Printable math worksheets for practicing addition and subtraction of fractions with unlike denominators through real-world word problems.

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Here are the problems from the worksheet, along with step-by-step solutions:

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Problem 1:

Cassie picked two songs for a playlist. One song is $4\frac{3}{4}$ minutes long. The other is $5\frac{1}{2}$ minutes long. How long is the playlist so far?

#### Step 1: Convert mixed numbers to improper fractions
- $4\frac{3}{4} = \frac{4 \times 4 + 3}{4} = \frac{16 + 3}{4} = \frac{19}{4}$
- $5\frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{10 + 1}{2} = \frac{11}{2}$

#### Step 2: Find a common denominator
The denominators are 4 and 2. The least common denominator (LCD) is 4.
- $\frac{11}{2} = \frac{11 \times 2}{2 \times 2} = \frac{22}{4}$

#### Step 3: Add the fractions
$$
\frac{19}{4} + \frac{22}{4} = \frac{41}{4}
$$

#### Step 4: Convert back to a mixed number
$$
\frac{41}{4} = 10\frac{1}{4}
$$

✔ Answer: The playlist is $10\frac{1}{4}$ minutes long.

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Problem 2:

Art walked $2\frac{1}{3}$ miles this morning and $4\frac{1}{2}$ miles this evening. How many miles did he walk today?

#### Step 1: Convert to improper fractions
- $2\frac{1}{3} = \frac{7}{3}$
- $4\frac{1}{2} = \frac{9}{2}$

#### Step 2: Find LCD of 3 and 2 → LCD = 6
- $\frac{7}{3} = \frac{14}{6}$
- $\frac{9}{2} = \frac{27}{6}$

#### Step 3: Add
$$
\frac{14}{6} + \frac{27}{6} = \frac{41}{6}
$$

#### Step 4: Convert to mixed number
$$
\frac{41}{6} = 6\frac{5}{6}
$$

✔ Answer: Art walked $6\frac{5}{6}$ miles today.

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Problem 3:

Ronen ran $7\frac{3}{8}$ miles yesterday and $3\frac{1}{4}$ miles today. How many more miles did he run yesterday than today?

This is a subtraction problem.

#### Step 1: Convert to improper fractions
- $7\frac{3}{8} = \frac{59}{8}$
- $3\frac{1}{4} = \frac{13}{4}$

#### Step 2: LCD of 8 and 4 → LCD = 8
- $\frac{13}{4} = \frac{26}{8}$

#### Step 3: Subtract
$$
\frac{59}{8} - \frac{26}{8} = \frac{33}{8}
$$

#### Step 4: Convert to mixed number
$$
\frac{33}{8} = 4\frac{1}{8}
$$

✔ Answer: Ronen ran $4\frac{1}{8}$ more miles yesterday.

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Problem 4:

Judah carried two boxes to the car. One weighed $4\frac{1}{2}$ pounds. The other weighed $6\frac{3}{4}$ pounds. How much did the two boxes weigh altogether?

#### Step 1: Convert to improper fractions
- $4\frac{1}{2} = \frac{9}{2}$
- $6\frac{3}{4} = \frac{27}{4}$

#### Step 2: LCD of 2 and 4 → LCD = 4
- $\frac{9}{2} = \frac{18}{4}$

#### Step 3: Add
$$
\frac{18}{4} + \frac{27}{4} = \frac{45}{4}
$$

#### Step 4: Convert to mixed number
$$
\frac{45}{4} = 11\frac{1}{4}
$$

✔ Answer: The two boxes weighed $11\frac{1}{4}$ pounds together.

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Problem 5:

Samantha drank $2\frac{1}{2}$ liters of water on the mountain. She drank $1\frac{1}{4}$ liters on the way down. How much water did she drink in all?

#### Step 1: Convert to improper fractions
- $2\frac{1}{2} = \frac{5}{2}$
- $1\frac{1}{4} = \frac{5}{4}$

#### Step 2: LCD of 2 and 4 → LCD = 4
- $\frac{5}{2} = \frac{10}{4}$

#### Step 3: Add
$$
\frac{10}{4} + \frac{5}{4} = \frac{15}{4}
$$

#### Step 4: Convert to mixed number
$$
\frac{15}{4} = 3\frac{3}{4}
$$

✔ Answer: Samantha drank $3\frac{3}{4}$ liters of water in total.

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✔ Summary of Answers:

1. $10\frac{1}{4}$ minutes
2. $6\frac{5}{6}$ miles
3. $4\frac{1}{8}$ miles more
4. $11\frac{1}{4}$ pounds
5. $3\frac{3}{4}$ liters

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