Worksheet featuring six word problems that require adding and subtracting fractions in real-world contexts.

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

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Problem 1:

Robert spent $16\frac{1}{2}$ hours on jogging and $12\frac{1}{2}$ hours on swimming. What is the total time he spent on the two activities?

#### Step 1: Convert mixed numbers to improper fractions.
- $16\frac{1}{2} = \frac{33}{2}$
- $12\frac{1}{2} = \frac{25}{2}$

#### Step 2: Add the fractions.
$$
\frac{33}{2} + \frac{25}{2} = \frac{58}{2} = 29
$$

✔ Answer: Robert spent 29 hours in total.

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Problem 2:

Mandy bought $22\frac{3}{5}$ kg of tomatoes and $19\frac{2}{3}$ kg of potatoes. Find the total weight of vegetables she bought.

#### Step 1: Convert to improper fractions.
- $22\frac{3}{5} = \frac{113}{5}$
- $19\frac{2}{3} = \frac{59}{3}$

#### Step 2: Find a common denominator (LCM of 5 and 3 is 15).
- $\frac{113}{5} = \frac{113 \times 3}{15} = \frac{339}{15}$
- $\frac{59}{3} = \frac{59 \times 5}{15} = \frac{295}{15}$

#### Step 3: Add.
$$
\frac{339}{15} + \frac{295}{15} = \frac{634}{15}
$$

#### Step 4: Convert to mixed number.
$$
\frac{634}{15} = 42\frac{4}{15}
$$

✔ Answer: Total weight = $42\frac{4}{15}$ kg

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Problem 3:

Julia spent $11\frac{1}{6}$ of her pocket money on movie tickets and $\frac{3}{4}$ on chocolates. How much money did she spend altogether?

Wait — this seems problematic. She can't spend more than her entire pocket money unless it's just parts of it. But $11\frac{1}{6}$ is greater than 1, which would mean she spent over 11 times her pocket money — that doesn’t make sense.

But looking closely: It says "$11\frac{1}{6}$ of her pocket money" — but that’s impossible unless it's a typo.

Wait — likely, this is meant to be:
> Julia spent $\frac{1}{6}$ of her pocket money on movie tickets and $\frac{3}{4}$ on chocolates.

Because otherwise, spending $11\frac{1}{6}$ times her money is nonsensical.

Assuming it's a typo and it should be:

> Julia spent $\frac{1}{6}$ of her pocket money on movie tickets and $\frac{3}{4}$ on chocolates.

We’ll proceed with that.

#### Step 1: Add $\frac{1}{6} + \frac{3}{4}$

Find LCM of 6 and 4 → 12

- $\frac{1}{6} = \frac{2}{12}$
- $\frac{3}{4} = \frac{9}{12}$

$$
\frac{2}{12} + \frac{9}{12} = \frac{11}{12}
$$

✔ Answer: Julia spent $\frac{11}{12}$ of her pocket money.

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Problem 4:

In a high jump contest, Sandy jumped $3\frac{6}{7}$ m and Mike jumped $4\frac{2}{9}$ m. Who jumped higher and by how much?

#### Step 1: Convert to improper fractions.
- $3\frac{6}{7} = \frac{27}{7}$
- $4\frac{2}{9} = \frac{38}{9}$

#### Step 2: Compare or subtract.

Find LCM of 7 and 9 → 63

- $\frac{27}{7} = \frac{27 \times 9}{63} = \frac{243}{63}$
- $\frac{38}{9} = \frac{38 \times 7}{63} = \frac{266}{63}$

Now compare:
- $\frac{243}{63} < \frac{266}{63}$ → Mike jumped higher.

#### Step 3: Subtract to find difference.
$$
\frac{266}{63} - \frac{243}{63} = \frac{23}{63}
$$

✔ Answer: Mike jumped higher by $\frac{23}{63}$ meters.

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Problem 5:

Frank had $15\frac{8}{9}$ liters of fuel in his car. After reaching home, he had $4\frac{5}{6}$ liters left. How much fuel was used?

This is subtraction.

#### Step 1: Convert to improper fractions.
- $15\frac{8}{9} = \frac{143}{9}$
- $4\frac{5}{6} = \frac{29}{6}$

#### Step 2: Find common denominator (LCM of 9 and 6 is 18)
- $\frac{143}{9} = \frac{143 \times 2}{18} = \frac{286}{18}$
- $\frac{29}{6} = \frac{29 \times 3}{18} = \frac{87}{18}$

#### Step 3: Subtract
$$
\frac{286}{18} - \frac{87}{18} = \frac{199}{18}
$$

#### Step 4: Convert to mixed number
$$
\frac{199}{18} = 11\frac{1}{18}
$$

✔ Answer: Frank used $11\frac{1}{18}$ liters of fuel.

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Problem 6:

Billy traveled $18\frac{1}{3}$ km by car, then took a boat, then cycled $13\frac{1}{6}$ km. If he covered $35\frac{3}{4}$ km in total, how many km did he travel by boat?

Let’s denote:
- Car: $18\frac{1}{3} = \frac{55}{3}$
- Cycle: $13\frac{1}{6} = \frac{79}{6}$
- Total: $35\frac{3}{4} = \frac{143}{4}$

We need to find:
$$
\text{Boat distance} = \text{Total} - (\text{Car} + \text{Cycle})
$$

#### Step 1: Add car and cycle distances.

First, find common denominator for $\frac{55}{3}$ and $\frac{79}{6}$ → LCM of 3 and 6 is 6.

- $\frac{55}{3} = \frac{110}{6}$
- $\frac{79}{6} = \frac{79}{6}$

Add:
$$
\frac{110}{6} + \frac{79}{6} = \frac{189}{6} = \frac{63}{2}
$$

#### Step 2: Subtract from total.

Total = $\frac{143}{4}$

So:
$$
\text{Boat} = \frac{143}{4} - \frac{63}{2}
$$

Convert $\frac{63}{2}$ to fourths: $\frac{126}{4}$

$$
\frac{143}{4} - \frac{126}{4} = \frac{17}{4} = 4\frac{1}{4}
$$

✔ Answer: Billy traveled $4\frac{1}{4}$ km by boat.

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✔ Final Answers Summary:

1. 29 hours
2. $42\frac{4}{15}$ kg
3. $\frac{11}{12}$ of her pocket money *(assuming typo in problem)*
4. Mike jumped higher by $\frac{23}{63}$ m
5. $11\frac{1}{18}$ liters
6. $4\frac{1}{4}$ km

Let me know if you'd like these explained with diagrams or visual models!