Math worksheet featuring six word problems that require adding and subtracting fractions, designed for educational practice.

Here is the step-by-step solution to each of the six word problems involving adding and subtracting fractions.

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Problem 1: Robert spent 16½ hours on jogging and 12½ hours on swimming. What is the total time he spent on the two activities?

We need to add the two mixed numbers:
`16½ + 12½`

Step 1: Add the whole numbers:
`16 + 12 = 28`

Step 2: Add the fractions:
`½ + ½ = 1`

Step 3: Add the results:
`28 + 1 = 29`

✔ Answer: 29 hours

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Problem 2: Mandy bought 22⅗ kg of tomatoes and 19⅔ kg potatoes. Find the total weight of vegetables she bought.

We need to add: `22⅗ + 19⅔`

Step 1: Add the whole numbers:
`22 + 19 = 41`

Step 2: Add the fractions: `⅗ + ⅔`

Find a common denominator. LCM of 5 and 3 is 15.

Convert:
- `⅗ = (3×3)/(5×3) = 9/15`
- `⅔ = (2×5)/(3×5) = 10/15`

Add: `9/15 + 10/15 = 19/15`

Step 3: Convert improper fraction to mixed number:
`19/15 = 1 4/15`

Step 4: Add to whole number part:
`41 + 1 4/15 = 42 4/15`

✔ Answer: 42⁴⁄₁₅ kg

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Problem 3: Julia spent 11¹⁄₆ of her pocket money on movie tickets and ¾ on chocolates. How much money did she spend altogether?

We need to add: `11¹⁄₆ + ¾`

Step 1: Add the whole number and fractions separately.

Whole number: `11`

Fractions: `¹⁄₆ + ¾`

Find common denominator. LCM of 6 and 4 is 12.

Convert:
- `¹⁄₆ = 2/12`
- `¾ = 9/12`

Add: `2/12 + 9/12 = 11/12`

Step 2: Combine with whole number:
`11 + 11/12 = 11¹¹⁄₁₂`

✔ Answer: 11¹¹⁄₁₂ of her pocket money

*(Note: This means she spent more than her entire pocket money — perhaps it’s a trick question or implies she used savings too. But mathematically, this is correct.)*

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Problem 4: In a high jump contest, Sandy jumped 3⁶⁄₇ m and Mike jumped 4²⁄₉ m. Who jumped higher and by how much?

We need to compare `3⁶⁄₇` and `4²⁄₉`, then find the difference.

Since 4 > 3, Mike jumped higher.

Now calculate: `4²⁄₉ - 3⁶⁄₇`

Step 1: Convert to improper fractions.

- `4²⁄₉ = (4×9 + 2)/9 = 38/9`
- `3⁶⁄₇ = (3×7 + 6)/7 = 27/7`

Step 2: Subtract: `38/9 - 27/7`

Find common denominator. LCM of 9 and 7 is 63.

Convert:
- `38/9 = (38×7)/(9×7) = 266/63`
- `27/7 = (27×9)/(7×9) = 243/63`

Subtract: `266/63 - 243/63 = 23/63`

✔ Answer: Mike jumped higher by ²³⁄₆₃ meters

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Problem 5: Frank had 15⁸⁄₉ liters of fuel in his car. After he reached home by car, he had only 4⁵⁄₆ liters left. How much fuel was used?

We need to subtract: `15⁸⁄₉ - 4⁵⁄₆`

Step 1: Convert to improper fractions.

- `15⁸⁄₉ = (15×9 + 8)/9 = 143/9`
- `4⁵⁄₆ = (4×6 + 5)/6 = 29/6`

Step 2: Subtract: `143/9 - 29/6`

LCM of 9 and 6 is 18.

Convert:
- `143/9 = (143×2)/(9×2) = 286/18`
- `29/6 = (29×3)/(6×3) = 87/18`

Subtract: `286/18 - 87/18 = 199/18`

Step 3: Convert to mixed number:

`199 ÷ 18 = 11 remainder 1 → 11¹⁄₁₈`

✔ Answer: 11¹⁄₁₈ liters of fuel were used

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Problem 6: Billy traveled 18¹⁄₃ km by car and then took a boat. Then he cycled 13¹⁄₆ km. If he had covered 35¾ km in total, then how many km did he travel by boat?

Total distance = Car + Boat + Cycle

So:
Boat = Total - Car - Cycle
→ `35¾ - 18¹⁄₃ - 13¹⁄₆`

Step 1: Convert all to improper fractions.

- `35¾ = (35×4 + 3)/4 = 143/4`
- `18¹⁄₃ = (18×3 + 1)/3 = 55/3`
- `13¹⁄₆ = (13×6 + 1)/6 = 79/6`

Step 2: Find a common denominator for subtraction. LCM of 4, 3, and 6 is 12.

Convert:
- `143/4 = (143×3)/(4×3) = 429/12`
- `55/3 = (55×4)/(3×4) = 220/12`
- `79/6 = (79×2)/(6×2) = 158/12`

Step 3: Subtract:

`429/12 - 220/12 - 158/12 = (429 - 220 - 158)/12 = 51/12`

Step 4: Simplify:

`51/12 = 17/4 = 4¼`

✔ Answer: Billy traveled 4¼ km by boat

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✔ Final Answers Summary:

1. 29 hours
2. 42⁴⁄₁₅ kg
3. 11¹¹⁄₁₂ of her pocket money
4. Mike jumped higher by ²³⁄₆₃ meters
5. 11¹⁄₁₈ liters
6. 4¼ km by boat

Let me know if you’d like visual diagrams or further explanation for any problem!