Adding and Subtracting Fractions Worksheets with Answer Key - Free Printable

Let’s solve each of the six word problems step by step, explaining the reasoning and calculations.

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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?

✔ Solution:

We need to add the two mixed numbers:

16½ + 12½

Add the whole numbers:
16 + 12 = 28

Add the fractions:
½ + ½ = 1

Now add them together:
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.

✔ Solution:

Add: 22⅗ + 19⅔

First, add the whole numbers:
22 + 19 = 41

Now add the fractions: ⅗ + ⅔

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

Convert:
- ⅗ = 9/15
- ⅔ = 10/15

Add: 9/15 + 10/15 = 19/15 = 1⁴⁄₁₅

Now add to the whole number:
41 + 1⁴⁄₁₅ = 42⁴⁄₁₅

✔ Answer: 42⁴⁄₁₅ kg

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Problem 3:

> Julia spent 11⅙ of her pocket money on movie tickets and ¾ on chocolates. How much money did she spend altogether?

✔ Solution:

Add: 11⅙ + ¾

Add the whole numbers: 11 + 0 = 11

Add the fractions: ⅙ + ¾

Common denominator of 6 and 4 is 12.

Convert:
- ⅙ = 2/12
- ¾ = 9/12

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

Total: 11 + 11/12 = 11¹¹⁄₁₂

✔ Answer: 11¹¹⁄₁₂ of her pocket money

*(Note: Since it says “of her pocket money”, this is a fraction of the total — so she spent more than 11 times her pocket money? That seems odd — but mathematically, we follow the problem as written.)*

Actually, re-reading — it probably means 11⅙ *units* (like dollars) and ¾ *units*. So the answer is just the sum: 11¹¹⁄₁₂ units.

✔ Final Answer: 11¹¹⁄₁₂

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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?

✔ Solution:

Compare 3⁶⁄₇ and 4²⁄₉

Clearly, 4 > 3, so Mike jumped higher.

Now find the difference: 4²⁄₉ - 3⁶⁄₇

Convert both to improper fractions:

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

Subtract: 38/9 - 27/7

Common denominator 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?

✔ Solution:

Fuel used = Initial fuel – Remaining fuel
= 15⁸⁄₉ - 4⁵⁄₆

Convert to improper fractions:

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

Subtract: 143/9 - 29/6

Common denominator of 9 and 6 is 18

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

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

Convert to mixed number:
199 ÷ 18 = 11 with remainder 1 → 11¹⁄₁₈

✔ Answer: 11¹⁄₁₈ liters

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Problem 6:

> Billy traveled 18⅓ km by car and then took a boat. Then he cycled 13⅙ km. If he had covered 35¾ km in total, then how many km did he travel by boat?

✔ Solution:

Total distance = Car + Boat + Cycle
So: Boat = Total – Car – Cycle

Given:
- Total = 35¾
- Car = 18⅓
- Cycle = 13⅙

Compute: 35¾ - 18⅓ - 13⅙

Do step-by-step:

First, subtract 18⅓ from 35¾:

Convert to improper fractions:

- 35¾ = (35×4 + 3)/4 = 143/4
- 18⅓ = (18×3 + 1)/3 = 55/3

Subtract: 143/4 - 55/3 → Common denominator 12

- 143/4 = 429/12
- 55/3 = 220/12

→ 429/12 - 220/12 = 209/12

Now subtract 13⅙:

13⅙ = (13×6 + 1)/6 = 79/6

Now: 209/12 - 79/6

Common denominator 12:

- 79/6 = 158/12

→ 209/12 - 158/12 = 51/12

Simplify: 51 ÷ 3 = 17, 12 ÷ 3 = 4 → 17/4 = 4¼

✔ Answer: 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 or units)
4. Mike jumped higher by 23/63 meters
5. 11¹⁄₁₈ liters
6. 4¼ km

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