Adding and Subtracting Fractions Worksheets with Answer Key - Free Printable

Let's solve each problem step by step.

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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?

#### Solution:
1. Convert mixed numbers to improper fractions:
\[
16 \frac{1}{2} = 16 + \frac{1}{2} = \frac{32}{2} + \frac{1}{2} = \frac{33}{2}
\]
\[
12 \frac{1}{2} = 12 + \frac{1}{2} = \frac{24}{2} + \frac{1}{2} = \frac{25}{2}
\]

2. Add the two fractions:
\[
\frac{33}{2} + \frac{25}{2} = \frac{33 + 25}{2} = \frac{58}{2} = 29
\]

#### Answer:
\[
\boxed{29}
\]

---

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.

#### Solution:
1. Convert mixed numbers to improper fractions:
\[
22 \frac{3}{5} = 22 + \frac{3}{5} = \frac{110}{5} + \frac{3}{5} = \frac{113}{5}
\]
\[
19 \frac{2}{3} = 19 + \frac{2}{3} = \frac{57}{3} + \frac{2}{3} = \frac{59}{3}
\]

2. Find a common denominator for \( \frac{113}{5} \) and \( \frac{59}{3} \). The least common multiple (LCM) of 5 and 3 is 15.

3. Rewrite the fractions with the common denominator:
\[
\frac{113}{5} = \frac{113 \times 3}{5 \times 3} = \frac{339}{15}
\]
\[
\frac{59}{3} = \frac{59 \times 5}{3 \times 5} = \frac{295}{15}
\]

4. Add the fractions:
\[
\frac{339}{15} + \frac{295}{15} = \frac{339 + 295}{15} = \frac{634}{15}
\]

5. Convert the improper fraction back to a mixed number:
\[
\frac{634}{15} = 42 \frac{4}{15}
\]

#### Answer:
\[
\boxed{42 \frac{4}{15}}
\]

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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?

#### Solution:
1. Convert the mixed number to an improper fraction:
\[
11 \frac{1}{6} = 11 + \frac{1}{6} = \frac{66}{6} + \frac{1}{6} = \frac{67}{6}
\]

2. Find a common denominator for \( \frac{67}{6} \) and \( \frac{3}{4} \). The LCM of 6 and 4 is 12.

3. Rewrite the fractions with the common denominator:
\[
\frac{67}{6} = \frac{67 \times 2}{6 \times 2} = \frac{134}{12}
\]
\[
\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
\]

4. Add the fractions:
\[
\frac{134}{12} + \frac{9}{12} = \frac{134 + 9}{12} = \frac{143}{12}
\]

5. Convert the improper fraction back to a mixed number:
\[
\frac{143}{12} = 11 \frac{11}{12}
\]

#### Answer:
\[
\boxed{11 \frac{11}{12}}
\]

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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?

#### Solution:
1. Convert mixed numbers to improper fractions:
\[
3 \frac{6}{7} = 3 + \frac{6}{7} = \frac{21}{7} + \frac{6}{7} = \frac{27}{7}
\]
\[
4 \frac{2}{9} = 4 + \frac{2}{9} = \frac{36}{9} + \frac{2}{9} = \frac{38}{9}
\]

2. Compare the two fractions:
- Sandy's jump: \( \frac{27}{7} \)
- Mike's jump: \( \frac{38}{9} \)

3. Find a common denominator for \( \frac{27}{7} \) and \( \frac{38}{9} \). The LCM of 7 and 9 is 63.

4. Rewrite the fractions with the common denominator:
\[
\frac{27}{7} = \frac{27 \times 9}{7 \times 9} = \frac{243}{63}
\]
\[
\frac{38}{9} = \frac{38 \times 7}{9 \times 7} = \frac{266}{63}
\]

5. Compare the numerators:
\[
\frac{243}{63} < \frac{266}{63}
\]
So, Mike jumped higher.

6. Find the difference:
\[
\frac{266}{63} - \frac{243}{63} = \frac{266 - 243}{63} = \frac{23}{63}
\]

#### Answer:
Mike jumped higher by \( \boxed{\frac{23}{63}} \) meters.

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Problem 5:

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

#### Solution:
1. Convert mixed numbers to improper fractions:
\[
15 \frac{8}{9} = 15 + \frac{8}{9} = \frac{135}{9} + \frac{8}{9} = \frac{143}{9}
\]
\[
4 \frac{5}{6} = 4 + \frac{5}{6} = \frac{24}{6} + \frac{5}{6} = \frac{29}{6}
\]

2. Find a common denominator for \( \frac{143}{9} \) and \( \frac{29}{6} \). The LCM of 9 and 6 is 18.

3. Rewrite the fractions with the common denominator:
\[
\frac{143}{9} = \frac{143 \times 2}{9 \times 2} = \frac{286}{18}
\]
\[
\frac{29}{6} = \frac{29 \times 3}{6 \times 3} = \frac{87}{18}
\]

4. Subtract the fractions:
\[
\frac{286}{18} - \frac{87}{18} = \frac{286 - 87}{18} = \frac{199}{18}
\]

5. Convert the improper fraction back to a mixed number:
\[
\frac{199}{18} = 11 \frac{1}{18}
\]

#### Answer:
\[
\boxed{11 \frac{1}{18}}
\]

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Problem 6:

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

#### Solution:
1. Convert mixed numbers to improper fractions:
\[
18 \frac{1}{3} = 18 + \frac{1}{3} = \frac{54}{3} + \frac{1}{3} = \frac{55}{3}
\]
\[
13 \frac{1}{6} = 13 + \frac{1}{6} = \frac{78}{6} + \frac{1}{6} = \frac{79}{6}
\]
\[
35 \frac{3}{4} = 35 + \frac{3}{4} = \frac{140}{4} + \frac{3}{4} = \frac{143}{4}
\]

2. Find the total distance traveled by car and cycling:
- Car: \( \frac{55}{3} \)
- Cycling: \( \frac{79}{6} \)

3. Find a common denominator for \( \frac{55}{3} \) and \( \frac{79}{6} \). The LCM of 3 and 6 is 6.
\[
\frac{55}{3} = \frac{55 \times 2}{3 \times 2} = \frac{110}{6}
\]
\[
\frac{79}{6} = \frac{79}{6}
\]

4. Add the fractions:
\[
\frac{110}{6} + \frac{79}{6} = \frac{110 + 79}{6} = \frac{189}{6} = \frac{63}{2}
\]

5. Convert \( \frac{63}{2} \) to a mixed number:
\[
\frac{63}{2} = 31 \frac{1}{2}
\]

6. Let \( x \) be the distance traveled by boat. The total distance is:
\[
31 \frac{1}{2} + x = 35 \frac{3}{4}
\]

7. Convert \( 31 \frac{1}{2} \) and \( 35 \frac{3}{4} \) to improper fractions:
\[
31 \frac{1}{2} = \frac{63}{2}
\]
\[
35 \frac{3}{4} = \frac{143}{4}
\]

8. Solve for \( x \):
\[
\frac{63}{2} + x = \frac{143}{4}
\]
\[
x = \frac{143}{4} - \frac{63}{2}
\]

9. Find a common denominator for \( \frac{143}{4} \) and \( \frac{63}{2} \). The LCM of 4 and 2 is 4.
\[
\frac{63}{2} = \frac{63 \times 2}{2 \times 2} = \frac{126}{4}
\]

10. Subtract the fractions:
\[
x = \frac{143}{4} - \frac{126}{4} = \frac{143 - 126}{4} = \frac{17}{4}
\]

11. Convert \( \frac{17}{4} \) to a mixed number:
\[
\frac{17}{4} = 4 \frac{1}{4}
\]

#### Answer:
\[
\boxed{4 \frac{1}{4}}
\]

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Final Answers:

1. \(\boxed{29}\)
2. \(\boxed{42 \frac{4}{15}}\)
3. \(\boxed{11 \frac{11}{12}}\)
4. \(\boxed{\frac{23}{63}}\)
5. \(\boxed{11 \frac{1}{18}}\)
6. \(\boxed{4 \frac{1}{4}}\)