Word problems with fractions worksheet - Free Printable

Here are the step-by-step solutions for each word problem on the worksheet.

1) Melanie completed $\frac{5}{6}$ of Wednesday's crossword and $\frac{7}{10}$ of Thursday's crossword. In total, what fraction of these crosswords did Melanie finish?

* Step 1: We need to add the two fractions: $\frac{5}{6} + \frac{7}{10}$.
* Step 2: Find a common denominator for 6 and 10. The least common multiple is 30.
* Step 3: Convert the fractions:
* $\frac{5}{6} = \frac{5 \times 5}{6 \times 5} = \frac{25}{30}$
* $\frac{7}{10} = \frac{7 \times 3}{10 \times 3} = \frac{21}{30}$
* Step 4: Add the numerators: $\frac{25}{30} + \frac{21}{30} = \frac{46}{30}$.
* Step 5: Simplify the fraction. Both numbers are divisible by 2: $\frac{23}{15}$. This can also be written as the mixed number $1 \frac{8}{15}$.

2) Nancy planted $\frac{5}{8}$ rows of beans and $\frac{5}{12}$ rows of spinach in a garden. In total, how many rows of vegetables did Nancy plant?

* Step 1: Add the fractions: $\frac{5}{8} + \frac{5}{12}$.
* Step 2: Find a common denominator for 8 and 12. The least common multiple is 24.
* Step 3: Convert the fractions:
* $\frac{5}{8} = \frac{5 \times 3}{8 \times 3} = \frac{15}{24}$
* $\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24}$
* Step 4: Add the numerators: $\frac{15}{24} + \frac{10}{24} = \frac{25}{24}$.
* Step 5: This is an improper fraction. It can be written as the mixed number $1 \frac{1}{24}$.

3) Fred has to read 2 books for school. Fred read $\frac{5}{12}$ of the first book on Friday, and $\frac{1}{12}$ of the second book on Thursday. What total fraction of these two books has Fred read?

* Step 1: Add the fractions: $\frac{5}{12} + \frac{1}{12}$.
* Step 2: Since the denominators are already the same (12), just add the top numbers: $5 + 1 = 6$.
* Step 3: The result is $\frac{6}{12}$.
* Step 4: Simplify the fraction. Both numbers divide evenly by 6: $\frac{1}{2}$.

4) Fred picked $\frac{4}{9}$ of a bucket of lemons, and Mary picked $\frac{4}{9}$ of a bucket of lemons. How many buckets total did they pick?

* Step 1: Add the fractions: $\frac{4}{9} + \frac{4}{9}$.
* Step 2: Add the numerators: $4 + 4 = 8$. Keep the denominator the same.
* Step 3: The result is $\frac{8}{9}$.

5) Tom did $\frac{10}{11}$ of a load of laundry on Monday and $\frac{3}{11}$ of a load of laundry on Saturday. What fraction of laundry did Tom do in total?

* Step 1: Add the fractions: $\frac{10}{11} + \frac{3}{11}$.
* Step 2: Add the numerators: $10 + 3 = 13$. Keep the denominator the same.
* Step 3: The result is $\frac{13}{11}$.
* Step 4: Convert to a mixed number: $1 \frac{2}{11}$.

6) Alyssa has $\frac{3}{4}$ of last week's allowance and $\frac{7}{9}$ of this week's allowance. How many weeks of allowance in total does Alyssa have left?

* Step 1: Add the fractions: $\frac{3}{4} + \frac{7}{9}$.
* Step 2: Find a common denominator for 4 and 9. The least common multiple is 36.
* Step 3: Convert the fractions:
* $\frac{3}{4} = \frac{3 \times 9}{4 \times 9} = \frac{27}{36}$
* $\frac{7}{9} = \frac{7 \times 4}{9 \times 4} = \frac{28}{36}$
* Step 4: Add the numerators: $\frac{27}{36} + \frac{28}{36} = \frac{55}{36}$.
* Step 5: Convert to a mixed number: $1 \frac{19}{36}$.

7) Mike had to complete chores. Mike has completed $\frac{11}{12}$ of the house chores and $\frac{9}{11}$ of the yard chores. What fraction of all the chores has Mike done?

* Step 1: Add the fractions: $\frac{11}{12} + \frac{9}{11}$.
* Step 2: Find a common denominator for 12 and 11. Multiply them: $12 \times 11 = 132$.
* Step 3: Convert the fractions:
* $\frac{11}{12} = \frac{11 \times 11}{12 \times 11} = \frac{121}{132}$
* $\frac{9}{11} = \frac{9 \times 12}{11 \times 12} = \frac{108}{132}$
* Step 4: Add the numerators: $\frac{121}{132} + \frac{108}{132} = \frac{229}{132}$.
* Step 5: Convert to a mixed number: $1 \frac{97}{132}$.

8) Keith ate $\frac{1}{2}$ of a pie, while Mary ate $\frac{1}{2}$ of a pie. In total, how much pie did these two eat?

* Step 1: Add the fractions: $\frac{1}{2} + \frac{1}{2}$.
* Step 2: Add the numerators: $1 + 1 = 2$.
* Step 3: The result is $\frac{2}{2}$.
* Step 4: Simplify: $\frac{2}{2} = 1$ whole pie.

9) Tom drank $\frac{8}{9}$ of a cup of milk at breakfast and $\frac{2}{5}$ of a cup of milk at dinner. In total, how many cups of milk did Tom drink today?

* Step 1: Add the fractions: $\frac{8}{9} + \frac{2}{5}$.
* Step 2: Find a common denominator for 9 and 5. Multiply them: $9 \times 5 = 45$.
* Step 3: Convert the fractions:
* $\frac{8}{9} = \frac{8 \times 5}{9 \times 5} = \frac{40}{45}$
* $\frac{2}{5} = \frac{2 \times 9}{5 \times 9} = \frac{18}{45}$
* Step 4: Add the numerators: $\frac{40}{45} + \frac{18}{45} = \frac{58}{45}$.
* Step 5: Convert to a mixed number: $1 \frac{13}{45}$.

10) A recipe called for $\frac{11}{12}$ cup of chopped tomatoes and $\frac{7}{12}$ cup of diced tomatoes. In total, how many cups of tomatoes did the recipe call for?

* Step 1: Add the fractions: $\frac{11}{12} + \frac{7}{12}$.
* Step 2: Add the numerators: $11 + 7 = 18$.
* Step 3: The result is $\frac{18}{12}$.
* Step 4: Simplify the fraction. Both divide by 6: $\frac{3}{2}$.
* Step 5: Convert to a mixed number: $1 \frac{1}{2}$.

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Final Answer:
1) $1 \frac{8}{15}$ (or $\frac{23}{15}$)
2) $1 \frac{1}{24}$ (or $\frac{25}{24}$)
3) $\frac{1}{2}$
4) $\frac{8}{9}$
5) $1 \frac{2}{11}$ (or $\frac{13}{11}$)
6) $1 \frac{19}{36}$ (or $\frac{55}{36}$)
7) $1 \frac{97}{132}$ (or $\frac{229}{132}$)
8) $1$
9) $1 \frac{13}{45}$ (or $\frac{58}{45}$)
10) $1 \frac{1}{2}$ (or $\frac{3}{2}$)