Fraction Word Problems – ASVAB Math Review

1. Part of a Whole

Finding a specific amount from a total

Amount = Total × Fraction

Multiply the total quantity by the fraction given to find the specific part.

Example

A library has 120 books, and $$\frac{3}{5}$$ of them are fiction. How many fiction books are there?

Show solution

Step 1: Identify total = 120 and fraction = $$\frac{3}{5}$$.

Step 2: Multiply Total × Fraction:

Amount $$= 120 \times (\frac{3}{5}) = \frac{(120 \times 3)}{5} = \frac{360}{5} = 72$$.

Result: 72 fiction books.

Practice problems

Problem 1
A class has 30 students, and $$\frac{2}{3}$$ of them are girls. How many girls are in the class?

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Answer: 20 girls

Step 1: Total students = 30, fraction = $$\frac{2}{3}$$.
Step 2: Calculate Girls $$= 30 \times (\frac{2}{3}) = \frac{(30 \times 2)}{3} = \frac{60}{3} = 20$$.
=> Correct Answer: A (20 girls).
Problem 2
A bakery made 240 cookies. If $$\frac{5}{8}$$ of the cookies were chocolate chip, how many chocolate chip cookies were made?

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Answer: 150 cookies

Step 1: Total cookies = 240, fraction = $$\frac{5}{8}$$.
Step 2: Calculate $$= 240 \times (\frac{5}{8}) = (\frac{240}{8}) \times 5 = 30 \times 5 = 150$$.
=> Correct Answer: A (150 cookies).
Problem 3
In a company of 450 employees, $$\frac{4}{9}$$ work in marketing and $$\frac{2}{5}$$ of the remainder work in sales. How many work in sales?

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Answer: 100 employees

Step 1: Marketing employees = $$450 \times (\frac{4}{9}) = 200$$.
Step 2: Remainder employees $$= 450 - 200 = 250$$.
Step 3: Sales employees $$= 250 \times (\frac{2}{5}) = 100$$.
=> Correct Answer: A (100 employees).

2. Remaining Balance

Finding what is left after a portion is used

Left = Total × (1 - Fraction)

Subtract the used fraction from 1 (the whole) to find the remaining fraction, then multiply by total.

Example

Alex had $80 and spent $$\frac{3}{4}$$ of it. How much money does he have left?

Show solution

Step 1: Remaining fraction = $$1 - \frac{3}{4} = \frac{1}{4}$$.

Step 2: Left = Total × Remaining fraction:

Left $$= 80 \times (\frac{1}{4}) = 20$$.

Result: $20 left.

Practice problems

Problem 4
Sarah had 15 apples and gave away $$\frac{1}{3}$$ of them. How many apples does she have left?

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Answer: 10 apples

Step 1: Remaining fraction = $$1 - \frac{1}{3} = \frac{2}{3}$$.
Step 2: Remaining apples $$= 15 \times (\frac{2}{3}) = 10$$.
=> Correct Answer: B (10 apples).
Problem 5
A tank contains 500 liters of water. $$\frac{3}{10}$$ of the water is drained. How much water remains in the tank?

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Answer: 350 liters

Step 1: Remaining fraction = $$1 - \frac{3}{10} = \frac{7}{10}$$.
Step 2: Remaining water $$= 500 \times (\frac{7}{10}) = 350$$ liters.
=> Correct Answer: A (350 liters).
Problem 6
Tom had $1,200. He spent $$\frac{1}{3}$$ on rent and $$\frac{1}{4}$$ of the original total on groceries. How much money does he have left?

Show solution

Answer: $500

Step 1: Total fraction spent = $$\frac{1}{3} + \frac{1}{4} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12}$$.
Step 2: Fraction left $$= 1 - \frac{7}{12} = \frac{5}{12}$$.
Step 3: Money left $$= 1{,}200 \times (\frac{5}{12}) = 500$$.
=> Correct Answer: A ($500).

3. Sharing / Division

Dividing a fraction into equal parts

Part = Fraction / Number of people

When a fraction is shared among whole numbers, multiply the denominator by that number.

Example

$$A \frac{3}{4}$$ kg cake is divided equally among 3 friends. How much cake does each friend get?

Show solution

Step 1: Share formula = $$\frac{(\frac{3}{4})}{3} = (\frac{3}{4}) \times (\frac{1}{3})$$.

Step 2: Multiply $$= \frac{3}{12} = \frac{1}{4}$$ kg.

Result: $$\frac{1}{4}$$ kg each.

Practice problems

Problem 7
$$A \frac{1}{2}$$ liter bottle of juice is shared equally between 2 children. How much juice does each child get?

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Answer: $$\frac{1}{4}$$ liter

Step 1: Calculation = $$\frac{(\frac{1}{2})}{2} = (\frac{1}{2}) \times (\frac{1}{2}) = \frac{1}{4}$$ liter.
=> Correct Answer: A ($$\frac{1}{4}$$ liter).
Problem 8
A pizza chef has $$\frac{5}{6}$$ of a large pizza and cuts it equally into 5 slices. What fraction of the original pizza is each slice?

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Answer: $$\frac{1}{6}$$

Step 1: Calculation = $$\frac{(\frac{5}{6})}{5} = (\frac{5}{6}) \times (\frac{1}{5}) = \frac{5}{30} = \frac{1}{6}$$.
=> Correct Answer: A ($$\frac{1}{6}$$)
Problem 9
A farmer divides a $$\frac{7}{8}$$ acre plot of land equally among his 4 children. What fraction of an acre does each child receive?

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Answer: $$\frac{7}{32}$$ acre

Step 1: Calculation = $$\frac{(\frac{7}{8})}{4} = (\frac{7}{8}) \times (\frac{1}{4}) = \frac{7}{32}$$ acre.
=> Correct Answer: A ($$\frac{7}{32}$$ acre).

4. Mixed Ops (Time)

Real-world time management with fractions

Total Time = Sum of Parts

Convert hours/minutes into fractions or decimals to add or subtract them.

Example

John spent $$1 \frac{1}{2}$$ hours studying math and $$\frac{3}{4}$$ hour studying English. How many total hours did he study?

Show solution

Step 1: Convert to improper fractions: $$1 \frac{1}{2} = \frac{3}{2}$$.

Step 2: Find common denominator $$(4)$$: $$\frac{3}{2} = \frac{6}{4}$$.

Step 3: Add fractions: $$\frac{6}{4} + \frac{3}{4} = \frac{9}{4} = 2 \frac{1}{4}$$ hours.

Result: $$2 \frac{1}{4}$$ hours (or 2 hours 15 minutes).

Practice problems

Problem 10
Emma ran for $$\frac{1}{2}$$ hour and walked for $$\frac{1}{4}$$ hour. How long was her workout in total?

Show solution

Answer: $$\frac{3}{4}$$ hour

Step 1: Find common denominator = 4 -> $$\frac{1}{2} = \frac{2}{4}$$.
Step 2: Add times: $$\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$$ hour (45 minutes).
=> Correct Answer: A ($$\frac{3}{4}$$ hour).
Problem 11
A train trip takes $$2 \frac{1}{3}$$ hours, and a bus trip takes $$1 \frac{1}{2}$$ hours. How much longer is the train trip than the bus trip?

Show solution

Answer: $$\frac{5}{6}$$ hour

Step 1: Convert to improper fractions: $$2 \frac{1}{3} = \frac{7}{3}$$, $$1 \frac{1}{2} = \frac{3}{2}$$.
Step 2: Common denominator $$(6)$$: $$\frac{7}{3} = \frac{14}{6}$$, $$\frac{3}{2} = \frac{9}{6}$$.
Step 3: Subtract: $$\frac{14}{6} - \frac{9}{6} = \frac{5}{6}$$ hour (50 minutes).
=> Correct Answer: A ($$\frac{5}{6}$$ hour).
Problem 12
David spent $$1 \frac{3}{4}$$ hours doing homework, $$\frac{2}{3}$$ hour exercising, and $$\frac{1}{2}$$ hour cooking. What was the total time spent?
Show solution
Answer: $$2 \frac{11}{12}$$ hours

Step 1: Convert to improper fractions: $$1 \frac{3}{4} = \frac{7}{4}$$.
Step 2: Common denominator for 4, 3, 2 is 12.
- $$\frac{7}{4} = \frac{21}{12}$$
- $$\frac{2}{3} = \frac{8}{12}$$
- $$\frac{1}{2} = \frac{6}{12}$$
Step 3: Add: $$\frac{(21 + 8 + 6)}{12} = \frac{35}{12} = 2 \frac{11}{12}$$ hours.
=> Correct Answer: A ($$2 \frac{11}{12}$$ hours).