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Quizzes > Mathematics > Basic Math & Arithmetic

Think You Can Solve These Fractions Word Questions?

Challenge yourself with fraction word problems and answers!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration promoting a free fractions word questions quiz on a golden yellow background.

This Fractions Word Questions quiz helps you practice solving real-world fraction problems with addition, subtraction, multiplication, and division, and check each answer as you go. You get instant feedback to fix mistakes fast. When you finish, try the full fractions quiz for more practice.

If John ate 1/4 of a pizza and Mary also ate 1/4 of the same pizza, what fraction of the pizza has been eaten in total?
1
3/4
1/2
1/4
To add fractions with the same denominator, simply add the numerators: 1 + 1 = 2 over 4, which simplifies to 1/2. This demonstrates basic fraction addition where the denominator remains constant. .
Which fraction is greater: 3/5 or 2/3?
3/5
Both are equal
Cannot determine
2/3
Compare by cross-multiplying: 3×3 = 9 and 5×2 = 10, so 2/3 is larger than 3/5. Cross-multiplication is a reliable way to compare fractions with different denominators. .
What is 5/6 minus 1/6?
2/3
5/12
4/6
1/2
Subtract the numerators: 5 ? 1 = 4 over the common denominator 6, giving 4/6, which simplifies to 2/3. Simplification reduces the fraction to simplest terms. .
What is 1/3 + 1/6?
2/5
1/6
1/2
3/9
Convert to a common denominator of 6: 1/3 = 2/6, so 2/6 + 1/6 = 3/6 = 1/2. Working with a common denominator makes addition straightforward. .
What is 2/3 × 3/4?
5/6
3/7
1/2
1/4
Multiply numerators and denominators: (2×3)/(3×4) = 6/12, which simplifies to 1/2. Fraction multiplication requires no common denominators. .
What is 3/5 ÷ 1/5?
5/3
2/5
3
1
Dividing by a fraction is the same as multiplying by its reciprocal: 3/5 × 5/1 = 15/5 = 3. Always flip the divisor when dividing fractions. .
Simplify the fraction 10/15.
4/6
3/5
2/3
5/8
Divide numerator and denominator by their GCD, which is 5: (10÷5)/(15÷5) = 2/3. Simplification makes fractions easier to read. .
What is 7/8 of 16?
7
8
12
14
Multiply the fraction by the whole number: 7/8 × 16 = (7×16)/8 = 112/8 = 14. Fraction-of-a-number problems use multiplication. .
Sarah has 3/4 yard of ribbon and uses 2/5 of it. How much ribbon does she use?
1/2 yard
3/10 yard
5/12 yard
1/5 yard
Multiply: 3/4 × 2/5 = 6/20, which simplifies to 3/10 yard. Fraction-of-a-quantity involves multiplication. .
A recipe calls for 2/3 cup of sugar. You want to make half the recipe. How much sugar do you need?
2/6 cup
2/5 cup
1/3 cup
1/4 cup
Half of 2/3 is (1/2)×(2/3) = 2/6 = 1/3 cup. You multiply the given fraction by 1/2. .
Sam ran 5/8 mile on Monday and 3/4 mile on Tuesday. How many miles did he run in total?
7/8 mile
11/8 mile
13/8 mile
1 1/4 miles
Convert to eighths: 3/4 = 6/8, so 5/8 + 6/8 = 11/8 miles. Adding with a common denominator combines the distances. .
4/5 of a class of 40 students finished a test in 30 minutes. How many students finished early?
20
36
32
8
Multiply: 4/5 × 40 = 160/5 = 32 students. Fraction-of-whole problems use multiplication directly. .
Lisa drank 2/3 liter of juice and John drank 3/8 liter. How much juice did they drink in total?
11/8 liter
25/24 liter
37/24 liter
1 1/2 liters
Convert to twenty-fourths: 2/3 = 16/24, 3/8 = 9/24, sum = 25/24 liters. Combining fractions often requires a common denominator. .
What is 4/9 ÷ 2/3?
1/3
3/4
2/3
4/5
Divide by multiplying the reciprocal: 4/9 × 3/2 = 12/18 = 2/3 after simplification. Reciprocal use is key for fraction division. .
What is 7/12 minus 1/3?
5/12
1/3
1/4
1/6
Convert 1/3 to 4/12, then subtract: 7/12 ? 4/12 = 3/12, which simplifies to 1/4. Consistent denominators simplify subtraction. .
A car travels 3/4 of its journey in 6 hours at a constant speed. How long will the entire journey take?
7.5 hours
8 hours
9 hours
10 hours
If 3/4 of the distance takes 6 hours, the full distance corresponds to 6 ÷ (3/4) = 6 × (4/3) = 8 hours. You invert the fraction of the distance to find total time. .
Compute 5/12 ? 1/18.
13/36
7/36
1/6
1/4
Find a common denominator of 36: 5/12 = 15/36, 1/18 = 2/36, so 15/36 ? 2/36 = 13/36. This uses the standard subtraction method. .
A tank is 2/3 full and contains 90 liters of water. How many liters are needed to fill it completely?
45 liters
30 liters
60 liters
15 liters
If 2/3 of capacity is 90 L, then full capacity is 90 ÷ (2/3) = 90 × (3/2) = 135 L. The amount needed is 135 ? 90 = 45 L. Alternatively, 1/3 of 135 is 45. .
A mixture contains 3/5 juice and water in a 20-liter container. How many liters of juice are in the mixture?
15 liters
10 liters
8 liters
12 liters
Multiply the fraction by the total: 3/5 × 20 = 60/5 = 12 L of juice. This is a straight fraction-of-whole calculation. .
Sam eats 2/3 of 3/4 of a cake. What fraction of the entire cake does he eat?
1/2
2/5
1/3
3/8
Multiply the fractions: 2/3 × 3/4 = 6/12 = 1/2. Sequential fraction multiplication gives the portion eaten. .
Evaluate 7/8 ÷ (1/2 ? 1/4).
3
7/2
2 1/2
14/8
Compute inside parentheses: 1/2 ? 1/4 = 1/4. Then divide: 7/8 ÷ 1/4 = 7/8 × 4/1 = 28/8 = 7/2. Parentheses must be resolved first. .
Solve for x: x/4 + x/6 = 5/12.
5/6
1/2
1
2
Multiply both sides by 12 (LCD): 3x + 2x = 5, so 5x = 5 and x = 1. Clearing denominators simplifies solving. .
A rectangular garden is 3/5 m wide and its length is 7/8 times its width. What is the area of the garden in square meters?
63/200
21/40
7/8
9/25
Width = 3/5, length = (7/8)×(3/5) = 21/40. Area = (3/5) × (21/40) = 63/200 m². Multi-step fraction multiplication is required. .
John spent 1/4 of his money, then 1/3 of the remaining. If he has $20 left, how much did he start with?
30
40
50
60
After spending 1/4, 3/4 remains; then spending 1/3 of that leaves 2/3 of 3/4 = 1/2 of the original. So 1/2 of the start = 20, start = $40. Track fractions of the remainder. .
A mixture is 5/8 A and 3/8 B. You remove 1/4 of the mixture and replace it with pure B. What fraction of the new mixture is A?
3/32
15/32
3/8
5/16
Initial A = 5/8. After removing 1/4 of total, A left = 5/8 × 3/4 = 15/32 of the original. You then add pure B, so total mixture is 1, and fraction A remains 15/32. .
0
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Study Outcomes

  1. Understand Fractions Word Questions -

    Identify key terms and conversion steps to translate text-based scenarios into fraction equations.

  2. Apply Addition and Subtraction Techniques -

    Execute accurate addition and subtraction of fractions in various word problem contexts.

  3. Interpret Fraction Word Problems with Answers -

    Use provided solutions to verify your work and reinforce effective fraction problem solving strategies.

  4. Analyze Equivalent Fractions -

    Simplify and compare fractions to streamline calculations and improve accuracy in word questions.

  5. Evaluate Solutions Using Instant Feedback -

    Diagnose errors quickly and refine your approach to fraction problem solving with answers.

  6. Master How to Solve Fraction Word Problems -

    Integrate all learned methods to confidently tackle and solve challenging fraction word problems.

Cheat Sheet

  1. Interpreting Fraction Phrases -

    Interpreting key fraction phrases in word problems helps translate sentences into operations. Terms like "half of," "third more," or "one-fifth left" map to specific fractions or arithmetic steps, and drawing pie charts or bar models from Purdue University's practice guides makes these associations concrete. For example, "three-fifths of 20" becomes 3/5 × 20 = 12.

  2. Converting Mixed Numbers -

    Converting mixed numbers to improper fractions ensures smooth arithmetic operations. Multiply the whole number by the denominator, add the numerator, then place that sum over the original denominator (e.g., 2 3/4 → (2×4+3)/4 = 11/4). Khan Academy's fraction word problems with answers resource recommends this method for consistent results.

  3. Finding Common Denominators -

    Finding common denominators is essential for adding and subtracting fraction word questions. Determine the least common multiple of denominators, adjust each fraction to an equivalent form (e.g., 1/4 + 1/6 → LCM 12 → 3/12 + 2/12 = 5/12), and only then combine numerators. University of Nottingham's math resources show this systematic approach avoids errors and streamlines calculation.

  4. Multiplying and Dividing Fractions -

    Multiply and divide fractions using consistent rules and the "keep-change-flip" (KCF) trick. Always multiply numerators together and denominators together, and for division invert the second fraction and multiply (e.g., 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6). The National Council of Teachers of Mathematics highlights KCF as a reliable fraction problem solving with answers strategy.

  5. Estimation and Inverse Operations -

    Use estimation and inverse operations to check your solutions in fraction word problems. Round fractions to the nearest half or whole to quickly approximate answers, then reverse the operation - like multiplying after an addition - to confirm accuracy. Stanford University studies on mathematical confidence advocate these techniques to catch errors early and build trust in your results.

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