Before you calculate, look at what you are given and what you are asked, because that decides the operation. For example, to subtract 7/9 − 1/6 you rewrite both fractions as eighteenths (14/18 − 3/18) and get 11/18. Below are 15 worked exercises, ordered by level, and each one ends with a check that does not just repeat the calculation. If you want exercises without the solution in view, open the worksheet generator.
| What you are given | What you do | Exercise |
|---|---|---|
| Two parts of the same whole that are put together or taken away | Add or subtract with a common denominator | 4 and 5 |
| A fraction of a quantity | Multiply | 3 and the recipe |
| How many times one quantity fits into another | Divide | 7 |
| Two values that have to be put in order | Cross-multiply | 2 |
| A part and its fraction, the total is missing | Divide the part by the fraction | Practice 3 |
The words in a problem help less than the relationship between the quantities, which is why the table asks what you are given. For more practice, the fraction worksheets index gathers sheets by topic.
Basic level
1. Equivalent fractions
Are 10/15 and 2/3 equal? Divide the numerator and denominator of 10/15 by 5 and you get 2/3. You can confirm it by cross-multiplying, since 10 × 3 = 30 and 15 × 2 = 30, which match. Dividing only the numerator would give 2/15, a much smaller value. To generate more ways of writing the same value, use equivalent fractions.
2. Comparing without rounding
Which is larger, 5/8 or 2/3? Cross-multiply, with 5 × 3 = 15 and 2 × 8 = 16. Since 15 is less than 16, 5/8 is less. In decimals, 5/8 = 0.625 and the other fraction is ≈ 0.667 (error less than 0.001), which gives the same order. Looking only at the numerators would suggest the opposite, because the denominators change the size of each part. To practice cross-multiplying with other pairs, use compare fractions.
3. A fraction of a quantity
Of 28 tiles, 3/7 are marked. One seventh of 28 is 4 tiles and three sevenths is 12. The result carries its unit: 12 tiles. To check, 12 out of 28 reduces by dividing by 4, which gives 3 out of 7.
Operations with fractions
4. Adding with different denominators
Find 1/6 + 3/8. The LCM of 6 and 8 is 24, so 1/6 = 4/24 and 3/8 = 9/24. The sum is 13/24, which cannot be simplified. In decimals, 1/6 ≈ 0.167 (error less than 0.001), 3/8 = 0.375 and 13/24 ≈ 0.542 (error less than 0.001), which agrees with the sum.
5. Subtracting
Find 4/5 − 1/3. The LCM of 5 and 3 is 15, so 12/15 − 5/15 = 7/15. The denominator is not subtracted, because both quantities are already in fifteenths. To check, add back what you subtracted: 7/15 + 5/15 = 12/15 = 4/5. In subtract fractions you can see the common denominator for any pair.
6. Multiplying and reducing
Find 4/9 × 3/8. Multiply top and bottom: 12/72, which reduces by dividing by 12 to give 1/6. You can also cancel first: 3 and 9 divide by 3, and 4 and 8 divide by 4, leaving one third times one half. The product of two fractions less than 1 has to be less than each factor. More practice in multiply fractions.
7. Dividing by a fraction
Find 9/10 ÷ 3/5. Keep the first fraction and flip the second, which gives 9/10 × 5/3 = 45/30 = 3/2. The question is how many three fifths fit into nine tenths, and one and a half do. To check, 3/2 × 3/5 = 9/10, which is the dividend. You flip the divisor, never the dividend. See also divide fractions.
8. Adding mixed numbers
Find 2 2/5 + 1 3/10. Convert each mixed number to an improper fraction to get 12/5 + 13/10 = 24/10 + 13/10 = 37/10 = 3 7/10. Working by parts gives the same result, because the wholes add up to 3 and the fractions are 4/10 + 3/10 = 7/10. Mixed numbers have their own calculator.
9. Combined operations
Find (5/6 − 1/3) × 4/5. Parentheses first, with 5/6 − 2/6 = 3/6 = 1/2. Then multiply by 4/5: 4/10 = 2/5. If you multiplied before subtracting, you would get 5/6 − 4/15 = 17/30, a different value. By size, the parentheses are worth less than 1, so the result must be less than 4/5. The full order of operations is in fraction expressions.
Word problems
In a word problem, the calculation is the easy part and deciding which one to do is the hard part. Write down what you are given, what you are asked, and in what unit, and then choose the operation.
Worked example: a recipe for 6 servings made for 4
A soup recipe for 6 servings uses 3/4 cup of broth. You want to make it for 4 servings. How much broth do you need?
- Decide. You are making 4 of the 6 servings, which is 4/6 of the recipe. Taking a fraction of a quantity means multiplying.
- Set up. 3/4 × 4/6.
- Cancel. The 4 in the numerator and the 4 in the denominator cancel, leaving 3/6.
- Reduce. 3/6 = 1/2.
You need 1/2 cup of broth.
Check: with 6 servings you have 3 of the 4 parts of a cup, so each serving gets 1/8 cup. Four servings take 4/8 cup. Since there are fewer servings, it has to be less broth than in the full recipe.
Worked example: a board with a piece cut off
A board is 2 1/2 m long and you cut off a piece 3/10 m long. How long is what is left?
- You take a part away from a length, so it is a subtraction.
- Convert 2 1/2 to an improper fraction: 5/2 = 25/10.
- Subtract with the same denominator: 25/10 − 3/10 = 22/10.
- Simplify: 22/10 = 11/5 = 2 1/5.
The board has 2 1/5 m left.
Check: 2 2/10 m plus the 3/10 m piece makes 2 5/10 m, the original length. Also, what is left is less than at the start.
Practice with four more problems
- In a class of 30 students, 2/5 ride the bus. How many ride the bus?
- A movie lasts 0.75 h. Write that as a fraction of an hour and in minutes.
- The 18 students who passed are 3/5 of the whole class. How many students are in the class?
- You read 1/5 of a book on Monday and 1/3 of what is left on Tuesday. What fraction of the book is still unread?
See the answers
- This is a fraction of a quantity, with 30 ÷ 5 = 6 and 2 × 6 = 12 students. To check, 12 out of 30 reduces by dividing by 6 and gives 2/5.
- 0.75 = 3/4 of an hour. A quarter of 60 minutes is 15, and three quarters is 3 × 15 = 45 minutes. To check, 45/60 reduces to 3/4. The fraction of an hour to minutes conversion covers more cases.
- The total is missing, so 18 ÷ 3/5 = 18 × 5/3 = 30 students. To check, 3/5 of 30 is 18.
- After Monday, 4/5 is left. On Tuesday you read 1/3 of that, which is 4/15, so 12/15 − 4/15 = 8/15 of the book is left. To check, 3/15 on Monday, 4/15 on Tuesday and 8/15 unread add up to 15/15.
How to keep practicing
Exercises 1 and 2 have their own sheets in equivalent fractions and comparing and ordering. Exercises 4 and 5 are in adding and subtracting, 6 in multiplying, 7 in dividing and 8 in mixed number operations. When you mix operations, use the sheets for all four operations and, for more word problems, the fraction word problems page.
Solve by hand and then check in the answer checker, which tells an equivalent fraction from one that can still be reduced. The main calculator can repeat any calculation on this page with exact values.
Sources
The Math Is Fun fractions index, accessed October 17, 2026, extends the explanations on this page with separate lessons on equivalent fractions, comparing, adding, subtracting, multiplying, dividing and mixed numbers, plus interactive tools. The exercises on this page run from elementary to middle school, and that index covers the same topics for extra practice.