Fractions Worksheets

What these worksheets practise

A fraction names part of a whole: in $\tfrac{3}{4}$, the denominator 4 says how many equal parts the whole is cut into, and the numerator 3 says how many of them you have. These worksheets practise the four operations on fractions, one operation per worksheet.

Choose a maximum denominator (6 or 12) and whether to use mixed numbers such as $2\tfrac{1}{2}$. Every fraction in a problem is in lowest terms, subtraction answers are never negative, and every answer is given in simplest form, with improper fractions written as mixed numbers.

How each operation works

• Add or subtract: rewrite both fractions with a common denominator, then add or subtract the numerators.
• Multiply: multiply the numerators and multiply the denominators.
• Divide: multiply by the reciprocal of the second fraction ("keep, change, flip").
• Mixed numbers: change them to improper fractions first, then use the rules above.

Worked examples

Addition: $\tfrac{1}{4} + \tfrac{2}{3}$

Subtraction: $\tfrac{5}{6} - \tfrac{1}{4}$

Multiplication: $\tfrac{2}{3} \times \tfrac{3}{5}$

Division: $\tfrac{3}{4} \div \tfrac{2}{5}$

Mixed numbers: $1\tfrac{2}{3} + 2\tfrac{1}{2}$

Check your answers

Estimate first: $\tfrac{1}{4} + \tfrac{2}{3}$ is a little less than 1, so $\tfrac{11}{12}$ is reasonable, while $\tfrac{3}{7}$ (less than a half) cannot be right.

Common mistakes

• Adding the denominators. $\tfrac{1}{4} + \tfrac{2}{3}$ is not $\tfrac{3}{7}$. Only the numerators are added, after the denominators match.
• Forgetting to flip when dividing. $\tfrac{3}{4} \div \tfrac{2}{5}$ is $\tfrac{3}{4} \times \tfrac{5}{2}$, not $\tfrac{3}{4} \times \tfrac{2}{5}$.
• Leaving the answer unsimplified. $\tfrac{6}{15}$ is correct but not finished; $\tfrac{2}{5}$ is the simplest form.
• Multiplying mixed numbers part by part. $2\tfrac{1}{2} \times 1\tfrac{1}{3}$ is not $2\tfrac{1}{6}$. As improper fractions, $\tfrac{5}{2} \times \tfrac{4}{3} = \tfrac{20}{6} = 3\tfrac{1}{3}$.

A practice path through the settings

1. Addition and subtraction, denominators up to 6. The common denominator is never more than 30 (for sixths and fifths), so it can be found by listing multiples.
2. Denominators up to 12. Common denominators can now reach 132 (for elevenths and twelfths), so the least common multiple becomes worth finding properly.
3. Multiplication, then division. No common denominator is needed, but simplifying the answer is.
4. Mixed numbers. Turn this on last: every problem then starts by converting to improper fractions.

Each answer is given in simplest form, so the answer sheet also shows whether a student finished simplifying.

Sample problems

These problems come from the same generator as the worksheet above. Press Generate for a fresh set.

Addition

1. $\dfrac{1}{4} + \dfrac{1}{5} =$
2. $\dfrac{1}{2} + \dfrac{1}{6} =$

Subtraction

3. $\dfrac{3}{5} - \dfrac{1}{2} =$
4. $\dfrac{2}{5} - \dfrac{1}{3} =$

Multiplication

5. $\dfrac{2}{3} \times \dfrac{1}{5} =$
6. $\dfrac{3}{5} \times \dfrac{1}{5} =$

Division

7. $\dfrac{2}{3} \div \dfrac{1}{2} =$
8. $\dfrac{4}{5} \div \dfrac{1}{2} =$

Mixed numbers

9. $3\tfrac{2}{3} + 4\tfrac{1}{2} =$
10. $5\tfrac{1}{3} + 3\tfrac{2}{3} =$

Tips for teachers and parents

• Start with denominators up to 6: the common denominators are small enough to find by listing multiples.
• Fraction bars or a pizza drawing make the need for a common denominator easy to see.
• Turn on mixed numbers only after the four operations are secure with simple fractions.

Related topics

• Decimals Basic Math 2
• Percentages Basic Math 2
• Ratios & Proportions Pre-Algebra