Fractions Operations Rules and Practice

A Grade 6 revision worksheet on mixed fractions, improper fractions, and operations with fractions.
Published

September 16, 2026

This worksheet is a short reminder of important fraction skills. Read each rule, study the example, and then try the practice sets.

1 Mixed fractions and improper fractions

A mixed fraction has a whole number and a fraction, such as \(2\frac{1}{3}\).

An improper fraction has a numerator that is equal to or greater than its denominator, such as \(\frac{7}{3}\).

1.1 Mixed fraction to improper fraction

  1. Multiply the whole number by the denominator.
  2. Add the numerator.
  3. Keep the same denominator.

Example: \(2\frac{1}{3}=\frac{2\times3+1}{3}=\frac{7}{3}\).

1.2 Improper fraction to mixed fraction

  1. Divide the numerator by the denominator.
  2. The answer from the division is the whole number.
  3. The remainder becomes the new numerator.
  4. Keep the same denominator.

Example: \(\frac{11}{4}=2\frac{3}{4}\) because \(11\) divided by \(4\) gives \(2\) with a remainder of \(3\).

2 Adding fractions

2.1 Same denominators

Keep the denominator, add the numerators, and simplify if possible.

Example: \(\frac{2}{7}+\frac{3}{7}=\frac{5}{7}\).

2.2 Different denominators

  1. Multiply the numerator and denominator of the first fraction by the denominator of the second fraction.
  2. Multiply the numerator and denominator of the second fraction by the denominator of the first fraction.
  3. Add the new numerators and keep the new denominator.
  4. Simplify the answer.

Example:

\[ \frac{1}{2}+\frac{1}{3}=\frac{1\times3}{2\times3}+\frac{1\times2}{3\times2}=\frac{3}{6}+\frac{2}{6}=\frac{5}{6} \]

2.3 Adding mixed fractions

  1. Change each mixed fraction into an improper fraction.
  2. Add the improper fractions.
  3. Change the answer back into a mixed fraction if needed.

Example: \(1\frac{2}{5}+2\frac{4}{5}=\frac{7}{5}+\frac{14}{5}=\frac{21}{5}=4\frac{1}{5}\).

3 Subtracting fractions

3.1 Same denominators

Keep the denominator, subtract the numerators, and simplify if possible.

Example: \(\frac{6}{9}-\frac{2}{9}=\frac{4}{9}\).

3.2 Different denominators

  1. Multiply the numerator and denominator of the first fraction by the denominator of the second fraction.
  2. Multiply the numerator and denominator of the second fraction by the denominator of the first fraction.
  3. Subtract the new numerators and keep the new denominator.
  4. Simplify the answer.

Example:

\[ \frac{3}{4}-\frac{1}{6}=\frac{3\times6}{4\times6}-\frac{1\times4}{6\times4}=\frac{18}{24}-\frac{4}{24}=\frac{14}{24}=\frac{7}{12} \]

3.3 Subtracting mixed fractions

  1. Change each mixed fraction into an improper fraction.
  2. Subtract the improper fractions.
  3. Change the answer back into a mixed fraction if needed.

Example: \(3\frac{1}{4}-1\frac{3}{4}=\frac{13}{4}-\frac{7}{4}=\frac{6}{4}=1\frac{1}{2}\).

4 Multiplying fractions

  1. Multiply the numerators.
  2. Multiply the denominators.
  3. Simplify the answer.

Example: \(\frac{2}{3}\times\frac{4}{5}=\frac{8}{15}\).

For a mixed fraction, first change it into an improper fraction. Example: \(1\frac{1}{2}\times\frac{2}{3}=\frac{3}{2}\times\frac{2}{3}=1\).

5 Dividing fractions

  1. Keep the first fraction.
  2. Change division to multiplication.
  3. Turn the second fraction upside down.
  4. Multiply and simplify.

Example: \(\frac{3}{4}\div\frac{2}{5}=\frac{3}{4}\times\frac{5}{2}=\frac{15}{8}=1\frac{7}{8}\).

For division by a whole number, write the whole number over \(1\). Example: \(\frac{5}{6}\div2=\frac{5}{6}\times\frac{1}{2}=\frac{5}{12}\).

6 Helpful reminders

  • The denominator tells the number of the equal parts.
  • The numerator tells how many parts we have.
  • For addition and subtraction, make the denominators the same by multiplying each fraction by the other fraction’s denominator.
  • For multiplication, just multiply the numerators and denominators directly.
  • For division, multiply by the reciprocal of the second fraction.
  • Always simplify the final answer when possible.
  • Check whether an improper answer should be written as a mixed fraction.

7 Practice set 1

  1. Change \(3\frac{2}{5}\) into an improper fraction.
  2. Change \(\frac{17}{4}\) into a mixed fraction.
  3. \(\frac{3}{8}+\frac{2}{8}\)
  4. \(\frac{1}{3}+\frac{1}{6}\)
  5. \(\frac{7}{10}-\frac{3}{10}\)
  6. \(\frac{5}{6}-\frac{1}{4}\)
  7. \(\frac{2}{5}\times\frac{3}{4}\)
  8. \(1\frac{1}{2}\times\frac{2}{3}\)
  9. \(\frac{3}{7}\div\frac{2}{5}\)
  10. \(2\frac{1}{4}\div\frac{3}{4}\)

8 Practice set 2

  1. Change \(4\frac{3}{7}\) into an improper fraction.
  2. Change \(\frac{23}{6}\) into a mixed fraction.
  3. \(2\frac{1}{5}+1\frac{3}{5}\)
  4. \(\frac{5}{8}+\frac{1}{4}\)
  5. \(4\frac{1}{3}-2\frac{2}{3}\)
  6. \(\frac{7}{9}-\frac{1}{6}\)
  7. \(\frac{3}{10}\times\frac{5}{6}\)
  8. \(2\frac{2}{3}\times\frac{3}{4}\)
  9. \(\frac{5}{8}\div\frac{10}{11}\)
  10. \(3\frac{1}{2}\div\frac{7}{8}\)

9 Practice set 3

  1. Change \(5\frac{5}{9}\) into an improper fraction.
  2. Change \(\frac{31}{5}\) into a mixed fraction.
  3. \(3\frac{3}{4}+2\frac{5}{8}\)
  4. \(\frac{7}{12}+\frac{5}{18}\)
  5. \(6\frac{1}{5}-3\frac{4}{5}\)
  6. \(\frac{11}{12}-\frac{2}{9}\)
  7. \(\frac{4}{7}\times\frac{14}{15}\)
  8. \(1\frac{3}{5}\times2\frac{1}{2}\)
  9. \(\frac{7}{9}\div\frac{14}{15}\)
  10. \(4\frac{1}{2}\div1\frac{1}{8}\)