Year 6 Fractions — Revision Notes & Free Printable Worksheets

Learn Year 6 fractions with simple explanations, visual examples and free printable worksheets. Revise each skill, then practise at Foundation, Developing or Challenge level.

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Fractions Revision Notes & Worked Examples

1. Understanding Fractions

A fraction shows part of a whole. The whole must be divided into equal parts.

3 shaded parts out of 4 equal parts

\frac{3}{4}

Numerator (3): The number of parts selected.
Denominator (4): The number of equal parts in one whole.

A proper fraction has a numerator smaller than its denominator. An improper fraction has a numerator greater than or equal to its denominator.

REMEMBER
The denominator tells us how many equal parts make one whole.

2. Equivalent Fractions

Equivalent fractions look different but have the same value.

\frac{1}{2}=\frac{2}{4}

Example: To change fifths into tenths, multiply the numerator and denominator by 2.

\frac{3}{5}=\frac{6}{10}

REMEMBER
Multiply or divide the numerator and denominator by the same non-zero number.

3. Simplifying Fractions

Simplifying means writing a fraction using the smallest possible whole numbers.

Example: Simplify twelve-eighteenths. Divide both numbers by 6.

\frac{12}{18}=\frac{2}{3}

12 ÷ 6 = 2 and 18 ÷ 6 = 3. The answer cannot be simplified further.

REMEMBER
Divide the numerator and denominator by the same common factor.

4. Finding a Fraction of an Amount

Divide the amount by the denominator, then multiply by the numerator.

Example: Find three-quarters of 20.

\frac{3}{4}\times20

20 ÷ 4 = 5
5 × 3 = 15
Answer: 15

REMEMBER
Divide by the denominator, then multiply by the numerator.

5. Adding and Subtracting Fractions

Fractions must have the same denominator before you add or subtract them.

Example: Add one-third and one-sixth.

\frac{1}{3}+\frac{1}{6}=\frac{2}{6}+\frac{1}{6}=\frac{1}{2}

Change one-third into two-sixths. Add the numerators, then simplify.

REMEMBER
Make the denominators the same. Add or subtract the numerators, not the denominators.

6. Multiplying a Fraction by a Whole Number

Multiply the numerator by the whole number. Keep the denominator the same.

Example: Multiply two-fifths by 3.

\frac{2}{5}\times3=\frac{6}{5}=1\frac{1}{5}

REMEMBER
Multiply the numerator by the whole number, then simplify if needed.

7. Dividing a Fraction by a Whole Number

Dividing a fraction into equal groups makes each share smaller.

Example: Divide three-quarters by 2.

Start with 6 shaded eighths

Share the 6 shaded eighths between 2 groups

Group 1: 3 eighths

Group 2: 3 eighths

Three-quarters is six-eighths. Share the six shaded eighths equally between two groups.

\frac{3}{4}\div2=\frac{3}{8}

REMEMBER
Dividing a positive fraction by a whole number greater than 1 gives a smaller answer.

8. Comparing and Ordering Fractions

Use equivalent fractions with a common denominator to compare their values.

Example: Which is greater, two-thirds or three-fifths?

\frac{2}{3}\qquad\frac{3}{5}

The lowest common denominator is 15.

\frac{2}{3}=\frac{10}{15}\qquad\frac{3}{5}=\frac{9}{15}

10 is greater than 9, so two-thirds is greater than three-fifths.

\frac{2}{3}>\frac{3}{5}

REMEMBER
A common denominator makes fractions easier to compare and order.

Practice Worksheets & Answer Keys

Practise your fractions skills with free printable worksheets. Start with Foundation and progress to more challenging questions.