Grade 5 · Free worked lesson

Equivalent Fractions for Grade 5

Equivalent fractions name the same amount in different ways. In this fifth-grade lesson, use equal-sized wholes to see why changing both numbers by the same factor keeps the value the same.

Practise renaming a fraction, simplifying it and using an equivalent fraction to compare amounts.

1. Keep the same whole

A fraction’s denominator says how many equal parts make one whole. Its numerator says how many of those parts you have. To compare the shaded amounts in a model, the wholes must be the same size.

The bars are the same length. Two thirds and four sixths cover the same amount.

Split every third into two equal pieces. Each piece is now a sixth. The two shaded thirds become four shaded sixths: 2/3 = 4/6.

2. Multiply both numbers by the same factor

2/3 = (2 × 2)/(3 × 2) = 4/6

The number of shaded pieces doubles and the number of pieces in the whole doubles. The shaded amount stays the same.

Another example: 3/4 = 6/8, because 3 × 2 = 6 and 4 × 2 = 8. Multiplying by 2/2 multiplies by 1, so it does not change the fraction’s value.

A common mix-up

Adding 1 to the top and bottom does not generally make an equivalent fraction. For example, 1/2 and 2/3 are different amounts: one half is 3/6, while two thirds is 4/6.

3. Simplify by dividing both numbers

For 6/8, divide both 6 and 8 by 2: 6/8 = 3/4. This works because 2 is a common factor. Three quarters is in simplest form because 3 and 4 have no common factor greater than 1.

Use the same nonzero factor for both numbers. Dividing just the numerator or just the denominator changes the amount.

4. Use equivalent fractions to compare

Which is greater: 5/8 or 3/4? Rename 3/4 as 6/8. Both fractions now describe eighths of the same whole. Since 6 eighths is greater than 5 eighths, 3/4 is greater than 5/8.

This is why common denominators help: the pieces being counted have the same size.

Check your understanding

Try each question before opening the explanation.

One half is how many eighths?

4/8. Multiply both numbers in 1/2 by 4: 1 × 4 = 4 and 2 × 4 = 8.

Complete the equivalent fraction: 2/5 = ?/10.

4/10. The denominator was multiplied by 2, so multiply the numerator by 2 as well.

Simplify 9/12.

3/4. Divide both numbers by 3: 9 ÷ 3 = 3 and 12 ÷ 3 = 4. The numbers 3 and 4 have no common factor greater than 1.

Put the idea into practice

The free fractions sample includes this idea alongside related skills. It has five fixed questions and an explanation after every answer.

Play the free sample

Grade 5 Fractions Practice · Grade 5 Math Games

Examples and answers checked on 30 October 2026. Report a question about this lesson.