Equivalent Fractions Worksheets

Practise equivalent fractions

Equivalent fractions name the same value with different numbers. 1/2, 2/4, and 5/10 are all equal. This generator builds worksheets where each problem shows a fraction equal to a scaled-up version with one term blanked, and the student finds the missing number. It is the perfect bridge between understanding fractions and simplifying them.

How equivalent fractions work

Multiply (or divide) the numerator and denominator by the same number and the fraction's value stays the same. So 2/3 = 8/12 because both top and bottom were multiplied by 4. To find a missing term, work out the scale factor from the part you can see, then apply it to the other.

What you can customise

• Maximum factor: how far the fractions are scaled up.
• Problems per sheet: short practice or a full page.
• Answer key, Name & Date: for marking and classroom use.

How to use it

1. Set the maximum scale factor and number of problems.
2. Toggle the answer key and Name/Date fields.
3. Preview, press Generate New for a fresh set, then download or print.

Teaching ideas

Use fraction walls or strips alongside the worksheet so pupils can see why the fractions match. Mixing missing-numerator and missing-denominator problems (the generator does this automatically) keeps pupils thinking about the scale factor rather than guessing.

Why one amount has infinitely many names

½, ²⁄₄, ⁵⁄₁₀ and ⁵⁰⁄₁₀₀ are all the same quantity written differently. The list never ends, because you can keep cutting the same amount into more, smaller pieces.

That idea is worth stating explicitly, because children often believe a fraction has one correct form. It also explains why simplest form is a convention rather than a truth — ²⁄₄ is not wrong, it is simply not the tidiest of the available names.

Establish it physically before any arithmetic. Fold a strip of paper in half and shade one part; fold the same strip into quarters and the shading now covers two parts without anything having moved. Nothing was added, and the name changed.

The two directions, and which is harder

Making an equivalent fraction means multiplying or dividing the numerator and denominator by the same number.

Multiplying up is the easier direction and where children should start: ²⁄₃ × 4 gives ⁸⁄₁₂. Any multiplier works, so there is no wrong answer and no factor to find.

Dividing down is harder, because it only works when a common factor exists and the child has to find it. This is where equivalence meets simplifying, and it is the point at which many children stall.

Keep the two apart at first. A sheet of multiply-up questions builds the idea that the value does not change; a sheet of divide-down questions is really factor practice wearing a fraction costume, and it needs times-table fluency first.

Use a fraction wall before the numbers

A fraction wall — rows of equal-width strips divided into halves, thirds, quarters, fifths and so on — makes equivalence visible in a way a written rule cannot.

Lining up the rows shows immediately that ½ reaches exactly as far as ²⁄₄ and ³⁄₆, and that ⅓ sits between ¼ and ½. Children who have looked at that picture stop producing answers like "⅓ is bigger than ½ because 3 is bigger than 2".

It also sets up comparing and adding unlike fractions later, because the wall shows why a common denominator is needed: you cannot combine strips that are cut differently until you re-cut them the same way.