Finding Equivalent Fractions Using Bar Models (Missing Numerator & Denominator)

Finding Equivalent Fractions Using Bar Models (A Visual Way to “See” Fractions)

Equivalent fractions can feel a little mysterious at first. How can one-half be the same amount as three-sixths? The numbers look different — but the value is the same. That’s exactly why visual practice matters.

This worksheet, Finding Equivalent Fractions Using Bar Models, helps students recognize equivalent fractions by using pictures first. Each problem includes two fraction bars (also called bar models). Students count the shaded parts, compare the two bars, and then fill in the missing number to complete an equivalent fraction equation. Some problems have a missing numerator, and others have a missing denominator, so students get balanced practice with both.

What are equivalent fractions?

Two fractions are equivalent when they represent the same part of a whole, even if the numerator and denominator are different.

For example:

• \(\frac{1}{2}\) is equivalent to \(\frac{2}{4}\)

• \(\frac{2}{3}\) is equivalent to \(\frac{8}{12}\)
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A helpful way to think about it is this: equivalent fractions are like two different names for the same amount. The picture looks the same size — it’s just divided into a different number of equal parts.

Why bar models help so much

Bar models are one of the clearest tools for teaching equivalent fractions because they make the idea visual and concrete. Instead of guessing, students can:

1. Count how many equal pieces the whole is divided into (the denominator)

2. Count how many pieces are shaded (the numerator)

3. Compare the bars to confirm they show the same shaded amount

This is especially helpful for students who are still developing fraction number sense — or for kids who understand the math but benefit from a visual check.

How to use this worksheet

Each problem shows two stacked bar models representing the same whole. One fraction is written with a missing value. Students fill in the blank by matching the shading.