How to Use Area Models to Subtract Fractions with Like Denominators

A step-by-step guide to Using Area Models to Subtract Fractions with Like Denominators

Here’s a step-by-step guide to using area models to subtract fractions with like denominators:

Step 1: Understand the problem

Make sure you fully understand the fractions you need to subtract. For this example, let’s say we want to subtract \(\frac{5}{6} – \frac{2}{6}\).

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Step 2: Draw the area models

Draw two rectangles of equal size to represent the two fractions you’re subtracting. Label each rectangle with its respective fraction.

Step 3: Divide the area models

Divide each rectangle into equal parts based on the denominator. In our example, both denominators are 6, so divide each rectangle into 6 equal parts.

Step 4: Shade the parts

Shade the parts of the area models based on the numerators. In our example, shade 5 parts of the first rectangle (\(\frac{5}{6}\)) and 2 parts of the second rectangle (\(\frac{2}{6}\)).

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Step 5: Align the area models

Place the second area model (\(\frac{2}{6}\)) directly above or below the first area model (\(\frac{5}{6}\)) with the shaded parts aligned.

Step 6: Subtract the shaded parts

To subtract the fractions, remove the shaded parts of the second rectangle from the shaded parts of the first rectangle. In our example, remove 2 shaded parts (\(\frac{2}{6}\)) from the 5 shaded parts (\(\frac{5}{6}\)), leaving 3 shaded parts.

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Step 7: Write the difference as a fraction

Write the difference using the remaining number of shaded parts as the numerator and the original denominator. In our example, the difference is \(\frac{3}{6}\).

Step 8: Simplify if necessary

1. If the resulting fraction can be simplified, do so. In our example, \(\frac{3}{6}\) simplifies to \(\frac{1}{2}\).

So, using area models, we found that \(\frac{5}{6} – \frac{2}{6}= \frac{1}{2}\).

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