How to Use Area Models to Find Equivalent Fractions

Using area models is an effective visual method for finding equivalent fractions. An area model is a rectangle that represents the whole (1) and is divided into equal parts, where each part represents a fractional unit. By dividing the rectangle into different numbers of equal parts and shading the corresponding parts, you can visually demonstrate equivalent fractions.

How to Use Area Models to Find Equivalent Fractions

A Step-by-step Guide to Using Area Models to Find Equivalent Fractions

Here’s a step-by-step guide to using area models to find equivalent fractions:

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Step 1: Identify the given fraction:

Determine the fraction for which you want to find an equivalent fraction. For example, let’s choose the fraction \(\frac{2}{3}\).

Step 2: Draw a rectangle:

Begin by drawing a rectangle that will represent the whole, or 1.

Step 3: Divide the rectangle into equal parts:

Divide the rectangle into a number of equal parts representing the denominator of the given fraction. For example, if the given fraction is \(\frac{2}{3}\), divide the rectangle into 3 equal parts.

Step 4: Shade the appropriate parts:

Shade the number of parts that correspond to the numerator of the fraction. In our example of \(\frac{2}{3}\), shade 2 out of the 3 equal parts.

Step 5: Create another area model:

Draw another rectangle of the same size, representing another whole.

Step 5: Choose a new denominator:

Decide on a new denominator for the equivalent fraction you want to find. For example, if you want to find an equivalent fraction with a denominator of 6, you will divide the new rectangle into 6 equal parts.

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Step 6: Divide the new rectangle into different equal parts:

Divide the new rectangle into the chosen number of equal parts, representing the denominator of the new fraction. In our example, divide the new rectangle into 6 equal parts.

Step 7: Shade equivalent parts:

Shade the same proportion of parts in the new rectangle as you did in the original rectangle. In our example, since we shaded 2 out of 3 parts in the original rectangle, we will shade 4 out of 6 parts in the new rectangle (because \(\frac{4}{6}\) represents the same proportion as \(\frac{2}{3}\)).

Step 7: Identify the equivalent fraction:

The shaded parts of the new rectangle represent the equivalent fraction. In our example, we shaded 4 out of 6 equal parts, so the equivalent fraction is \(\frac{4}{6}\).

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