Using the area model to show equivalent fractions

We have seen that the fractions \(\dfrac{6}{8} \text{and} \dfrac{3}{4}\) mark the same point on the number line and so are equivalent.

Equivalence can also be shown using rectangles shaded to represent each fraction.

We start with a rectangle of area 1. Then we shade to show the fractions we want to compare. In each case the same area is shaded.

In this rectangle 6 out of 8 equal pieces have been shaded. So we say that \(\dfrac{6}{8}\) has been shaded.

In this rectangle 3 out of 4 equal pieces have been shaded. So we say that \(\dfrac{3}{4}\) has been shaded.