Multiplying Fractions Using Area Model

An area model is a rectangular diagram that visually illustrates the multiplication of two fractions. The rectangle is divided into sections based on the denominators of the fractions, with one fraction represented along the length and the other along the width. The intersection of these sections highlights the product of the fractions.

Here is a video showing the multiplication of two fractions. 

Steps

Let us multiply ${\dfrac{2}{5}\times \dfrac{3}{4}}$

Drawing a Rectangle

First, we will draw a large rectangle.

Representing the First Fraction

The denominator of the first fraction indicates the number of columns to divide the rectangle into, while the numerator tells us how many of those columns should be shaded.

Here, ${\dfrac{2}{5}}$ represents 2 shaded columns out of 5 columns of the rectangle.

Representing the Second Fraction   

The denominator of the second fraction determines the number of rows to divide the rectangle into, while the numerator specifies how many of those rows should be shaded.

Here, ${\dfrac{3}{4}}$ represents 3 shaded rows out of 4 rows in the rectangle.

Finding the Product

The numerator of the product is the number of sections that have been shaded twice (the overlapping area), while the denominator is the total number of sections within the rectangle.

Here, 6 parts are shaded twice out of 20 total parts.

Thus, the product is ${\dfrac{6}{20}}$

Simplifying (If Necessary)

Simplifying further, we get 

${\dfrac{6}{20}}$ = ${\dfrac{3}{10}}$