Multiplication of Fractions

The multiplication of fractions starts with the multiplication of the given numerators, followed by the multiplication of the denominators. Then, the resultant fraction is simplified further and reduced to its lowest terms, if needed.

There is an interesting rhyme to remember the steps given above. "Multiplying fractions is no big problem; Top times top over bottom times bottom. And don’t forget to simplify, Before it’s time to say goodbye." With this, let us now look ahead to learn more about the multiplication of fractions.

The multiplication of fractions is not like the addition or subtraction of fractions, where the denominator should be the same. Here, any two fractions with different denominators can easily be multiplied. The only thing to be kept in mind is that the fractions should not be in the mixed form, they should either be proper fractions or improper fractions. Let us learn how to multiply fractions through the following steps:

1. Multiply the numerators.
2. Multiply the denominators.
3. Reduce the resultant fraction to its lowest terms.

For example, let's multiply the following fractions: 2/3 × 4/5. We start by multiplying the numerators: 2 × 4 = 8, then, the denominators: 3 × 5 = 15. This can be written as: (2 × 4)/(3 × 5) = 8/15. Now, the product is already in its lowest terms, so we need not reduce it and we give this as the answer.

Now, let us see the visual representation for the multiplication of fractions. Visualizing multiplication of fractions using fractional squares is a very interesting method to understand the concept. Do you know what are fractional squares? Fractional squares are a representation of the given fraction in the form of squares where the numerator is indicated as the shaded portion. Let us see how to multiply a fraction using fractional squares. Let's multiply these two fractions: 2/3 × 1/2.

In the above figure, the fractional square on the left has 2 orange-shaded parts out of 3 equal sections. This orange area represents two-thirds of the fractional square. Similarly, the second shaded area represents half of the fraction square. By multiplying these two fraction squares, we get  2/6. This can be reduced to its simplest form and represented by one part of three squares. Thus, 2/3 × 1/2 = 2/6 = 1/3. Now that you have the insight into multiplying fractions, let us explore this topic further.

Now let us change the improper fraction obtained into a mixed fraction. 8/3 =  \(2\frac{2}{3}\). Two whole and two thirds which is equal to 8/3. Finally, we get the following representation.

Important Notes:

Here are a few important notes which are helpful in the multiplication of fractions.

• Generally, students simplify a fraction after multiplication. However, to make calculations easier, check if the two fractions to be multiplied are already in their lowest forms. If not, first simplify them and then multiply. For example, \(\begin{align} \frac{4}{12}\times \frac{5}{13}\end{align}\) will be difficult to multiply directly.
• Now, if we simplify the fraction first, we get: \(\begin{align}\frac{1}{3}\times \frac{5}{13} = \frac{5}{39}\end{align}\).
• Simplification can also be done across two fractions. If there is a common factor between the numerator of one of the fractions and the denominator of the other fraction, you can simplify them and proceed. For example, \(\begin{align}\frac{5}{28}\times \frac{7}{9}\end{align}\) can be simplified to \(\begin{align}\frac{5}{4}\times \frac{1}{9}\end{align}\) before multiplying.

How do You Multiply Fractions?

To multiply any two fractions, we can follow the steps given below:

• Multiply the numerators.
• Multiply the denominators.
• Simplify the resultant fraction to its lowest terms.

How do You Multiply Mixed Fractions?

The following steps can be used for the multiplication of mixed fractions:

• Change the mixed fraction to an improper fraction.
• Simplify if possible.
• Multiply the numerators and then the denominators.
• Ensure that the answer is in the lowest terms

How do you Multiply a Fraction With a Whole Number?

To understand the multiplication of a fraction with a whole number, we can take a simple numerical example of multiplication. 2/7 × 3. Start by rewriting the whole number (3 in this example) as a fraction, 3/1. Now, we can apply the steps that we use to multiply fractions.
2/7 × 3/1 = (2 × 3)/(7 × 1) = 6/7.

How do You Multiply a Fraction by a Fraction?

The multiplication between two fractions is the simplest form of arithmetic operations between two fractions. The numerators of both the fractions are to be multiplied first, followed by the multiplication of the denominators. Then, the resultant fraction is simplified to its lowest terms, if needed.

How do You Solve Fractions?

The solving of fractions involves two simple steps. First, the fractions, if given in the mixed fraction form, need to be converted into improper fractions. Then we can perform the required arithmetic operations between the fraction, and simplify the answer to its lowest terms.

How do You Add or Multiply Fractions?

The addition of fractions is different from the multiplication of fractions. In multiplication, first the numerators of the two fractions are multiplied, then the denominators are multiplied to obtain the resultant fraction. But in the process of addition of fractions, we first need to make the denominators of both the fractions equal and then we add the numerators to obtain the resultant fraction.

What is the Rule When You Multiply Fractions?

There are two simple rules for multiplying fractions. First, multiply the numerators, and then the denominators of both the fractions to obtain the resultant fraction. Secondly, we need to simplify the fraction obtained, to get the final answer. This can be understood by a simple example. 2/6 × 4/7 = ( 2 × 4)/(6 × 7) = 8/42 = 4/21

How do You Teach Multiplication of Fractions?

The multiplication of fractions can be taught in the same way as the multiplication of whole numbers. The important aspect, before the multiplication of fractions, is to convert the mixed fraction into an improper fraction. After this step, we multiply the numerators of both the fractions and then the denominators of both the fractions to obtain the resultant fraction.