Fractions are a basic part of mathematics that are taught at the primary school level. It is a very crucial concept of mathematics that helps students understand and solve many real-life problems in their careers at later stages. So, it is necessary to understand fractions and how we can perform different operations on these fractions. In this article, we will learn about fractions and how to multiply fractions using a calculator. Cuemath offers many such articles that help students learn mathematics and understand the concept well.

What are Fractions?

When we divide an object into smaller parts, then each part represents the fraction of the object. As an example, if we order a small size pizza, then it can be divided into four equal slices, and each slice can be represented by ¼ (fraction). In simple terms, a fraction represents a part of something.

The fraction consists of two parts, i.e., numerator and denominator. Both numerator and denominator get separated by a division sign ‘/’. We can write it as 

Numerator / Denominator.

Types of Fractions

Fractions are of three types:

  1. Proper Fractions:

Proper fractions have a numerator smaller than the denominator. For example, 1/2, 5/6, 2/7, 3/9, etc. are all proper fractions.

2. Improper Fractions:

Improper fractions are the type of fractions in which the numerator is greater than the denominator. The examples of improper fractions include 4/3, 7/2, 9/5, 11/6, 54/5, etc.

3. Mixed Fractions:

Mixed fractions are the type of fractions which consist of a whole number and a fraction. The examples of mixed fractions include 1 ½, 2 ¾, 5 1/3, 11 ½, etc.

All mathematical operations such as addition, subtraction, multiplication, and division can be performed on fractions. To perform these operations on mixed fractions, they need to be converted into the proper or improper fractions.

Conversion of the Mixed Fraction

We can convert the mixed fractions by multiplying the denominator with the whole number and then adding it to the numerator. The denominator will remain as it is. Follow the below step for conversion:

a b/c= (ac+b)/c

Example: Convert 3 1/2 into a simplified form

3 1/2 = 3×2+1/2 = 7/2

What is Multiplication?

Multiplication is an operation in mathematics that gives a product of two or more than two numbers. It can also be said to be the process of repeated additions. Multiplication is represented by the symbol ‘x’. Refer to the below terms used in reference to the multiplication operation:

  • Multiplicand: This is the number which is being multiplied.
  • Multiplier: This is the number which multiplies.
  • Product: This is the output of the multiplication. When multiplicand and multiplier multiplies, the product is generated.

It is written as:

Multiplicand x Multiplier = Product

As an example, 2 x 3 = 6

How to Multiply Fractions?

Multiplication of fractions is as simple as the multiplication of whole numbers. In fact, the fractions’ multiplication can be of below types:

  1. Multiplication of fraction with a fraction
  2. Multiplication of fraction with a whole number
  3. Multiplication of mixed type of fraction

Let us understand these types of fraction multiplications in detail.

Multiplication of Fraction with a Fraction

While multiplying two fractions, the numerators are multiplied with each other, and the denominators of the fractions are multiplied with each other.

Step1: Multiply numerator with numerator.

Step2: Multiply denominator with denominator.

Step3: Reduce the fraction if possible.

Let us understand it with the below illustration:

Suppose there are two fractions Numerator1/ Denominator1 and Numerator2/ Denominator2. When we multiply these two fractions, it can be written as

Numerator1/ Denominator1 x Numerator2/ Denominator2 = 

Numerator1 x Numerator2/ Denominator1 x Denominator2

Let us see some examples:

Example1: Multiply fractions 2/3 and 3/7

2/3 x 3/7 = 2 x 3 / 3 x 7 = 6 / 21

Example2: Multiply fractions 1/7 and 1/5

1/7 x 1/5 = 1 x 1 / 7 x 5 = 1/ 35

Similarly, we can multiply more than two fractions.

Example3: Multiply fractions 1/3, 2/3, and 1/5

1/3 x 2/3 x 1/5 = 1 x 2 x 1 / 3 x 3 x 5 = 2/ 45

Multiplication of Fraction with a Whole Number

When a whole number is multiplied with the fraction, the number gets multiplied with the numerator of the fraction.

Step1: Multiply the whole number with a numerator.

Step2: Keep the denominator as it is.

Step3: Reduce the resulting fraction if possible.

Consider the below illustration to understand this:

Multiply the whole number Num1 with Fraction Numerator / Denominator. It can be represented as

Num1 x Numerator / Denominator = Num1 x Numerator / Denominator

It can be understood with the below examples:

Example1: Multiply 2 and 3/5

2 x 3/5 = 2 x 3 / 5 = 6/5

Example2: Multiply 2, 1/3, and 1/5

2 x 1/3 x 1/5 = 2 x 1 x 1 / 3 x 5 = 2/15

Multiply Mixed Fractions

It is so simple to multiply the mixed fractions. You only need to convert the mixed fraction to a proper or improper fraction. As an example, the mixed fraction 3½ can be converted as 3×2+1/2 = 7/2.

Step1: Change the mixed fraction to proper or improper fraction.

Step2: Multiply the numerator with the numerator.

Step3: Multiply the denominator with the denominator.

Step4: Reduce the product if possible.

Let us check some example:

Example1: Multiply 1 ½ and 2¼.

1 ½ x 2 ¼ = 3/2 x 9/4 = 3 x 9 / 2 x 4 = 27/8

Example2: Multiply 3 ¼, ½, and 2¼.

3 ¼ x ½ x 2 ¼ = 13/4 x 1/2 x 9/4 = 13 x 1 x 9 / 4 x 2 x 4 = 117/32

Example3: Multiply 2 ¼, 3/2, and 3.

2 ¼ x 3/2 x 3 = 9/4 x 3/2 x 3 = 9 x 3 x 3 / 4 x 2 = 81/8

Multiply Fractions on a Calculator

The fractions multiplication can be simplified and made easy with the use of a calculator. Not all calculators multiply fractions. The scientific calculator has the fraction button using which you can multiply the fractions, however, you can use the traditional method too to multiply the fractions. Let us see both the methods to multiply fractions using a calculator.

  1. Multiply fractions using a scientific calculator.
  2. Multiply fractions using a traditional calculator.

Method1: Multiply Fractions Using a Scientific Calculator

The scientific calculators have a fractions button that lets you multiply the fractions directly.

Step1: Enter the numerator on the calculator and press the fraction button.

Step2: Enter the denominator.

Step3: Press the multiply button on the calculator.

Step4: Enter the numerator of the second fraction and press the fraction button.

Step5: Enter the denominator of the second fraction and press the equal to the button.

The product of the fractions will be visible on the calculator screen. You can change it to decimal form as well using the decimal button on the scientific calculator.

Method2: Multiply Fractions on a Traditional Calculator

In a traditional calculator, there is no fraction button. To multiply the fractions on a traditional calculator, you need to convert the fractions into decimal form and then multiply.

Step1: Change the fraction 1 to decimal form.

Step2: Change the fraction 2 to decimal form.

Step3: Multiply the decimal forms of the fractions on the calculator.

The product of the fractions will get displayed on the calculator screen in decimal form.

You can easily multiply two or more fractions using these methods. Also, you can multiply the whole number to the fraction or mixed fractions with any kinds of fractions.

Important Points About Fractions Multiplication

The fractions can be simplified before multiplying them. It will make multiplication easy and fast. This can be illustrated with the below example:

Consider the multiplication of 2/4 and 3/9.

2/4 x 3/9 = 2 x 3 / 4 x 9 = 6/36

Now, 6/36 can get simplified to 1/6.

If we simplify the fractions before multiplication, then the calculation will become easy. Here, 2/4 can get simplified to ½, and 3/9 can get simplified to 1/3.

Therefore, we will multiply the simplified forms of fractions as:

1/2 x 1/3 = 1 x 1 / 2 x 3 = 1/6

We can simplify the fractions across the multiple fractions too. It implies that if there is some common factor across the numerator of one fraction and denominator of the other fraction, then these fractions can be simplified, thus, making the multiplication easy. Consider the below example to understand.

Multiply 2/5 and 25/3.

Here 2/10 x 25/3 = 2 x 25 / 10 x 3 = 50/30 = 5/3

It can be done in a fast and easy way as below:

2/10 x 25/3

Here, the denominator of 2/5 has factors 5 and 2. Similarly, the numerator of fraction 25/3 has factors 5 and 5. So, 5 and 2 are the common factors between these two fractions.

So, 2/10 x 25/3 = 2 x 25 / 10 x 3 = 2 x 5 x 5 / 2 x 5 x 3 = 5/3

Final Words

We hope you have understood fractions and how to multiply fractions with the help of a calculator. You will find many such useful articles on Cuemath. If you also want to learn numbers, then Cuemath is the best source. Happy learning!