Multiplying Fraction With Whole Numbers - Cuemath

Multiplying Fractions With Whole Numbers

For multiplying fractions with whole numbers, the whole number is written in the fraction form and then multiplied with the given fraction using the rules of multiplication of fractions. While multiplying fractions with whole numbers, it should also be remembered that the given fractions should be in the form of a proper fraction or an improper fraction. Let us learn more about multiplying fractions with whole numbers, along with some examples.

1.	What is Multiplying Fractions With Whole Numbers?
2.	How to Multiply Fractions With Whole Numbers?
3.	How to Multiply Mixed Fractions with Whole Numbers?
4.	FAQs on Multiplying Fractions With Whole Numbers

What is Multiplying Fractions With Whole Numbers?

Multiplying fractions with whole numbers is similar to repeated addition where the fraction is added the same number of times as the whole number. For multiplying fractions, we first multiply the numerators, then multiply the denominators, and finally, reduce the resultant fraction to its lowest terms. However, when we need to multiply fractions with whole numbers, we write the whole number in the form of a fraction by writing 1 as its denominator. After this step, we can multiply it using the same rules. For example, when we multiply the fraction a/b × c/d, we get (a × c) / (b × d). This rule is applicable while multiplying fractions with whole numbers as well.

How to Multiply Fractions With Whole Numbers?

Multiplying fractions with whole numbers is an easy concept. We just need to convert the whole number into a fraction by writing 1 as the denominator and writing the whole number as the numerator. Then it is multiplied by the given fraction. After multiplying these, the final result should be in the form of a proper fraction or a mixed fraction. If the result is in an improper fraction, we convert it to a mixed fraction. Let us understand the steps with the help of an example.

Example: Multiply 1/8 × 5

Solution: Here, 1/8 is the fraction and 5 is the whole number.

• Step 1: Convert the whole number to a fraction by writing 1 as the denominator. This means 5 is written as 5/1
• Step 2: Multiply the numerators. Here, 1 × 5 = 5
• Step 3: Multiply the denominators. Here, 8 × 1 = 8
• Step 4: Simplify and reduce the product, if needed. If the result is an improper fraction, we convert it to a mixed fraction. So, the product is 5/8

Let us look at another example to understand this better.

Example 2: Multiply 5 × 3/10.

Solution: Here, 5 is the whole number and 3/10 is the proper fraction.

• Step 1: We convert the whole number 5 into a fraction by writing 1 as the denominator. This means 5 is written as 5/1.
• Step 2: Multiply the numerators of both the fractions. 5/1 × 3/10 = 5 × 3 = 15.
• Step 3: Multiply the denominators of both the fractions. 5/1 × 3/10 = 1 × 10 = 10.
• Step 4: Simplify the fractions. 5/1 × 3/10 = 15/10. We can simplify this further as both 15 and 10 can be divided by 5. This means, (15 ÷ 5) / (10 ÷ 5) = 3/2. Therefore, 5 × 3/10 = 3/2 = \(1\dfrac{1}{2}\)

How to Multiply Mixed Fractions with Whole Numbers?

In order to multiply mixed fractions with whole numbers, we convert the mixed fraction to an improper fraction and then multiply it with the whole number.

Example: Multiply \(1\dfrac{2}{5}\) with 10.

Solution: Let us see how to multiply the given mixed fraction with a whole number.

• Step 1: First let us convert the mixed fraction to an improper fraction. This means \(1\dfrac{2}{5}\) = 7/5.
• Step 2: Then, convert the whole number 10 into a fraction. This means 10 = 10/1. This makes it 7/5 × 10/1
• Step 3: Multiply the numerators of both the fractions. 7 × 10 = 70. Multiply the denominators of both the fractions. This means 5 × 1 = 5.
• Step 4: Simplify and reduce the fraction, that is, 70/5 = (70 ÷ 5) / (5 ÷ 5) = 14/1. Therefore, \(1\dfrac{2}{5}\) × 10 = 14.

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