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.

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.

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 = \(1\dfrac{1}{2}\)

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.

☛ Related Articles

• Multiplying Mixed Fractions
• Division of Fractions
• Reduce Fractions
• Addition and Subtraction of Fractions
• Fractions Formula

What is Meant by Multiplying Fractions With Whole Numbers?

Multiplying fractions with the whole numbers is considered as repeated addition where the fraction is added the same number of times as the whole number. The multiplication of fractions with whole numbers is done using the same multiplication rules, where the numerators are multiplied together, then the denominators are multiplied together and then they are reduced to get the product.

How to Multiply Fractions With Whole Numbers?

In order to multiply fractions with whole numbers, we use the following steps.

• Step 1: Convert the whole number into a fraction by writing 1 as its denominator.
• Step 2: After this, we have two fractions to multiply. So, we use the multiplication rule of fractions to multiply the fractions.
• Step 3: This means, first the numerators are multiplied together and then the denominators are multiplied together.
• Step 4: Finally, the product is simplified or reduced, if needed.

How to Multiply Mixed Fractions with Whole Numbers?

The following steps show how to multiply mixed fractions with whole numbers:

• Step 1: Convert the mixed fraction to an improper fraction.
• Step 2: Convert the whole number into a fraction with a denominator of 1.
• Step 3: Multiply the numerators.
• Step 4: Multiply the denominators.
• Step 5: Simplify the final result to its lowest terms.

How to Multiply Improper Fractions with Whole Numbers?

For multiplying improper fractions with whole numbers, we use the same rules of multiplication. This means the whole number is written in the form of a fraction and then multiplied with the improper fraction. The numerators are multiplied together, then the denominators are multiplied together and then they are simplified, if needed.

How to Multiply 3 Fractions with Whole Numbers?

In order to multiply 3 fractions with whole numbers, we use the following steps. Let us multiply 4/5 × 10/6 × 1/4 × 25.

• Step 1: Here, 25 is the whole number and the rest of them are fractions, so we will convert the whole number into a fraction by writing its denominator as 1. This means, 25 is written as 25/1
• Step 2: Now, we have 4 fractions to multiply. So, we use the multiplication rule of fractions to multiply all these fractions. 4/5 × 10/6 × 1/4 × 25/1
• Step 3: This means, first the numerators are multiplied together and then the denominators are multiplied together. Here, the product of the numerators will be 4 × 10 × 1 × 25 = 1000. The product of the denominators will be 5 × 6 × 4 × 1 = 120.
• Step 4: The fraction that we get as the product is 1000/120. Finally, the product is simplified or reduced, this means, 1000/120 = 25/3 = \(8\dfrac{1}{3}\)

How to Multiply Negative Fractions with Whole Numbers?

For multiplying negative fractions with whole numbers, we use the same rules of multiplication. This means the whole number is written in the form of a fraction and then multiplied with the negative fraction. The numerators are multiplied together, then the denominators are multiplied together and then they are simplified if needed. However, it should be remembered that the product will have the sign according to the sign given in the fraction. This means if a negative fraction is multiplied with a positive whole number, the product will have a negative sign. For example, -6/4 × 5 = -6/4 × 5/1. Now we can multiply the numerators and denominators to get -30/4 which will be further reduced to -15/2.

What is the Rule of Multiplying Fractions?

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