Wondering How to Divide Fractions With Whole Numbers? We’ll Tell You

Children tend to get pretty scared when they see two very different types of numbers, one whole number and a fraction side-by-side. And it is fairly clear that out of the four main mathematics functions, division has to be the toughest. Put two different types of numbers together and ask a student to divide them, and the poor kid will be in a mess.

The Procedure

Take a whole number and a fraction. For example, the fraction 3/4 and the whole number 5. The fraction part is the dividend (number that is to be divided) while the whole number is the divisor (the number that divides). Thus, you will numerically represent the problem as:

³/₄ ÷ 5.

Solution

Step 1: Convert the whole number into a fraction. Take 5 as the numerator, and 1 as the denominator under 5. Now, you have a fraction 5/1. Your question will be-

³/₄ ÷ ⁵/₁

Step 2: The next step is to find the reciprocal of the newly converted fraction. Recipro...what? A reciprocal is a fraction turned up-side-down. So the reciprocal of 5/1 is 1/5. Now this reciprocal allows you to turn the division sign into a multiplication sign.

Your question now looks like this.

³/₄ × ¹/₅.

Step 3: Multiply the two numerators and the two denominators, and will get your answer.

^{3 × 1}/_{4 × 5}.

= ³/₂₀.

Let’s review the steps once again in case you have forgotten them:

• Whole number divide by 1
• Reciprocal
• Multiply

How to Divide Whole Numbers by Fractions

Let’s take the same two numbers, but reverse the order.

5 ÷ ³/₄

Step 1: Convert the whole number into a fraction.

You question now looks like this -

⁵/₁ ÷ ³/₄

Step 2: Get the reciprocal of the divisor, and put in the multiplication sign.

Now, you have:

⁵/₁ × ⁴/₃

Step 3: Multiply the two, and you will get your answer.

^{5 × 4}/_{1 × 3}

= ²⁰/₃

Turning a whole number into a fraction before dividing draws on core math skills most students forget by adulthood.