How to Divide Decimals by Whole Numbers

Dividing decimals by whole numbers is a fundamental math skill that plays a crucial role in daily life, from handling money to measuring ingredients. Understanding how to divide decimals by whole numbers accurately ensures you can solve a variety of mathematical problems with ease.

In this article, we are going to learn about different methods of dividing decimals by whole numbers and some solved examples based on the division of decimals by whole numbers.

What is a Decimal?

A decimal is a number that has two parts. A decimal has a whole number part and a fractional part separated by a decimal point. Decimals are used to represent fractions or parts of a whole. They are used in money, and measurements, and also have real-life applications.

Example- 4.52 is a decimal number, where 5 is the whole number part, and .52 is the fractional part.

What is Whole Numbers?

Whole Numbers are a set of natural numbers (1, 2, 3, 4. . . . .) including zero. The whole number does not include negative numbers, fractions, and decimals.

Example- {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 . . . . . } are whole numbers.

Different Methods to Divide Decimals by Whole Numbers

Some of the common methods to divide decimals by whole numbers are:

• Fractional Method
• Multiplication Method
• Estimation Method

Using Fractional Method

In this method, we convert the decimal into a fraction and then divide it by a whole number. Steps for this method are:

Step 1: First, convert the decimal into a fraction.

Step 2: Then, divide the fraction by the whole number.

Step 3: Now, if you want then convert the result back into decimal, otherwise it leave as it is.

Let's discuss example for better understanding.

Example: Divide 0.75 by 5.

Solution:

First, convert 0.75 to a fraction: 0.75 = 75/100 = 3/4.

Divide 3/4 by 5.

To do this we, multiply 3/4 by the reciprocal of 5 (which is 1/5), so:

(3/4) * (1/5) = 3/20.

Convert 3/20 back to a decimal:

3 divided by 20 equals 0.15.

Multiplication Method

In this method, we multiply both the decimal and the divisor b the the same power of 10 to make the decimal a whole number. Then, we divide as usual.

Steps for this method are:

Steps 1: First, we multiply both the decimal and the divisor by the same power of 10 to eliminate the decimal.

Steps 2: Now, divide the resulting numbers as usual.

Steps 3: Adjust the decimal problem in the final answer based on the given original problem.

Example: Divide 5.4 by 2.

Solution:

Multiply both numbers by 10 to remove the decimal:

5.4 becomes 54, and 2 becomes 20.

Divide 54 by 20, which equals 2.7.

So, the answer is 2.7

Using Estimation (For Rough Answer)

In this method, we can quickly calculate the answer, but it does not give the correct answer. We can also use this method to check our answer, whether it is correct or not. Don't use this method where we need accurate and answers answer such as measurement.

Steps for this method are:

Steps 1: Round the decimal to a nearby whole number or a simpler decimal.

Steps 2: Perform the division.

Steps 3: We, can use this estimate to check our answer or get a close approximate answer.

Example: Divide 7.85 by 3.

Solution:

Round 7.85 to 8.

Divide 8 by 3 and the approximate answer we got is 2.67.

Use the any of two above mentioned method to find exact answer. The actual answer is 2.6166... (or 2.62 if rounded to two decimal places).

Solved Examples on Dividing Decimals by Whole Numbers

Examples 1. Divide 0.6 by 3 using fractional method.

Solution:

Convert 0.6 to a fraction: 0.6 = 6/10 = 3/5.

Divide 3/5 by 3.

Multiply 3/5 by the reciprocal of 3 (which is 1/3): (3/5) * (1/3) = 3/15 = 1/5.

Convert 1/5 back to a decimal: 1 divided by 5 equals 0.2.

Examples 2. Divide 7.2 by 3 using multiplication method.

Solution:

Multiply both numbers by 10 to remove the decimal:

7.2 becomes 72, and 3 becomes 30.

Divide 72 by 30, which equals 2.4.

Examples 3. Divide 0.9 by 6 using fractional method.

Solution:

Convert 0.9 to a fraction: 0.9 = 9/10.

Divide 9/10 by 6.

Multiply 9/10 by the reciprocal of 6 (which is 1/6): (9/10) * (1/6) = 9/60 = 3/20.

Convert 3/20 back to a decimal: 3 divided by 20 equals 0.15.

Examples 4. Divide 1.4 by 4using fractional method.

Solution:

Convert 1.4 to a fraction: 1.4 = 14/10 = 7/5.

Divide 7/5 by 4.

Multiply 7/5 by the reciprocal of 4 (which is 1/4): (7/5) * (1/4) = 7/20.

Convert 7/20 back to a decimal: 7 divided by 20 equals 0.35.

Examples 5. Divide 3.5 by 5 using fractional method.

Solution:

Convert 3.5 to a fraction: 3.5 = 35/10 = 7/2.

Divide 7/2 by 5.

Multiply 7/2 by the reciprocal of 5 (which is 1/5): (7/2) * (1/5) = 7/10 = 0.7.

Practice Question on Dividing Decimals by Whole Numbers

Question 1. Divide 9.8 by 2 using multiplication method.

Question 2. Divide 8.4 by 4 using multiplication method.

Question 3. Divide 6.3 by 3 using multiplication method.

Question 4. Divide 9.23 by 4 using estimate.

Question 5. Divide 14.7 by 5 using estimate method.

Conclusion

We can find exact value after dividing decimals by whole numbers. There are different approaches of dividing decimals by whole numbers such as fractional methods, multiplication method, and estimation method. We should practice a lot of questions using these methods.

Read More,

• Are Decimal whole numbers?
• Long Division method