Multiplication and Division of Decimal Fractions

From our childhood, we learned about all the operations of Maths, whether it's subtraction, addition, multiplication, or division. And we learned how to use all these mathematical operations in everyday life. But today, we will learn about the division of different forms, which is the division of the (decimal fraction). So in this article, we are going to learn about the division of decimal fractions.

We will learn what decimal is a decimal fraction, how to divide the decimal, and how to convert it into the simplest form. We are going to clear our concept with the help of solved decimal division examples. Dividing decimals is easy and simple as a normal division, but if we do it in the correct manner. So let's learn about the division of decimal fractions.

Multiplication Fraction

Multiplying fractions starts with the multiplication of the given numerators, followed by the multiplication of the denominators. Then, the resultant fraction is simplified further and reduced to its lowest terms, if needed.

How to Multiply Fraction?

The multiplication of fractions is not like the addition or subtraction of fractions, where the denominator should be the same. Here, any two fractions with different denominators can easily be multiplied.

Let us learn how to multiply fractions through the following steps:

Step 1: Multiply the numerators.

Step 2: Multiply the denominators.

Step 3: Reduce the resultant fraction to its lowest terms.

Example: Multiply: $\dfrac{1}{3} \times \dfrac{3}{5}$

Step 1: Multiply the numerators and the denominator.

$\dfrac{1 \times 3}{3 \times 5}=\dfrac{3}{15}$

Step 2: Simplifying the fraction.

$\dfrac{1}{5}=\dfrac{1}{5}$

$\therefore \dfrac{1}{3} \times \dfrac{3}{5}=\dfrac{1}{5}$

Division

Division means sharing an item equally. We have learned about the division of whole numbers. Now let us see how to divide fractions. A fraction has two parts - a numerator and a denominator. Dividing fractions is almost the same as multiplying them. For the division of fractions, we multiply the first fraction by the reciprocal (inverse) of the second fraction.

How to Divide Decimals?

Dividing Decimals is similar to dividing whole numbers. Remember the position of the decimal point in mind. While dividing decimal numbers, we need to follow a set of rules, but the basic division process remains the same. A decimal number and a fractional part are separated by a dot which is the decimal point. The number after the decimal point has a value smaller than 1.

For example, 34.25 is a decimal number in which 34 is the whole number part, and 25 is the fractional part. For dividing decimal numbers, we have 2 scenarios - one in which we need to divide decimals by a whole number and the second in which we divide decimals by decimals. Dividing decimals by whole numbers is the same as normal division. A dividend is a decimal number, and a divisor is a whole number, although the decimal point in the quotient will be placed according to the decimal point of the dividend.

Solved Examples of Dividing Decimals and Multiplying Decimals

We need to convert the divisor into a whole number by dividing decimals by another decimal number. Then continue the division. Let's solve some examples.

1. Divide 55.318 $\div$ 3.4

Following are the steps:

Step 1: Write in standard form.

Step 2: Move the decimal point in the divisor and dividend.

Step 3: Keep dividing until the quotient repeats or comes out evenly.

Step 4: Add zeros on the right of the dividend as needed.

Division of 55.318 by 3.4

2. Divide 48.65 $\div$ 3.5

Following are the steps:

Step 1: The dividend is 48.65, and the divisor is 3.5. We need to change the divisor to a whole number and multiply it by 10 so that the decimal point shifts to the right and becomes a whole number. This means 3.5 × 10 = 35.

Step 2: We need to treat the dividend the same way we treated the divisor. So, we will multiply the dividend by 10 as well. This means it will be 48.65 × 10 = 486.5. In other words, we need to move both decimal points to the right until the divisor becomes a whole number.

Step 3: Now, we have 486.5 as the dividend and 35 as the divisor. This can be divided as we do the usual division, and get 13.9 as the quotient.

Division of 48.65 by 3.5

3. Multiply: $\dfrac{1}{4} \times \dfrac{2}{3}$

Multiplying the numerator and the denominator.

$=\dfrac{1 \times 2}{4 \times 3}$

On simplifying the fraction, we get

$=\dfrac{2}{12}$

Now make it in the simplest form, we get

$=\dfrac{1}{6}$

Practice Questions

To clear your concept, there is one free worksheet that you can solve and clear your doubt.

1. 1.25 $\div$ 0.5

Ans: 2.5

2. 36.9 $\div$ 3

Ans: 12.3

3. Multiply: $\dfrac{3}{4} \times \dfrac{2}{5}$

Ans: $\dfrac{6}{20}$

Summary

So in this article, we learned about the division of decimal fractions, division, what is a decimal fraction, and how to divide decimals. We cleared our concepts of the division of decimal numbers with the help of examples. We learned how to solve the division of decimal numbers.

And after solving decimal division examples, there is a worksheet that will clear our whole concept because, with the help of practice, we can understand what we learned. The division of the decimal fraction is also simple and the same as a normal division, but we just need to clear our concept.