LESSON: Dividing by Decimals

Dividing by Decimals

READ: Dividing Decimals by Whole Numbers

Divide Decimals By Whole Numbers

To divide means to split up into equal parts. You have learned how to divide whole numbers in an earlier lesson. Now we are going to learn how to divide decimals by whole numbers.When we divide a decimal by a whole number, we are looking at taking that decimal and splitting it up into sections.

Example

4.64 \div 2 = ______

The first thing that we need to figure out when working with a problem like this is which number is being divided by which number. In this problem, the two is the divisor. Remember that the divisor goes outside of the division box. The dividend is the value that goes inside the division box. It is the number that you are actually dividing.

2 \overline{)4.64 \;}

We want to divide this decimal into two parts. We can complete this division by thinking of this problem as whole number division. We divide the two into each number and then we will insert the decimal point when finished. Here is our problem.

& \overset{232}{2\overline{ ) 4.64 \;}}

Finally, we can insert the decimal point into the quotient. We do this by bringing up the decimal point from its place in the division box right into the quotient. See the arrow in this example to understand it better, and here are the numbers for each step of the division.

& \overset{\overset{ \ 2.32} {\uparrow}}{2 \overline{ ) 4.64 \;}}\\ & \quad \underline{4 \quad }\\ & \quad \ 0 6\\ & \quad \ \underline{ \ \ 6 \ }\\ & \qquad 04

Our answer is 2.32.


How do we divide decimals by whole numbers when there is a remainder?

Example

14.9 \div 5 = ______

The first thing that we can do is to set up this problem in a division box. The five is the divisor and the 14.9 is the dividend.

5 \overline{)14.9 \;}

Next we start our division. Five goes into fourteen twice, with four left over. Then we bring down the 9. Five goes into 49, 9 times with four left over. That four is our remainder.

& \overset{2.9 \ \ } { \ 5 \overline{ ) {14.9}} \ {r \ 4} \;}\\ & \underline{- \ 10 \ \; \;}\\ & \quad \ 49\\ & \ \underline{- \ 45 \; \;}\\ & \quad \ \ \ 4

However, when we work with decimals, we don’t want to have a remainder. We can use a zero as a placeholder. In this example, we can add a zero to the dividend and then see if we can finish the division. We add a zero and combine that with the four so we have 40. Five divides into forty eight times.

Here is what that would look like.

& \overset{ \quad 2.98}{5 \overline{ ) {14.90 \;}}}\\ & \underline{-10 \ \ }\\ & \quad \ 49\\ & \ \ \underline{-45 \ }\\ & \qquad 40

Our final answer is 2.98.

When working with decimals, you always want to add zeros as placeholders so that you can be sure that the decimal is as accurate as it can be. Remember that a decimal shows a part of a whole. We can make that part as specific as we can possible make it.