# Decimal Division (whole number divisors)

To divide with decimals, students must be good at long division, and careful about lining up place values when doing long division. When using long division to divide decimals (with decimals in the dividend, but not the divisor) **all students have to do is bring the decimal up from the dividend and into the answer row.** If the student lines up answer digits correctly, the decimal will land in the correct place in the answer!

The trickiest part of long division is keeping numbers and place values oriented properly, and when dividing with decimals, if students do not keep numbers lined up correctly, decimals will end up in the wrong place.

For more on the long division process, see lessons Long Division (1-digit divisor) and Long Division (multi-digit divisor). Once students master long division, they can work with decimals easily.

Bottom line, **if there is a decimal in the dividend, bring it up to the answer row before beginning long division.**

Example: $7.85\div 5=$

Set the problem up:

$$\eqalign{5&\overline{)7.85}\qquad&&\text{Write the problem in a house}}$$

Deal with your decimal. Bring it straight up, from the dividend to the answer row. Then, students can proceed with long division, ignoring the decimal (but making sure to put answer digits above the proper dividend digit.

$$\eqalign{\quad & \quad\color{red}{ .} \\5&\overline{)7.85}\qquad&&\text{Bring the decimal up from the dividend into the answer row}}$$

Do the first "division" step. How many times does 5 go into the first digit in the dividend?

$$\eqalign{ \quad & \; \color{red}{1}.\qquad && \color{red}{\text{5 goes into 7 one time, write 1 over the 7}}\\5 & \overline{)7.85}\qquad && \quad \\&\!\! \underline{-5} \qquad && \text{5 times 1 is five; subtract from 7}\\ &\;\; 2 \qquad && \text{7 minus 5 equals 2}}$$

Now, you bring down. Divide the divisor into the new number you created by bringing down.

$$\eqalign{ \quad & \; \color{red}{1}.\color{green}5\qquad && \color{green}{\text{5 goes into 28 five times, write the 5 over the 8}}\\5 & \overline{)7.85}\qquad && \quad \\&\!\! \underline{-5} \color{green}{\downarrow} \qquad && \\ &\;\; 2\color{green}{8} \qquad && \text{Bring down the 8 and put it next to the 2}\\&\!\!\underline{-25}\qquad &&\text{5 times 5 is 25}\\&\;\;\;3\qquad&&\text{28 minus 25 is 3}}$$

There is one more digit in the dividend, so you'll bring down one more time, then divide again into the new number.

$$\eqalign{ \quad & \; \color{red}{1}.\color{green}5\color{blue}{7}\qquad && \color{blue}{\text{5 goes into 35 seven times, write the 7 over the 5}}\\5 & \overline{)7.85}\qquad && \quad \\&\!\! \underline{-5} \color{green}{\downarrow} \qquad && \\ &\; 2\color{green}{8} \qquad && \\&\!\!\!\underline{-25}\color{blue}{\downarrow}\qquad &&\\&\;\;3\color{blue}{5}\qquad&&\text{Bring down the 5}\\&\!\underline{-35}\qquad&&\text{7 times 5 is 35}\\&\quad0\qquad&&\text{35 minus 35 is 0, you are done}}$$

The answer is now at the top of the "house." $\color{purple}{7.85 \div 5 = 1.57 }$ or $\color{purple}{7.85 \div 5 = 1.57 }$

Overall, the process of dividing with a decimal in the dividend is just like normal long division, just bring the decimal up into the answer (and, ideally, do it before you begin, so you don't forget!).

Note: There are no remainders when you divide with decimals. If you have a remainder, add zeros to the end of the dividend, and keep bringing down until the decimal terminates or repeats. (You can keep adding zeros to the end of a decimal without changing the value of the number.)

#### Practice Problems:

## Decimal Division (Decimal Dividend, No Decimal Divisor)

Find the quotient. Round all numbers to the nearest thousandth.

- $63.516\div4=$
- $84.56\div8=$
- $97.736\div8=$
- $12.012\div3=$
- $6.092\div4=$
- $6.392\div94=$
- $24.505\div65=$
- $28.35\div63=$
- $9,830.6\div52=$
- $13.377\div21=$
- $5,358.7\div82=$
- $617.227\div79=$