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# Multiplying and Dividing with Decimals

It's common to encounter real-life problems that involve decimals such as when dealing with money or measured quantities like weight or volume. Let's take a look at some word problems from real-life scenarios that require you to multiply or divide with decimals.

## Solving word problems by multiplying with decimals

Susie wants to bake a smaller cake than her recipe calls for, $\frac{1}{2}$ (or 0.5) of one cake. One cake requires 0.25 cups of sugar. How many cups of sugar will Susie need?

You can use the standard algorithm for multiplying decimals to multiply the cups of sugar for one cake by the number of cakes needed $\left(0.25×0.5\right)$ . To do this, multiply the numbers as if they were whole numbers (don't include the decimals):

$\begin{array}{cc}& \hfill 25\\ & \hfill \underset{_}{×\phantom{\rule{10pt}{0ex}}5}\\ & \hfill 125\end{array}$

Once the problem has been multiplied, count the total number of places to the right of the decimal point in each number you're multiplying (two for 0.25 and one for 0.5). Start from the right of 125, move 3 places to the left, and place your decimal point (0.125).

The final answer is Susie will need 0.125 cups of sugar to bake $\frac{1}{2}$ of one cake.

## Solving word problems by dividing with decimals

Let's look at the following word problem:

Jeremy ran a total of 16.15 miles in track practice over 4.25 days. How many miles did he run per day?

For $x÷y=z$ , the dividend is x, the divisor is y, and the quotient is z.

It can also be rewritten as: $y\overline{)x}$

Now, let's divide the following:

$16.15÷4.25$

Since the divisor (4.25) isn't a whole number, move the decimal two places to the right to create a whole number. Also, move the decimal for the dividend (16.15) two places to the right.

Divide normally, adding extra zeros to the right of 1615 when needed:

$\begin{array}{cc}& \hfill 38\\ \hfill 425& \hfill \overline{)1615.0}\\ & \hfill \underset{_}{1275}\phantom{10}\\ & \hfill 3400\\ & \hfill \underset{_}{3400}\\ & \hfill 0\end{array}$

Put the decimal point in the quotient directly above the decimal point in the dividend:

$\begin{array}{cc}& \hfill 3.8\\ \hfill 425& \hfill \overline{)1615.0}\\ & \hfill \underset{_}{1275}\phantom{10}\\ & \hfill 3400\\ & \hfill \underset{_}{3400}\\ & \hfill 0\end{array}$

The final answer is Jeremy ran 3.8 miles per day.

## Practice questions on multiplying and dividing with decimals

a. If Devin needs 0.45 teaspoons of vanilla to make 1 pie, how much vanilla does he need for 0.5 of a pie?

$\begin{array}{cc}& \hfill 45\\ & \hfill \underset{_}{×\phantom{\rule{10pt}{0ex}}5}\\ & \hfill 225\end{array}$

b. If Alexis needs 0.75 tablespoons of milk to make 1 pan of brownies, how much milk will she need to make 0.2 of a pan of brownies?

$\begin{array}{cc}& \hfill 75\\ & \hfill \underset{_}{×\phantom{\rule{10pt}{0ex}}2}\\ & \hfill 150\end{array}$

c. If Kara is preparing Easter baskets and adds 0.25 of a box of candy to 1 large basket, how much of the box of candy will she need for 1 small basket (which equals 0.5 of a large basket)?

$\begin{array}{cc}& \hfill 25\\ & \hfill \underset{_}{×\phantom{\rule{10pt}{0ex}}5}\\ & \hfill 125\end{array}$

d. If Charles needs 0.4 eggs to prepare 1 pancake, how many eggs will he need to make 0.75 pancakes?

$\begin{array}{cc}& \hfill 75\\ & \hfill \underset{_}{×\phantom{\rule{10pt}{0ex}}4}\\ & \hfill 300\end{array}$

e. If Erik dug 7.65 holes in his garden over a period of 12.75 days, how many holes did he dig per day?

$\begin{array}{cc}& \hfill 0.6\\ \hfill 1275& \hfill \overline{)765.0}\\ & \hfill \underset{_}{765 0}\\ & \hfill 0\end{array}$

f. A bottle contains 19.20 ounces of medicine. If each dose of medicine is 1.5 ounces, how many doses are in the bottle?

$\begin{array}{cc}& \hfill 12.8\\ \hfill 15& \hfill \overline{)192.0}\\ & \underset{_}{15}\phantom{10}\\ & 42\\ & \underset{_}{30}\\ & \hfill 120\\ & \hfill \underset{_}{120}\\ & \hfill 0\end{array}$