Familiar with the tricks for dividing fractions and decimals? Homework Unlocked is here to help. Homework Unlocked offers homework help to parents so you can help your kids excel in math. Here, Homework Unlocked explains dividing decimals using multiplication.

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## Dividing Decimals by Turning a Division Problem into a Multiplication Problem

A fraction divided by another fraction is equal to that fraction times the reciprocal of the divisor. Since this is true, we can turn a division problem into a multiplication problem by following three steps:

Step 1: Rewrite each decimal as a fraction without a decimal.

Step 2: Change the problem from division to multiplication by multiplying by the reciprocal fraction.

Step 3: Solve and simplify!

Every number except for 0 has a reciprocal, which is simply 1 divided by that number. For fractions, this means that the reciprocal is a fancy term for flipping the numerator and denominator.

For example:

since is the reciprocal of

For more information, please watch the Homework Unlocked video, “What is a reciprocal?”

Let’s walk through some examples so you can explain this to your kids!

**Example 1. Solve 0.84 ÷ 0.4 by multiplying fractions**

**Step 1.**** Rewrite 0.84 and 0.4 as a fraction **

Start by rewriting each number as fractions with decimals. We can do this simply by putting each number over 1.

Now we need to get rid of those decimals. Let’s begin with 0.84. First, let’s figure out how many time we would have to multiply 0.84 by 10 to make it a whole number.

0.84 x 10 = 8.4

8.4 x 10 = 84, 85 is a whole number so we are done.

0.84 x 10 x 10 = 84. Our multiplier is 100. So we have to multiply the top and bottom of the fraction by 100 to remove that decimal.

Now let’s do the same for

0.4 x 10 = 4 , 4 is a whole number so we are done.

We had to multiply 0.4 by 10 to make it a whole number, thus we have to multiply the numerator and denominator by 10.

**Step 2.**** Change the problem from division to multiplication.**

Now, here is where things get a tiny bit tricky, but remind your kids that fraction A divided by fraction B is equivalent to fraction A multiplied by the reciprocal of fraction B.

Therefore is equal to

**Step 3.**** Solve and simplify!**

Multiply the numerator by the numerator and the denominator by the denominator.

When asked to simplify, first check to see if the denominator fits evenly into the numerator. If not, find the largest common factor of the denominator and numerator and divide each number by that factor.

To simplify this example, divide both the numerator and denominator by the largest common factor 40.

0.84 ÷ 0.4 =

Let’s try one more example.

**Example 2. Solve 0.93 ÷ 0.31 by multiplying fractions**

**Step 1.**** Rewrite 0.93 and 0.31 as fraction.**

Start by rewriting them as fractions with decimals simply by putting each number over 1.

**Step 2.*** Change the problem from division to multiplication.*

Now that we have removed the decimals let’s rewrite the problem.

Now remember we can transform this into a multiplication problem by finding the reciprocal of our divisor.

is equal to

**Step 3.**** Solve and Simplify**

To simplify we can first cross out the common zeros (each number ends with 2 zeros) which leaves us with

Now we need to check if our denominator fits evenly into our numerator, in this case it does. 31 goes into 93 3 times.

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