 # Decimals in the Problem

Up until this point, we have been working with whole numbers and not worrying about fractions of numbers. Now that you're working with decimals, we can start working with values in between the whole numbers. You will use decimal division in many jobs, such as finance or science.

When you divide with decimals, the rules are easy. Before you start, move the decimal point of your divisor over to the right until it becomes a whole number. For example, if your divisor is 1.5, you need to move the decimal over one place. If you have 1.2345, you need to move the point four places. When you do the move, you need to move the same number of places in your dividend. Let's look at some examples...

6 ÷ 1.5 = ? (One place in the divisor.)
Convert to...
60 ÷ 15 = ? (We moved the decimal one place to the right for both values.)

20 ÷ 0.25 = ? (Two places in the divisor.)
Convert to...
2000 ÷ 25 = ?

Just shift the point to the right for both values using the divisor as your guide. Let's do a full example.

Example:
6 ÷ 1.5 = ?
Step 1: Shift the decimal one place to the right for both values.
60 ÷ 15 = ?
Step 2: How many times does 15 go into 60? 4.
Step 3: Since there are no more places in the dividend and the remainder is 0, your answer is...
6 ÷ 1.5 = 4

- or -
 ? 1.5 ) 6 --> ? 15 ) 60 --> 4 15 ) 60 - 60     0

Next, you're going to find decimals instead of your remainders. When you use a calculator, you won't see remainders, you will see decimals. Type in 34/10. Your calculator will give you the answer 3.4. Let's see how it came up with that one.

Example:
34 ÷ 10 = ?

Step 1: Does 10 go into 34? Yes, three times. Write the 3 in your quotient.
Step 2: 10 x 3 = 30
Step 3: 34 - 30 = 4
Step 4: There are no values left in your dividend. You cannot have a remainder in your answer, since your teacher wants a decimal answer. So, write a decimal point in your dividend and two zeros after it. Instead of working with 34, we will work with 34.00. Also write a decimal point in your quotient after the 3.
Step 5: Now you can bring a 0 down and place it next to the 4.
Step 6: Does 10 go into 40? Yes, 4 times. Write the 4 in your quotient after the decimal point.
Step 7: 10 x 4 = 40
Step 8: 40 - 40 = 0. (No remainder and no more numbers in the dividend.)
34 ÷ 10 = 3.4

- or -
 ? 10 ) 34 3 10 ) 34 - 30     4 3.   10 ) 34.0 - 30        40 3.4 10 ) 34.0 - 30        40  - 40      0

You can check your answer by multiplying. 3.4 * 10 = 34.

# In the Problem and Remainder

Okay, one last example where we put both ideas together. Remember to shift your decimal place over when you start and then add zeros at the end of the dividend if you need to.

Example:
100.75 ÷ 6.5 = ?

Step 1: Reformat the problem by shifting the decimal places. The divisor has one place after the point.
1007.5 ÷ 65 = ? (Now do normal division.)
Step 2: Does 65 go into 1? No.
Step 3: Does 65 go into 10? No.
Step 4: Does 65 go into 100? Yes, one time. Write 1 in your quotient.
Step 5: 65 x 1 = 65
Step 6: 100 - 65 = 35
Step 7: Bring down the 7 from the dividend to make 357.
Step 8: Does 65 go into 357? Yes, five times. Write the 5 in your quotient. (don't forget the decimal point!)
Step 9: 65 x 5 = 325
Step 10: 357 - 325 = 32
Step 11: Bring down the 5 from the dividend to make 325.
Step 12: Does 65 go into 325. Yes, five times. Write 5 in the quotient after the decimal point.
Step 13: 65 x 5 = 325
Step 14: 325 - 325 = 0 (No remainder and no more numbers in the dividend.)
100.75 ÷ 6.5 = 15.5

Check your work: 15.5 * 6.5 = 100.75

Here it is in a stacked format (we shifted the decimal point for you):
 15.5 65. ) 1007.5 - 65          357    - 325        325  - 325      0

We walked you through every step. As you do more of these problems, you will be able to skip some things and go much faster. Since this is the first time some of you might be dividing decimals, we wanted to show you everything. One last note: when we were kids, we always forgot to write the decimal place in the quotient. We got a lot of problems wrong when we were first learning. Pay attention to your work and you will get all of the right answers.

## Related Activities Adding Tenths on a Number Line - Play Activity Identify Thousandth Values - Play Activity

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