DECIMAL ARITHMETIC

• Addition
• Subtraction
• Multiplication
• Division
• Go to the Decimal home page
• contact me

On this page I will be using concepts that were discussed in previous units. If you are unfamiliar, or unsure of any of these concepts, please take this time to go back and review them. The concepts used on this page and the links taking you to their page are listed below:

• Whole number arithmetic

14.58 + 8.34

Both 14.58 and 8.34 have two digits after the decimal point, so we can proceed.
First line up the two numbers as shown below. Make sure you put a decimal point directly below the decimal in the problem

                              14.58
                               8.34
                                .  

Now look at the first column. You have 8 + 4. Now 8+4=12. Write the 2 directly underneath the 4 and "carry" the 1.

                              14.58
                               8.34
                                . 2 

Moving on to the next column we have 5 + 3 + "our carried 1."
5+3+1=9. Write down the 9.

                              14.58
                               8.34
                                .92

Now moving on to the third column we have 4 + 8 = 12. Write down 2 and carry 1.

                              14.58
                               8.34
                               2.92  

Now moving on we have 1 plus "our carried 1" giving us 2.

                              14.58
                               8.34
                              22.92  

14.58 + 8.34 = 22.92

14.518 + 8.3

Both 14.518 and 8.3 have a different number of digits after the decimal point, but we can make 8.3 into 8.300 and then proceed.

First line up the two numbers as shown below. Make sure you put a decimal point directly below the decimal in the problem

                            14.518
                             8.300
                              .
 

Now I know you can do the arithmetic and after you do, you'll end up with the following:

                            14.518
                             8.300
                            22.818
 

Now it's your turn to add some decimals

Let's look and see subtraction in action

3.857 - 2.19


First add a "zero" to 2.19 making it 2.190
Now line the numbers up as shown.
Make sure your answer space has a decimal point directly below the decimal in the problem

                            3.857
                           -2.190
                             .

Starting on the right we have 7 - 0.
7 - 0 = 7. Write a "7" in your answer space

                            3.857
                           -2.190
                             .  7

Moving on we have 5 - 9.
Borrow from the 8 in the next column and consider it to be a 7 from here on out
Consider the 5 to be a 15.
15 - 9 = 6. Write "6" in your answer

                            3.857
                           -2.190
                             . 67

Moving on we have the 8 "that we borrowed from" - 1.
7 - 1 = 6. Write "6" in your answer.

                            3.857
                           -2.190
                             .667

Finally we're left with 3 - 2.
3 - 2 = 1.

                            3.857
                           -2.190
                            1.667

3.857 - 2.190 = 1.667

Now before going on to the problem section, I'm going to take present a word example illustrating the addition and subtraction of decimals.

Suppose you went shopping and you bought a loaf of bread for $1.39 ; a pound of lunch meat for $5.56 ; a pound of cheese for $3.45 ; a head of lettuce for $1.19 ;and a jar of mayonnaise for $3.50.
At checkout you hand the cashier a twenty dollar bill. How much change should you expect back?

This problem has two parts. First you have to add together your complete order and then subtract this sum from 20.00.

1.39 + 5.56 + 3.45 + 1.19 + 3.50 = 15.09
20.00 - 15.09 = 4.91

Your change should be $4.91

Now at last you get your chance to shine.
Subtract the decimals in the following problems

As usual, I'll show you a few examples of this, and then give you a few exercises to try it out on your own.

3.2 * 0.82

First consider 32 * 82
Now 32 * 12 = 2624

Now consider the first factor: 3.2
3.2 has one decimal place (one digit after the decimal)

Now consider the second factor: 0.82
0.82 has two decimal places (two digits after the decimal)

The sum of the decimal places from the two factors is 1 + 2 = 3
The product must have three decimal places
Counting from the left we find
3.2 * 0.82 = 2.624

3.2 * 0.02

First consider 32 * 2
Now 32 * 2 = 64

Now consider the first factor: 3.2
3.2 has one decimal place (one digit after the decimal)

Now consider the second factor: 0.02
0.82 has two decimal places (two digits after the decimal)

The sum of the decimal places from the two factors is 1 + 2 = 3
The product must have three decimal places
Counting from the left we find
3.2 * 0.02 = 0.064

Meat costs $3 a pound. You bought 2 1/2 lbs How much did this order cost you?

Basically we have to multiply 3 by 2 1/2.
2 1/2 = 2.5 {see changing fractions into decimals}
So we need to multiply 3 * 2.5
Now 3 * 25 = 75
We are going to need 1 decimal space (no decimals in 3 + 1 decimal in 2.5)
3 * 2.5 = 7.5

Your meat order we come to $7.50

• Dividing a decimal by a whole number
• Dividing a whole number by a decimal
• Dividing a decimal by a decimal.

First write the problem and place a decimal in your answer directly above the decimal in the problem




Now proceed as though you were doing a regular division problem
26/5 = 5 with a remainder of 1.
The 1 becomes 15
15/5=3

First write the problem and place a decimal in your answer directly above the decimal in the problem



Now multply both .5 and 265 by ten, so that .5 becomes 5. In the process 265 will become 2650.



Now proceed as though you were doing a regular division problem

First write the problem and place a decimal in your answer directly above the decimal in the problem



Now multply both .5 and 2.65 by ten, so that .5 becomes 5. In the process 2.65 becomes 26.5



Now proceed as though you were doing a regular division problem

On a trip you drove 128 miles of highway in 2 1/2 hours
How fast were you travelling? Round you answer to the nearest whole number

We have to divide 128 by 2.5 (2.5 = 2 1/2)
128/2.5 = 51.2 miles per hour
51.2 can be rounded off to 51

You were travelling at 51 miles per hour

Enjoy working out the next few division problems