Unit 1-Decimal Operations

DECIMAL OPERATIONS
Decimal Cheat  Sheet

Adding and Subtracting decimals
 
(courtesy of softschools.com)
When asked to add or subtract decimals, the most important step is to line up the decimal points.
           The steps to adding and subtracting are this:

1.) Line up the place values of the numbers by lining up the decimals.
2.) Add in filler zeros if needed.
3.) Add or Subtract the numbers in the same place value positions.


Adding:

Ex.1) 13.6 + 17.8

Step 1: Line up the decimal points so that similar place values are lined up. (Remember, the tens place in both numbers should be lined up, the ones place in both numbers should be lined up, etc.)

Step 2: Add the digits together that are lined up.



Ex. 2) 14.86 + 22.9

If the numbers do not have the same number of digits after the decimal point, you can use "filler zeros" to help you line up the numbers.



Subtracting:

The steps for subtracting numbers with decimals are exactly the same as adding decimals. Let's take a look at a couple of examples.

Ex. 3) 239.83 - 125.51 

First we will line up the numbers by making sure the decimals are lined up. Then we just subtract the numbers that are in common place value positions.


Ex. 4) 98.3 - 45.67

We will start by lining them up.


In the subtraction examples, the filler zeros are even more helpful. Some make the mistake of placing a 7 in the hundredths place of the answer. However, take a look at what happens with the filler zero.

 With the zero here, we can see that we need to borrow in order to subtract.

Multiplying Decimals 

Step 1: Multiply the numbers and ignore the decimal points.

Step 2: Count up how many number of digits that come after the decimal points in both factors.

Step 3: Place the decimal in the product so that the same number of digits comes after the decimal point in the answer.

Step 4: (Optional) Estimate the answer to see if your answer and the placement of your decimal point are reasonable.

***To multiply decimals we use a different set of steps than we would use to add or subtract decimals. In fact, you do not have to line up the decimals at all.


Ex. 1) 23.8 x 4.1

To solve this problem, we will first pretend that there are no decimals at all. Start by solving the question 238 x 41.

 

Now, we need to put the decimal back in. Let's think about this: 23.8 is about 20. And 4.1 is about 4.

So we could estimate that the answer should be around 20 x 4 = 80. That would mean that the decimal should go after the 97, to give us an answer of 97.58.

Therefore, 23.8 x 4.1 = 97.58.

However, there is a rule that you can use to know where to put the decimal without having to estimate.

Take a look at how many numbers come after the decimal point in each of the numbers we multiplied.

 

There is one digit after each of the decimal points, making two numbers total. This tells us that there needs to be two numbers after the decimal point in our answer as well.

Ex. 2) 16.903 x 2.2

Start by multiplying 16903 x 22

 

Now, take a look at how many digits are after the decimal points.



Therefore, 16.903 x 2.2 = 37.1866

Dividing Decimals

Type 1: Decimal in the dividend


If you are faced with a decimal inside, you can simply pull the decimal up and divide like it isn't there.

315.9 ÷ 13 

Step 1: Pull up the decimal. Be sure to keep it in the same position as it started.



Step 2: Start dividing as usual. In this problem, we would start by determining how many times 13 goes into 31 tens. We should get 2 tens. So we will put a 2 in the tens place.



Step 3: Continue the process.



Here we can see that the quotient is 24.3

Type 2: There is a decimal in the divisor.

The steps are slightly different if there is a decimal in the divisor.

1909.38 ÷ 24.2 

It becomes a challenge to try and carry out the long division process when there is a decimal in the divisor. So we will first move it out. To move it out, we multiply by powers of ten.

24.2 x 10 = 242 Now we don't have a decimal in the divisor. However, we cannot just change the value of one of the numbers. This would also change the quotient. So we will do the same change to the dividend.

1909.38 x 10 = 19093.8

Now we are ready to divide: 19093.8 ÷ 242

Start again by pulling up the decimal.



Then divide like you normal.



At the end, there is no reason to have to move the decimal back. Because you did the same change to both the divisor and dividend, you have still gotten the correct answer. The answer is 78.9. You are finished. 
     



Comments