Multiplying and Dividing Decimals is a unit of instruction that shows students how to estimate decimal products and quotients, multiply and divide decimals by whole numbers, and to multiply and divide decimals by decimals. This video shows a step by step process for completing these equations.
For more help, check out our Multiplying and Dividing Decimals Lessons Page
Credit goes to Math Antics
How To Multiplying Decimals
To multiply decimals, follow these steps:
Step 1) Write Down the Decimals
Write down the decimals you want to multiply. For example, let’s say you want to multiply:
2.5 by 1.2
Step 2) Ignore the Decimals Temporarily
Treat the decimals as if they were whole numbers. In other words, ignore the decimal points for now. So,
2.5 becomes 25 and 1.2 becomes 12.
Step 3) Multiply the Whole Numbers
Multiply the whole numbers together. In this case, 25 x 12 = 300.
Step 4) Count the Decimal Places
Count the total number of decimal places in the original decimals you’re multiplying. In this case, 2.5 has one decimal place and 1.2 has one decimal place, making a total of two decimal places.
Step 5) Place the Decimal Point in the Product
Place the decimal point in the product so that the total number of decimal places matches the count from step 4. In this example, the product is 300, so place the decimal point two places from the right to get 3.00.
Step 6) Simplify (if needed):
If the result has trailing zeros, you can remove them without changing the value. In this case, 3.00 can be simplified to 3.
So, 2.5 x 1.2 = 3.
Remember, the key is to treat decimals like whole numbers, perform the multiplication, and then adjust the placement of the decimal point in the product based on the number of decimal places in the original decimals.
How To Divide Decimals
To divide decimals, follow these steps:
Step 1) Set up the Division Problem
Write down the division problem as you normally would, with the divisor (the number you’re dividing by) outside the division symbol and the dividend (the number you’re dividing into) inside the division symbol. For example, let’s say you want to divide 4.8 by 1.2.
4.8/1.2
Step 2) Move the Decimal Point
Adjust the decimal point in both the divisor and dividend to make the divisor a whole number. Move the decimal point in both numbers the same number of places to the right until the divisor becomes a whole number. Keep track of how many places you moved the decimal.
48/12
Step 3) Perform the Division
Divide the adjusted numbers as you normally would. Divide the adjusted dividend by the whole number divisor.
48/12 = 4
Step 4) Count Decimal Places
Count the total number of decimal places in the original dividend.
The original dividend, 4.8, has one decimal place.
Step 5) Place the Decimal Point in the Quotient
Place the decimal point in the quotient so that the number of decimal places in the quotient matches the count from step 4. This means you’ll place the decimal point directly above the decimal point in the original dividend.
The example gives us 4.0.
Step 6) Simplify (if needed)
If there are trailing zeros in the quotient, you can remove them without changing the value.
Since 4.0 is the same as 4, there’s no need to include the trailing zero.