HFCC Math Lab Arithmetic - 6. Adding, Subtracting, Multiplying and Dividing Decimals

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1 HFCC Math Lab Arithmetic - 6 Adding, Subtracting, Multiplying and Dividing Decimals Part I: Adding and Subtracting Decimals Procedure: When adding or subtracting decimal numbers, 1. Arrange the numbers in a column so that the decimal points are all aligned. 2. Insert zeros so that each number has the same number of decimal places. 3. Add or subtract the numbers just as you would if they were whole numbers. 4. Place the decimal point in the answer so it is in the same column as in the other numbers. Ex 1: Add: 324.6, 79.4, 3.786, and.567. Arrange the numbers in a column with the decimal points aligned Insert zeros so that each number has the same number of decimal places. Then add Notice that the decimal point in the answer is in the same column as the decimal points in the other numbers. Revised 4/1 1

2 Ex 2: Add: Since 89 is a whole number, the decimal point is understood to be on the right. That is 89 = Align the decimal points Add insert zeros Note: The decimal point in the answer is in the same column as the decimal points in the other numbers. Ex 3: Subtract 3.8 from Align the decimal points, insert zeros, and subtract. Borrow when needed. Be sure that the decimal point in the answer is in the same column as the decimal points in the other numbers Ex 4: Subtract from 7, Align the decimal points, insert zeros, and subtract. Borrow when needed. Be sure that the decimal point in the answer is in the same column as the decimal points in the other numbers. Exercises: Add or subtract Subtract 2.79 from Subtract from 96.1 Revised 4/1 2

3 Part II: Multiplying Decimals Procedure: When multiplying decimal numbers, 1. Multiply the numbers as if they were whole numbers. That is, ignore the decimal points. 2. Place the decimal point in the answer so that the number of places to the right of the decimal point is equal to the total of the number of places to the right of the decimal in the numbers being multiplied. Ex 5: Multiply.4 x.3..4 one place to the right of the decimal.3 one place to the right of the decimal.12 total of two places to the right of the decimal Ex 6: Multiply two places to the right of the decimal point 4.8 one place to the right of the decimal point total of three places to the right of the decimal point Exercises: Multiply (.321)(.95) 15. (2.7)(.927) Revised 4/1 3

4 Part III: Dividing Decimals Procedure: When dividing decimal numbers, 1. Move the decimal point in the divisor all the way to the right to make a whole number. 2. Move the decimal point in the dividend the same number of places to the right. Add zeros, if necessary. We now have an equivalent division problem whose answer is the answer to the original division problem. 3. Place the decimal point in the quotient directly above the newly placed decimal in the dividend. Remember: quotient divisor dividend Ex 7: Divide: Move the decimal point in the divisor one place. Move the decimal point in the dividend one place. This gives us an equivalent division problem: 2 18 Now divide: Therefore: Ex 8: Divide: Round the answer to the nearest hundredth Move the decimal point in the divisor two places. Move the decimal point in the dividend two places. This gives us an equivalent division problem: Revised 4/1 4

5 Now divide: Notice that the decimal point in the quotient is 172 directly above the decimal point in the dividend Rounded off to the hundredth, the quotient is Therefore: Ex 9: Divide: Round the answer to the nearest tenth Move the decimal point in the divisor two places to the right. Revised 4/1 5 Move the decimal point in the dividend two places to the right. Remember that We must insert two zeros to show that the decimal point in the dividend moved two places to the right. This gives us the equivalent division problem: Now divide: Notice that the decimal point in the quotient is 72 directly above the decimal point in the dividend Rounded off to the nearest tenth, the quotient is Therefore:

6 Ex 1: Divide: Move the decimal point in the divisor three places to the right. Move the decimal point in the dividend three places to the right. We must insert two zeros to show that the decimal point in the dividend moved three places to the right. This gives us the equivalent division problem: Now divide: Notice that the decimal point in the quotient is 13 directly above the decimal point in the dividend Therefore: , 4 Exercises: Divide Round to the nearest tenth Revised 4/1 6

7 Answers to the odd numbered problems and solutions to the even numbered problems. Adding and subtracting: Multiplying: Revised 4/1 7

8 Dividing: Therefore: , Rounded to the nearest tenth, the quotient is 6.89 Therefore: Revised 4/1 8

9 Therefore: Therefore: Revised 4/1 9