Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 4.2 Adding and Subtracting Decimals

22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Adding and Subtracting Decimals Adding or Subtracting Decimals Step 1: Write the decimals so that the decimal points line up vertically. Step 2: Add or subtract as with whole numbers. Step 3: Place the decimal point in the sum or difference so that it lines up vertically with the decimal points in the problem.

33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Recall that 0s may be inserted to the right of the decimal point after the last digit without changing the value of the decimal. This may be used to help line up place values when adding or subtracting decimals. becomes 85  becomes  two 0s inserted Helpful Hint

44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Adding Decimals StepExample Step 1: Write the decimals so that the decimal points line up vertically. Add: Step 2: Add or subtract as with whole numbers. Step 3: Place the decimal point in the sum or difference so that it lines up vertically with the decimal points in the problem.

55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Add: Insert one zero

66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Subtract: – 5.9 Insert decimal point and one zero

77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Subtract: 28 – 3.3 Insert decimal point and one zero 24.7 Line up decimal points Subtract.

88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Estimating when Adding or Subtracting Decimals To help avoid errors, we can estimate to see if our answer is reasonable by rounding the given numbers and adding or subtracting. Example: 7.6 – 2.1 rounds to Exact Since the exact answer is close, it is reasonable.

99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Add Estimating When Adding Decimals Exact Estimate rounds to This is a reasonable answer.

10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example A pair of eyeglasses costs a total of $ The frames of the glasses are $ How much do the lenses of the eyeglasses cost? The lenses of the eyeglasses cost $

11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. When rounding to check a calculation, you may want to round the numbers to a place value of your choosing so that your estimates are easy to compute mentally. Helpful Hint

12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Evaluate x + y for x = 5.5 and y = 2.8. Evaluating with Decimals x + y = ( ) + ( ) Replace x with 5.5 and y with 2.8 in x + y = 8.3