Math 64
5.2 "Adding and Subtracting Decimals"
Objectives:
*
Add or subtract decimals.
*
Estimate when adding or subtracting decimals.
*
Evaluate expressions with decimal replacement values.
*
Simplify expressions containing decimals.
*
Solve problems that involve adding or subtracting decimals.
Adding or Subtracting Decimals
Adding or subtracting decimals is similar to adding or subtracting whole numbers. We add or subtract digits in
corresponding place values from right to left, carrying or borrowing if necessary. To make sure that digits in corresponding
place values are added or subtracted, we line up the decimal points vertically.
Adding or Subtracting Decimals:
1: Write the decimals so that the decimal points line up vertically.
2: Add or subtract as with whole numbers.
3: Place the decimal point in the sum or di¤erence so that it lines
up vertically with the decimal points in the problem.
Recall that 0s may be placed after the last digit to the right of the decimal point without changing the value of the
decimal. This may be used to help line up place values when adding decimals.
Example 1: (Adding decimals)
Add:
a) 40:08 + 17:612
b) 34:567 + 129:43 + 2:8903
c)
d) 17 + 4:88 + 50:033 + 0:6
19
26:072
Page: 1
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
5.2
Example 2: (Subtracting decimals)
Subtract:
a) 73
c) 9:72
29:31
b) 29:6
4:068
d)
7:23
13:71
( 1:05)
Estimating when Adding or subtracting Decimals
To help avoid errors, we can also estimate to see if our answer is reasonable when adding or subtracting decimals.
Example 3: (Estimating sums and di¤erences)
Estimate the following sum and di¤ erence and then …nd the actual sum.
a) 5:63 + 16:8 + 35:47
b) 18:56 + ( 8:23)
Using Decimals as Replacement Values
Example 4: (Using decimals as replacement values)
Evaluate each expression for x = 3:6; y = 5; and z =0:21:
a) y
x+z
b) x + y + z
Page: 2
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
5.2
Simplify Expressions Containing Decimals
Example 5: (Simplifying expressions containing decimals)
Simplify by combining like terms.
a)
4:3y + 7:8
20:1y + 14:6
b)
8:96x
2:31
4:08x + 9:68
Solving Problems by Adding or Subtracting Decimals
Example 6: (Application)
This bar graph shows the predicted decrease in home video rental revenue for chains such as Blockbuster and Hollywood
Video. Use this graph to answer the following questions.
a) Find the decrease in video rental revenue from the year 2002 to 2008
b) It is predicted that home video sales (not shown on the bar graph)
will increase from $15.3 billion in 2002 to $24.6 billion in 2008.
Find the amount of increase.
Example 7: (Application)
A landscape architect is planning a border for a ‡ower garden shaped like a triangle. The sides of the garden measure 12.4
feet, 29.34 feet, and 25.7 feet. Find the amount of border material needed.
Page: 3
Notes by Bibiana Lopez