4 Chapter Chapter 2 Decimals

Adding and Subtracting Decimals Section 4.2 Adding and Subtracting Decimals

Objective A Add Decimals.

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. Objective A

Helpful Hint 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. 85 - 13.26 becomes 85.00 - 13.26 two 0s inserted 71.74

Adding Decimals Step Example Step 1: Write the decimals so that the decimal points line up vertically. Add: 0.004 + 0.085 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. Objective A 6

Example Add: 756.23 + 26.504 + 1.087 Insert one zero 783.821 Objective A 7

Example Add: 19 + 26.072 19.000 insert a decimal point and add 0’s + 26.072 45.072

Example Add: 7.12 + (–9.92) Recall that to add two numbers with different signs, we find the difference of the larger absolute value and the smaller absolute value. The sign of the answer is the same as the sign of the number with the larger absolute value. 9.92 – 7.12 2.80 The sign will be negative. 7.12 + (–9.92) = –2.8

Objective B Subtract Decimals.

Example Subtract: 56.21 – 5.9 Objective A 11

Example Subtract: 28 – 3.3 24.7 Insert decimal point and one zero Line up decimal points 24.7 Subtract. Objective A 12

Example Subtract 19 from 25.91. 25.91 – 19.00 insert 2 0s 6.91

Example Subtract: –5.4 – 9.6 Recall that to subtract 9.6, we add the opposite of 9.6 or –9.6. –5.4 – 9.6 = –5.4 + (– 9.6) = –15

Example Subtract: –1.05 – (–7.23) To subtract, add the opposite of –7.23. –1.05 – (–7.23) = –1.05 + 7.23 = 6.18

Estimate when Adding or Subtracting Decimals. Objective C Estimate when Adding or Subtracting Decimals.

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 Exact rounds to Objective A Since the exact answer is close, it is reasonable. 17

Chapter 1 / Whole Numbers and Introduction to Algebra Example Add 23.8 + 32.1. Exact Estimate rounds to rounds to This is a reasonable answer.

Evaluate Expressions with Decimal Replacement Values. Objective D Evaluate Expressions with Decimal Replacement Values.

Chapter 1 / Whole Numbers and Introduction to Algebra Example Evaluate x + y for x = 5.5 and y = 2.8. Replace x with 5.5 and y with 2.8 in x + y. x + y = ( ) + ( ) 5.5 2.8 = 8.3

Example Simplify by combining like terms: –4.3y + 7.8 – 20.1y + 14.6 = –4.3y + (–20.1y) + 7.8 + 14.6 = –24.4y + 22.4

Solve Problems That Involve Adding or Subtracting Decimals. Objective E Solve Problems That Involve Adding or Subtracting Decimals.

Example Find the total monthly cost of owning and operating a certain automobile given the expenses shown. Monthly car payment: $563.52 Monthly insurance cost: $52.68 Average gasoline bill per month: $127.50 $563.52 + $52.68 + $127.50 Continued

Example (cont) $563.52 rounds to 600 $52.68 round to 50 + $127.50 rounds to 100 $743.70 750 estimate Check your work. Since the estimate is close to the exact answer, our answer is reasonable. The total monthly cost is $743.70.

Example The bar graph shows the current average heights for adults in various countries. How much greater is the average height in the Netherlands than the average height in Czechoslovakia? Continued

Example (cont) Netherlands = 72.6 Czechoslovakia = 70.8 Subtract to find how much greater. 72.6 rounds to 73 – 70.8 rounds to 71 1.8 2 Our estimate is close to our exact answer. The average height is 1.8 inches greater.