Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

A. 0.3 + (–1.2) Think: Find the difference of |1.2| and |3|. 0.9

Add or subtract.

Example 1: Adding and Subtracting Decimals

– 1.2 is greater than 0.3; use the sign of 1.2.

B. 17.2 – 4.39 Line up the decimal points. Use a zero as a placeholder. – 4.39

17.20

12.81 Subtract.

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

In August 2001, at the World University Games in Beijing, China, Jimyria Hicks ran the 200-meter dash in 24.08 seconds. Her best time at the U.S. Senior National Meet in June of the same year was 23.35 seconds. How much faster did she run in June?

She ran 0.73 second faster in June.

24.08–23.35

0.73Line up the decimal points.

Example 2: Sports Application

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

Remember!

Subtracting a number is the same as adding its opposite.

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational NumbersExample 3: Adding and Subtracting Fractions with Like

Denominators

Subtract numerators. Keep the denominator.

2 9– – 5

92 9– – 5

9 = –7 9

= 3 7

6 7 + – 3

7

–2 – 5 9=

6 + (–3) 7=

can be written as . – 3 7

–3 7

Add or subtract. Write each answer in simplest form

6 7 + –3

7

A.

B.

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

4 5= 3

+ 7 10

31 10

Add numerators, keep the denominator.

7 + 31 10

Simplify.

+ m for m = 37 10

1 10

38 10 =

+ 3 7 10

1 10 Substitute 3 for m.1

10

3(10) + 1 103 = = 31

101

10

Evaluate the expression for the given value of the variable.

Example 4B: Evaluating Expressions with Rational Numbers

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

12.1 – x for x = –0.1

Substitute –0.1 for x.12.1 – (–0.1)

12.2 Think: 12.1 – (–0.1) = 12.1 + 0.1

Evaluate the expression for the given value of the variable.

Example 4A: Evaluating Expressions with Rational Numbers

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

A. 0.4 + 2.2

Line up the decimal points. + 2.2

Add or subtract.Check It Out! Example 1

0.4

2.6 Add.

B. 12.4 – 3.29 Line up the decimal points. Use a zero as a placeholder. – 3.29

12.40

9.11 Subtract.

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

Tom ran the 100-meter dash in 11.5 seconds last year. This year he improved his time by 0.568 seconds. How fast did Tom run the 100-meter dash this year?

Check It Out! Example 2

Tom ran the 100-meter dash in 10.932 seconds this year.

Subtract 0.568 from 11.5 to determine the new time.

10.932–0.56811.5 Add two zeros so

the decimals align.00

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

= 1 9

5 9 + – 4

9 5 + (–4)

9=5 9 + –4

9

Check It Out! Example 3

Subtract numerators. Keep the denominator.

1 5– – 3

51 5– – 3

5 = – 4 5

–1 – 3 5=

Add or subtract. Write each answer in simplest formA.

B. can be written as . – 4 9

–4 9

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

52.3 – y for y = –7.8

Substitute –7.8 for y. 52.3 – (–7.8)

60.1 Think: 52.3 – (–7.8) = 52.3 + 7.8

Check It Out! Example 4AEvaluate the expression for the given value of the variable.

Evaluating Algebraic Expressions

2-3 Adding and Subtracting Rational Numbers

+ 5 8

47 8

Add numerators, keep the denominator.

5 + 47 8

Simplify.

+ m for m = 5 5 8

7 8

52 8=

+ 5 5 8

7 8 Substitute 5 for m.7

8

5(8) + 7 85 = = 47

87 8

Check It Out! Example 4BEvaluate the expression for the given value of the variable.

1 2= 6