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Adding and Subtracting Rational Numbers

3-2

1 2

1

21 14

24 56

12 30

2 5

3 7

3 20

11 50

1

–

Course 3

Warm Up

Divide.

1.2.

3.

Write each decimal as a fraction in simplest form.

4. 1.15 5.–0.22

Adding and Subtracting Rational Numbers

3-2

Course 3

Problem of the Day

Four sprinters run a race. In how many different ways can they arrive at the finish line, assuming there are no ties?

24

Adding and Subtracting Rational Numbers

3-2

Course 3

Learn to add and subtract decimals and rational numbers with like denominators.

Adding and Subtracting Rational Numbers

3-2

Course 3

The 100-meter dash is measured in thousandths of a second, so runners must react quickly to the starter pistol.

If you subtract a runner’s reaction time from the total race time, you can find the amount of time the runner took to run the actual 100-meter distance.

Adding and Subtracting Rational Numbers

3-2

24.08

–23.35

Course 3

Additional Example 1: Sports Application

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?

Align the decimals.

0.73

She ran 0.73 second faster in June.

Adding and Subtracting Rational Numbers

3-2

Course 3

Try This: Example 1

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?

Subtract 0.568 from 11.5 to determine the new time.

Add 2 zeros so the decimals align.

00

11.5

–0.568

10.932

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

Adding and Subtracting Rational Numbers

3-2

Course 3

Additional Example 2A: Using a Number Line to Add Rational Decimals

Use a number line to find the sum.

A. 0.3 + (–1.2)

Move right 0.3 units.

From 0.3, move left 1.2 units.

–1.2

0.3

–0.4

0

–1.0

0.4

–1.4

You finish at –0.9, so 0.3 + (–1.2) = –0.9.

Adding and Subtracting Rational Numbers

3-2

3 5

You finish at , so

1 5

2 5

1 5

3 5

2 5

1 5

Move right units.

+

= .

2 5

1 5

From , move right units.

Course 3

Additional Example 2B: Using a Number Line to Add Rational Decimals

Use a number line to find the sum.

2 5

1 5

+

B.

4 5

2 5

3 5

1 5

0

1

Adding and Subtracting Rational Numbers

3-2

Course 3

Try This: Example 2A

Use a number line to find the sum.

A. 1.5 + (–1.8)

Move right 1.5 units.

From 1.5, move left 1.8 units.

–1.8

1.5

0

0.8

–0.4

1.6

1.4

0.4

You finish at –0.3, so 1.5 + (–1.8) = –0.3.

Adding and Subtracting Rational Numbers

3-2

1 8

3 8

3 8

Move right units.

1 8

3 8

From , move right units.

4 8

You finish at , which simplifies to .

1 2

Course 3

Try This: Example 2B

Use a number line to find the sum.

1 8

3 8

+

B.

1 4

3 8

1 2

5 8

1 8

0

Adding and Subtracting Rational Numbers

3-2

ADDING AND SUBTRACTING WITH LIKE DENOMINATORS

Words

Numbers

To add or subtract rational numbers with the same denominator, add or subtract the numerators and keep the denominator.

4 7

+– =

2 + (–4) 7

2 7

2 7

= , or –

–2 7

Course 3

Adding and Subtracting Rational Numbers

3-2

a + b d

b d

a d

=

+

Course 3

ADDING AND SUBTRACTING WITH LIKE DENOMINATORS

Words

Algebra

To add or subtract rational numbers with the same denominator, add or subtract the numerators and keep the denominator.

Adding and Subtracting Rational Numbers

3-2

2 9

2 9

5 9

5 9

–

–

–

–

–2 – 5 9

7 9

=

= –

3 7

–3 7

–

can be written as .

6 7

–3

7

+

6 + (–3) 7

3 7

=

=

Course 3

Additional Example 3: Adding and Subtracting Fractions with Like Denominators

Add or subtract.

Subtract numerators. Keep the denominator.

A.

6 7

3 7

B.

+ –

Adding and Subtracting Rational Numbers

3-2

1 5

1 5

3 5

3 5

–

–

–

–

–1 – 3 5

4 5

=

= –

4 9

–4 9

–

can be written as .

5 9

–4

9

+

5 + (–4) 9

1 9

=

=

Course 3

Try This: Example 3

Add or subtract.

Subtract numerators. Keep the denominator.

A.

5 9

4 9

B.

+ –

Adding and Subtracting Rational Numbers

3-2

Course 3

Additional Example 4A: Evaluating Expressions with Rational Numbers

Evaluate the expression for the given value of the variable.

A. 12.1 – x for x = –0.1

12.1– (–0.1)

Substitute –0.1 for x.

12.2

Think: 12.1 – (–0.1) = 12.1 + 0.1

Adding and Subtracting Rational Numbers

3-2

1 10

7 10

+ m for m = 3

1 10

7 10

1 10

Substitute 3 for m.

+ 3

7 10

31 10

3(10) + 1 10

31 10

110

+

3 = =

38 10

7 + 31 10

=

4 5

= 3

Course 3

Additional Example 4B: Evaluating Expressions with Rational Numbers

Evaluate the expression for the given value of the variable.

B.

Add numerators, keep the denominator.

Simplify.

Adding and Subtracting Rational Numbers

3-2

Course 3

Try This: Example 4A

Evaluate the expression for the given value of the variable.

A.

52.3 – y for y = –7.8

52.3– (–7.8)

Substitute –7.8 for y.

Think: 52.3 – (–7.8) = 52.3 + 7.8

60.1

Adding and Subtracting Rational Numbers

3-2

7 8

5 8

+ m for m = 5

7 8

5 8

7 8

Substitute 5 for m.

+ 5

5 8

47 8

5(8) + 7 8

31 8

7 8

+

5 = =

52 8

5 + 47 8

=

1 2

= 6

Course 3

Try This: Example 4B

Evaluate the expression for the given value of the variable.

B.

Add numerators, keep the denominator.

Simplify.

Adding and Subtracting Rational Numbers

3-2

1 2

–

Course 3

Lesson Quiz: Part 1

Simplify.

1. –1.2 + 8.4

7.2

–0.3

2. 2.5 + (–2.8)

3 4

5 4

3.

+

–

Evaluate.

4. 62.1 + x for x = –127.0

–64.9

Adding and Subtracting Rational Numbers

3-2

Course 3

Lesson Quiz: Part 2

5.

Sarah’s best broad jump is 1.6 meters, and Jill’s best is 1.47 meters. How much farther can Sarah jump than Jill?

0.13 m

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