Learn to write rational numbers in equivalent forms.

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# Learn to write rational numbers in equivalent forms. - PowerPoint PPT Presentation

Learn to write rational numbers in equivalent forms. Vocabulary. rational number relatively prime. A rational number is any number that can be written as a fraction , where n and d are integers and d  0. n. d.

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Presentation Transcript

Vocabulary

rational number

relatively prime

A rational numberis any number that can be written as a fraction , where n

and d are integers and d  0.

n

d

The goal of simplifying fractions is to make the numerator and the denominator relatively prime.

Relatively prime numbers have no common factors other than 1.

12

15

12 of the 15 boxes are shaded.

4 of the 5 boxes are shaded.

=

12

4

15

5

You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can simplify the fraction to by dividing both the numerator and denominator by 3.

4

5

The same total area is shaded.

;16 is a common factor.

16

80

= 1 for a ≠ 0

=0 for ≠ 0

0

a

a

a

7

8

7

8

7

8

1 5

=

16 ÷ 16

=

=

=

80 ÷ 16

Simplify.

16 = 1 • 4 • 4

80 = 5 • 4 • 4

16 80

Divide the numerator and denominator by 16.

Remember

;There are no common factors.

–18

29

–18

29

=

Simplify.

–18

29

18 = 2 • 9

29 = 1 • 29

18 and 29 are relatively prime.

18 ÷ 9

18

=

27

27 ÷ 9

2 3

=

Check It Out: Example 1A

Simplify.

18 = 3 • 3 • 2

27 = 3 • 3 • 3

18 27

; 9 is a common factor.

Divide the numerator and denominator by 9.

17 –35

17 35

= –

Check It Out: Example 1B

Simplify.

17 –35

; There are no common factors.

17 = 1 • 17 35 = 5 • 7

17 and 35 are relatively prime.

Decimals that terminate or repeat are rational numbers.

To write a terminating decimal as a fraction, identify the place value of the digit farthest to the right. Then write all of the digits after the decimal point as the numerator with the place value as the denominator.

622 1000

=

311 500

=

37 100

=5

Additional Example 2: Writing Decimals as Fractions

Write each decimal as a fraction in simplest form.

A. 5.37

7 is in the hundredths place.

5.37

B. 0.622

2 is in the thousandths place.

0.622

Simplify by dividing by the common factor 2.

2625 10,000

=

21 80

=

75 100

=8

3 4

=8

Check It Out: Example 2

Write each decimal as a fraction in simplest form.

A. 8.75

8.75

5 is in the hundredths place.

Simplify by dividing by the common factor 25.

B. 0.2625

5 is in the ten-thousandths place.

0.2625

Simplify by dividing by the common factor 125.

denominator

To write a fraction as a decimal, divide the numerator by the denominator. You can use long division.

numerator

denominator

numerator

9 11

–9

Writing Math

–1

8

A repeating decimal can be written with a bar over the digits that repeat. So 1.2222… = 1.2.

_

11 9

The fraction is equivalent to the decimal 1.2.

Additional Example 3A: Writing Fractions as Decimals

Write the fraction as a decimal.

11 9

1

.2

.0

The pattern repeats.

0

2

2

20 7

–0

–6 0

0

–1 0

7 20

The fraction is equivalent to the decimal 0.35.

Additional Example 3B: Writing Fractions as Decimals

Write the fraction as a decimal.

.3

0

5

This is a terminating decimal.

7 20

0

.0

0

7

0

1 0

The remainder is 0.

0

9 15

–9

0

–5

4

15 9

The fraction is equivalent to the decimal 1.6.

Check It Out: Example 3A

Write the fraction as a decimal.

15 9

1

.6

.0

The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal.

6

6

40 9

–0

–8 0

– 8

0

9 40

0

2

0

0

– 2

The fraction is equivalent to the decimal 0.225.

Check It Out: Example 3B

Write the fraction as a decimal.

9 40

.2

0

2

5

This is a terminating decimal.

0

0

.0

0

9

0

1 0

0

The remainder is 0.

0

3 7

5 7

5 8

27100

2.16

Do You Know It?

Simplify.

18 42

15 21

1.

2.

Write each decimal as a fraction in simplest form.

3. 0.27

4. –0.625

13 6

5. Write as a decimal

Do You Know It?

6.

Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal.)

0.325

Homework

pgs. 8-9

#’s 30-66 EVEN