slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Learn to write rational numbers in equivalent forms. PowerPoint Presentation
Download Presentation
Learn to write rational numbers in equivalent forms.

Loading in 2 Seconds...

play fullscreen
1 / 21

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


  • 108 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Learn to write rational numbers in equivalent forms.' - moira


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2

Vocabulary

rational number

relatively prime

slide3

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

and d are integers and d  0.

n

d

slide4

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.

slide5

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.

slide6

;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

Additional Example 1A: Simplifying Fractions

Simplify.

16 = 1 • 4 • 4

80 = 5 • 4 • 4

16 80

Divide the numerator and denominator by 16.

Remember

slide7

;There are no common factors.

–18

29

–18

29

=

Additional Example 1B: Simplifying Fractions

Simplify.

–18

29

18 = 2 • 9

29 = 1 • 29

18 and 29 are relatively prime.

slide8

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.

slide9

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.

slide10

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.

slide12

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.

slide13

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.

slide14

denominator

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

numerator

denominator

numerator

slide15

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

slide16

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

slide17

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

slide18

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

slide19

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

slide20

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

slide21

Homework

pgs. 8-9

#’s 30-66 EVEN