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Preview. Warm Up. California Standards. Lesson Presentation. 0.3. 0.6. Warm Up Write each fraction as a decimal. 1 3. 45. 2. 0.8. 1. 3 4. 23. 3. . 0.75. 4. . California Standards.

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Preview

Warm Up

California Standards

Lesson Presentation

0.3

0.6

Warm Up

Write each fraction as a decimal.

1 3

45

2.

0.8

1.

3 4

23

3.

0.75

4.

California

Standards

NS1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10), compare rational numbers in general.

Also covered: NS1.3

Vocabulary

least common denominator (LCD)

To compare fractions with unlike denominators, you can find a common denominator. This could be the least common denominator (LCD), which is the least common multiple of the denominators.

50 60

42 60

10 10

6 6

7 10

5 6

7  6 10  6

5  10 6  10

=

=

=

=

50 60

42 60

5 6

7 10

>

,so

>

Additional Example 1A: Comparing Fractions by Finding a Common Denominator

Compare. Write <, >, or =.

5 6

7 10

>

Method 1: Multiply to find a common denominator.

Multiply 6 and 10 to find a common denominator.

6  10 = 60

Write the fractions with a common denominator.

Compare the fractions.

Remember!

The least common multiple (LCM) of two numbers is the smallest number, other than 0, that is a multiple of both numbers.

10 15

12 15

5 5

3 3

4 5

2 3

4  3 5  3

2  5 3  5

=

=

=

=

10 15

12 15

2 3

4 5

<

,so

<

Additional Example 1B: Comparing Fractions by Finding a Common Denominator

Compare. Write <, >, or =.

2 3

4 5

>

Method 2: Find the least common denominator.

List multiples of 3 and 5. The LCM is 15.

3; 3, 6, 9, 12, 15… 5; 5, 10, 15

Write the fractions with a common denominator.

Compare the fractions.

5 10

4 10

5 5

2 2

2 5

1 2

2  2 5  2

1  5 2  5

=

=

=

=

5 10

4 10

1 2

2 5

>

,so

>

Check It Out! Example 1A

Compare. Write <, >, or =.

1 2

2 5

>

Method 1: Multiply to find a common denominator.

Multiply 2 and 5 to find a common denominator.

2  5 = 10

Write the fractions with a common denominator.

Compare the fractions.

8 12

9 12

4 4

3 3

3 4

2 3

3  3 4  3

2  4 3  4

=

=

=

=

8 12

9 12

2 3

3 4

<

,so

<

Check It Out! Example 1B

Compare. Write <, >, or =.

2 3

3 4

>

Method 2: Find the least common denominator.

List multiples of 3 and 4. The LCM is 12.

3; 3, 6, 9, 12, … 4; 4, 8, 12…

Write the fractions with a common denominator.

Compare the fractions.

_

_

_

_

_

2 9

2 9

2 7

2 7

2 9

_

5 = 5.2 and 5 = 5.285714…

_

5.2 < 5.285714…, so 5 < 5

Additional Example 2: Comparing by Using Decimals

Compare. Write <, >, or =.

_

2 7

<

A. 5 5

Write the fractions as decimals.

Compare the decimals.

_

_

_

_

_

_

_

_

1 9

2 5

2 5

1 9

2 5

2 5

1 9

1 9

Write - as decimal.

Write as decimal.

– = –0.4

–0.44 < –0.4, so –0.44 < –

= 0.1

0.1 > 0.1, so > 0.1

Additional Example 2: Comparing by Using Decimals

Compare. Write <, >, or =.

<

B. –0.44 –

Compare the decimals.

C. 0.1

>

Compare the decimals.

_

_

_

_

_

2 9

3 5

3 5

2 9

2 9

_

4 = 4.2 and 4 = 4.6

4.2 < 4.6, so 4 < 4

Check It Out! Example 2

Compare. Write <, >, or =.

_

3 5

<

A. 4 4

Write the fractions as decimals.

Compare the decimals.

_

_

_

_

_

_

_

_

5 6

4 5

4 5

5 6

5 6

5 6

4 5

4 5

Write – as decimal.

Write as decimal.

– = –0.8

–0.80 = –0.8, so –0.80 = –

= 0.83

_

0.83 > 0.8, so > 0.8

Check It Out! Example 2

Compare. Write <, >, or =.

=

B. –0.80 –

Compare the decimals.

C. 0.8

>

Compare the decimals.

To order fractions and decimals, you can either write them all in the same form and then compare them, or place them on a number line. Recall that numbers increase in value as you move from left to right along a number line.

The numbers , –3.4, 6.0, and –2.5

represent the percent changes in populations for four states. List these numbers in order from least to greatest.

Place the numbers on a number line and read them from left to right.

The percent changes in population from least to greatest are –3.4, –2.5, , and 6.0.

14 4

__

14 4

__

–3.4

–4 –3 –2 –1 0 1 2 3 4 5 6

__

14 4

Additional Example 3: Social Studies Application

6.0 

–2.5 

The numbers , 3.0, –2.2, and –3.9

represent the percent changes in populations for four states. List these numbers in order from least to greatest.

Place the numbers on a number line and read them from left to right.

7 2

__

7 2

__

–3.9

–5 –4 –3 –2 –1 0 1 2 3 4 5

The percent changes in population from least to greatest are –3.9, –2.2, 3.0, and .

7 2

Check It Out! Example 3

3.0 

–2.2 

9 11

7 8

6 7

2 9

1 4

8 9

<

Lesson Quiz

Compare. Write <, >, or =.

1 3

1.

>

2. – –0.29

>

3. –2 –2

4.Sarah competed in a long-jump contest. Her

first jump was 3.75 m, her second jump was 3 m,

and her third jump was 3 m. Which jump was the longest?

second jump