Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers Warm Up Warm Up California Standards California Standards Lesson Presentation

Evaluating Algebraic Expressions

2-2 Comparing and Ordering Rational Numbers

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California StandardsCalifornia Standards

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Warm UpWrite each fraction as a decimal.

1. 1 3

0.3 2. 45

3. 4.

0.8

0.753 4

23

0.6



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

California Standards



least common denominator (LCD)

Vocabulary



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.


2-2 Comparing and Ordering Rational NumbersAdditional Example 1A: Comparing Fractions by Finding a

Common DenominatorCompare. Write <, >, or =.

Multiply 6 and 10 to find a common denominator.

5 6

7 10

Write the fractions with a common denominator.

Compare the fractions.

Method 1: Multiply to find a common denominator.

6 10 = 60

5 10 6 10

=5 6

10 10

= 50 60

7 6 10 6

=7 10

6 6

= 42 60

50 60

5 6

> 42 60

,so 7 10

>

>



Remember!

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


2-2 Comparing and Ordering Rational NumbersAdditional Example 1B: Comparing Fractions by Finding a

Common DenominatorCompare. Write <, >, or =.

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

2 3

4 5



Method 2: Find the least common denominator.

3; 3, 6, 9, 12, 15… 5; 5, 10, 15

2 5 3 5

=2 3

5 5

= 10 15

4 3 5

3

=4 5

3 3

= 12 15

10 15

2 3

< 12 15

,so 4 5

<

>



Check It Out! Example 1A

Compare. Write <, >, or =.

Multiply 2 and 5 to find a common denominator.

1 2

2 5



Method 1: Multiply to find a common denominator.

2 5 = 10

1 5 2 5

=1 2

5 5

= 5 10

2 2 5 2

=2 5

2 2

= 4 10

5 10

1 2

> 4 10

,so 2 5

>

>



Check It Out! Example 1BCompare. Write <, >, or =.

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

2 3

3 4



Method 2: Find the least common denominator.

3; 3, 6, 9, 12, … 4; 4, 8, 12…

2 4 3 4

=2 3

4 4

= 8 12

3 3 4

3

=3 4

3 3

= 9 12

8 12

2 3

< 9 12

,so 3 4

<

>



A. 5 5

Additional Example 2: Comparing by Using Decimals


2 9 _ 2

7 _

Write the fractions as decimals.

5 = 5.2 and 5 = 5.285714… 2 9 _ 2

7 __

5.2 < 5.285714…, so 5 < 5 _ 2

9 _ 2

7 _ Compare the

decimals.

<



B. –0.44 –

Additional Example 2: Comparing by Using Decimals

Compare. Write <, >, or =.2 5 _

– = –0.4 2 5 _

–0.44 < –0.4, so –0.44 < –2 5 _ Compare the

decimals.

<

Write - as decimal.2 5 _

C. 0.1 1 9 _

Compare the decimals.

Write as decimal.1 9 _

>

1 9 _ = 0.1

0.1 > 0.1, so > 0.11 9

_



A. 4 4

Check It Out! Example 2


2 9 _ 3

5 _

Write the fractions as decimals.

4 = 4.2 and 4 = 4.6 2 9 _ 3

5 __


<

4.2 < 4.6, so 4 < 4 2 9 _ 3

5 _



B. –0.80 –

Check It Out! Example 2


4 5 _

– = –0.8 4 5 _

–0.80 = –0.8, so –0.80 = –4 5 _ Compare the

decimals.

=

Write – as decimal.4 5 _

C. 0.8 5 6 _


Write as decimal.5 6 _

>

0.83 > 0.8, so > 0.85 6

_ _

5 6 _ = 0.83



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.



Additional Example 3: Social Studies Application

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.

14 4__

–4 –3 –2 –1 0 1 2 3 4 5 6

–2.5

6.0

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

–3.4

14 4__

14 4

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


2-2 Comparing and Ordering Rational NumbersCheck It Out! Example 3

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.

7 2__

–5 –4 –3 –2 –1 0 1 2 3 4 5

–2.2

3.0

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

–3.9

7 2__

The percent changes in population from least to greatest are –3.9, –2.2, 3.0, and .7

2


2-2 Comparing and Ordering Rational NumbersLesson Quiz


1.

2. – –0.29

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?

3. –2 –2 >

>

<1 3

second jump

1 4

2 9

6 7

7 8

8 99

11

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Evaluating Algebraic Expressions 2-2 Comparing and Ordering Rational Numbers Warm Up Warm Up California Standards California Standards Lesson Presentation