1. Preview
Warm Up
California Standards
Lesson Presentation

2. Warm Up
Write each fraction as a decimal.
0.3
1 3 45 1. 2.
0.8
0.6
3 4 23 3.
0.75 4.

3. 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

4. Vocabulary
least common denominator (LCD)

5. 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.

6. Multiply 6 and 10 to find a common denominator.
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
5   10 =
5 6 
10 10
50 60
Write the fractions with a common denominator.
7   6 =
7 10 
6 6
42 60
50 60
5 6
>
42 60
,so
7 10
Compare the fractions.

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

8. List multiples of 3 and 5. The LCM is 15.
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
2  5 3  5 =
2 3 
5 5
10 15
Write the fractions with a common denominator.
4   3 =
4 5 
3 3
12 15
10 15
2 3
<
12 15
,so
4 5
Compare the fractions.

9. Multiply 2 and 5 to find a common denominator.
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
1  5 2  5 =
1 2 
5 5
5 10
Write the fractions with a common denominator.
2   2 =
2 5 
2 2
4 10
5 10
1 2
>
4 10
,so
2 5
Compare the fractions.

10. List multiples of 3 and 4. The LCM is 12.
Check It Out! Example 1B
Compare. Write <, >, or =.
2 3
3 4
>
Method 2: Find the least common denominator.
3; 3, 6, 9, 12, … 4; 4, 8, 12…
List multiples of 3 and 4. The LCM is 12.
2  4 3  4 =
2 3 
4 4
8 12
Write the fractions with a common denominator.
3   3 =
3 4 
3 3
9 12
8 12
2 3
<
9 12
,so
3 4
Compare the fractions.

11. Additional Example 2: Comparing by Using Decimals
Compare. Write <, >, or =.
2 9 _
2 7 _ A
<
5 = 5.2 and 5 = …
2 9 _
2 7
Write the fractions as decimals.
5.2 < …, so 5 < 5 _
2 9
2 7
Compare the decimals.

12. Additional Example 2: Comparing by Using Decimals
Compare. Write <, >, or =.
2 5 _
B. – –
<
– = –0.4
2 5 _
Write - as decimal.
2 5 _
–0.44 < –0.4, so –0.44 < –
2 5 _
Compare the decimals.
1 9 _ C
>
1 9 _
= 0.1
Write as decimal.
1 9 _
0.1 > 0.1, so > 0.1
1 9 _
Compare the decimals.

13. _ _ _ _ Write the fractions as decimals. Compare the decimals.
Check It Out! Example 2
Compare. Write <, >, or =.
2 9 _
3 5 _ A
<
4 = 4.2 and 4 = 4.6
2 9 _
3 5
Write the fractions as decimals.
4.2 < 4.6, so 4 < 4
2 9 _
3 5
Compare the decimals.

14. _ _ _ _ _ _ _ _ Write – as decimal. Compare the decimals.
Check It Out! Example 2
Compare. Write <, >, or =.
4 5 _
B. – – =
– = –0.8
4 5 _
Write – as decimal.
4 5 _
–0.80 = –0.8, so –0.80 = –
4 5 _
Compare the decimals.
5 6 _ C
>
5 6 _
= 0.83
Write as decimal.
5 6 _
0.83 > 0.8, so > 0.8
5 6 _
Compare the decimals.

15. 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.

16. 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. __
Place the numbers on a number line and read them from left to right. 
14 4 __ 
–3.4
6.0 
–2.5 
–4 –3 –2 –
14 4
The percent changes in population from least to greatest are –3.4, –2.5, , and 6.0. __

17. __ Check It Out! Example 3 7 2 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 __ 
–3.9
3.0 
–2.2 
–5 –4 –3 –2 –
The percent changes in population from least to greatest are –3.9, –2.2, 3.0, and .

18. < > > Lesson Quiz Compare. Write <, >, or =. 1 4 1 3 1.
2 9
>
2. – –0.29
6 7
7 8
3. – –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 m. Which jump was the longest?
8 9
9 11
second jump