1. Comparing and Ordering Rational Numbers
3-10
Comparing and Ordering Rational Numbers
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Comparing and Ordering Rational Numbers
Course 2
3-10
Comparing and Ordering Rational Numbers
Warm Up
Write each mixed number as an improper fraction.
1. 1
3. 1 3 4 7 4 7 8 23 8
2. 2 5 6 11 6 1 12 97 12
4. 8

3. Comparing and Ordering Rational Numbers
Course 2
3-10
Comparing and Ordering Rational Numbers
Problem of the Day
Hot dogs are sold in packs of 6. Buns are sold in bags of 8. What is the least number of hot dog packages and the least number of bun packages you would need to buy in order to have the same number of hot dogs and buns?
4 packages of hot dogs and 3 packages of buns

4. Learn to compare and order fractions and decimals.
Course 2
3-10
Comparing and Ordering Rational Numbers
Learn to compare and order fractions and decimals.

5. Comparing and Ordering Rational Numbers
Course 2
3-10
Comparing and Ordering Rational Numbers 7 9 2 9
Which is greater, or ?
When two fractions have the same
denominator, just compare the numerators. 7 9 2 9
>
because 7 > 2. 7 9 = 2 9 =

6. Additional Example 1A: Comparing Fractions
Course 2
3-10
Comparing and Ordering Rational Numbers
Additional Example 1A: Comparing Fractions
Compare the fractions. Write < or >. 7 9 5 8 A.
Both fractions can be written with a denominator of 72. 7 9
7 · 8
9 · 8 56 72
Write as fractions with
common denominators. = = 5 8
5 · 9
8 · 9 45 72 = = 56 72
> 45
, and so 7 9
> 5 8

7. Additional Example 1B: Comparing Fractions
Course 2
3-10
Comparing and Ordering Rational Numbers
Additional Example 1B: Comparing Fractions
Compare the fractions. Write < or >. 2 5 B. 3 7 – –
Both fractions can be written with a denominator of 35. 2 5
–2 · 7
5 · 7
–14 35
Write as fractions with
common denominators.
Put the negative signs
in the numerators. – = = 3 7
–3 · 5
7 · 5
–15 35 – = = 14 35 15 35 2 5 3 7 –
> –
, and so – > –

8. Comparing and Ordering Rational Numbers
Course 2
3-10
Comparing and Ordering Rational Numbers
Try This: Example 1A
Compare the fractions. Write < or >. 5 6 7 8 A.
Both fractions can be written with a denominator of 48. 5 6
5 · 8
6 · 8 40 48
Write as fractions with
common denominators. = = 7 8
7 · 6
8 · 6 42 48 = = 40 48
< 42
, and so 5 6
< 7 8

9. Comparing and Ordering Rational Numbers
Course 2
3-10
Comparing and Ordering Rational Numbers
Try This: Example 1B
Compare the fractions. Write < or >. 6 8 B. 5 7 – –
Both fractions can be written with a denominator of 56. 6 8
–6 · 7
8 · 7
–42 56
Write as fractions with
common denominators.
Put the negative signs
in the numerators. – = = 5 7
–5 · 8
7 · 8
–40 56 – = = 42 56 40 56 6 8 5 7 –
< –
, and so – < –

10. Course 2
3-10
Comparing and Ordering Rational Numbers
To compare decimals, line up the decimal points and compare digits from left to right until you find the place where the digits are different.

11. Additional Example 2: Comparing Decimals
Course 2
3-10
Comparing and Ordering Rational Numbers
Additional Example 2: Comparing Decimals
Compare the decimals. Write < or >.
0.427
0.425
0.427 7
Line up the decimal points.
The tenths and hundredths are
the same.
0.425 5
Compare the thousandths:
7 > 5.
0.427 > 0.425

12. Comparing and Ordering Rational Numbers
Course 2
3-10
Comparing and Ordering Rational Numbers
Try This: Example 2
Compare the decimals. Write < or >.
0.535
0.538
0.535 5
Line up the decimal points.
The tenths and hundredths are
the same.
0.538 8
Compare the thousandths:
5 < 8.
0.535 < 0.538

13. Additional Example 3: Ordering Fractions and Decimals
Course 2
3-10
Comparing and Ordering Rational Numbers
Additional Example 3: Ordering Fractions and Decimals
Order the numbers from least to greatest. 4 5 ,
0.93, and 0.9
Write as decimals with the same number of places. 4 5
= 0.80
0.93 = 0.93
0.9 = 0.90
Graph the numbers on a number line.
0.93

14. Additional Example 3 Continued
Course 2
3-10
Comparing and Ordering Rational Numbers
Additional Example 3 Continued
Order the numbers from least to greatest. 4 5 ,
0.93, and 0.9
The values on a number line increase as we
move from left to right.
0.80 < 0.90 < 0.93
Place the decimals in order. 4 5
, 0.9, 0.93
0.93

15. Comparing and Ordering Rational Numbers
Course 2
3-10
Comparing and Ordering Rational Numbers
Try This: Example 3
Order the numbers from least to greatest. 3 5 ,
0.84, and 0.7
Write as decimals with the same number of places. 3 5
= 0.60
0.84 = 0.84
0.7 = 0.70
Graph the numbers on a number line.
0.84

16. Try This: Example 3 Continued
Course 2
3-10
Comparing and Ordering Rational Numbers
Try This: Example 3 Continued
Order the numbers from least to greatest. 3 5 ,
0.84, and 0.7
The values on a number line increase as we
move from left to right.
0.60 < 0.70 < 0.84
Place the decimals in order. 3 5
, 0.7, 0.84
0.84

17. Insert Lesson Title Here
Course 2
3-10
Comparing and Ordering Rational Numbers
Insert Lesson Title Here
Lesson Quiz: Part 1
Choose the greater number. 1.
Place the numbers in order from least to greatest
3. 0.3, 0.32, 0.312 3 7 4 10 3 7 5 8 2 3 2 3 or 2. or
0.3, 0.312, 0.32 4. 5 6
0.8, 0.826, 5 6
, 0.8, 0.826

18. Insert Lesson Title Here
Course 2
3-10
Comparing and Ordering Rational Numbers
Insert Lesson Title Here
Lesson Quiz: Part 2
5. Dana’s cross-country team is getting ready for a big meet. On Monday they ran 3.7 miles, on Tuesday they ran 3 miles, and on Wednesday they ran miles. On which day did they run the greatest distance? 3 8 11 4
Monday