16
3-10 Comparing and Ordering Rational Numbers Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation
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3-10 Comparing and Ordering Rational Numbers
Course 2
Warm UpWarm UpProblem of the DayProblem of the DayLesson PresentationLesson Presentation
Learn to compare and order fractions and decimals.
Course 2
3-10 Comparing and Ordering Rational Numbers
Which is greater, or ?79
29
When two fractions have the same denominator, just compare the numerators.
79 > 2
9 because 7 > 2.
= 79
= 29
Course 2
3-10 Comparing and Ordering Rational Numbers
Compare the fractions. Write < or >.
Additional Example 1A: Comparing Fractions
A. 79
58
Both fractions can be written with a denominator of 72.79 = 7 · 8
9 · 8 = 5672
58 = 5 · 9
8 · 9 = 4572
5672 > 45
72 , and so . 79 > 5
8
Write as fractions with common denominators.
Course 2
3-10 Comparing and Ordering Rational Numbers
Additional Example 1B: Comparing Fractions
Compare the fractions. Write < or >.B. 2
537– –
25– = –2 · 7
5 · 7 = –14 35
37– = –3 · 5
7 · 5 = –15 35
– 1435 > – 15
35 , and so – > .25 – 3
7
Write as fractions withcommon denominators.Put the negative signs in the numerators.
Both fractions can be written with a denominator of 35.
Course 2
3-10 Comparing and Ordering Rational Numbers
Compare the fractions. Write < or >.
A. 56
78
Both fractions can be written with a denominator of 48.56 = 5 · 8
6 · 8 = 4048
78 = 7 · 6
8 · 6 = 4248
4048 < 42
48 , and so . 56 < 7
8
Write as fractions with common denominators.
Try This: Example 1A
Course 2
3-10 Comparing and Ordering Rational Numbers
Compare the fractions. Write < or >.B. 6
857– –
68– = –6 · 7
8 · 7 = –42 56
57– = –5 · 8
7 · 8 = –40 56
– 4256 < – 40
56 , and so – < .68 – 5
7
Write as fractions withcommon denominators.Put the negative signs in the numerators.
Try This: Example 1B
Both fractions can be written with a denominator of 56.
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.
Course 2
3-10 Comparing and Ordering Rational Numbers
Compare the decimals. Write < or >.
Additional Example 2: Comparing Decimals
0.427 0.425
0.427
0.425
0.427 > 0.425
Line up the decimal points.The tenths and hundredths arethe same.Compare the thousandths:
7
57 > 5.
Course 2
3-10 Comparing and Ordering Rational Numbers
Compare the decimals. Write < or >.
0.535 0.538
0.535
0.538
0.535 < 0.538
Line up the decimal points.The tenths and hundredths arethe same.Compare the thousandths:
5
85 < 8.
Try This: Example 2
Course 2
3-10 Comparing and Ordering Rational Numbers
Order the numbers from least to greatest.Additional Example 3: Ordering Fractions and Decimals
45 0.93, and 0.9 ,
45 = 0.80
Graph the numbers on a number line.
0 0.2 0.4 0.6 0.8 1
0.93
Write as decimals with the same number of places.
0.93 = 0.93 0.9 = 0.90
Course 2
3-10 Comparing and Ordering Rational Numbers
Additional Example 3 Continued
The values on a number line increase as we move from left to right.
0.80 < 0.90 < 0.93
45 , 0.9, 0.93
Place the decimals in order.
Order the numbers from least to greatest.45 0.93, and 0.9 ,
0 0.2 0.4 0.6 0.8 1
0.93
Course 2
3-10 Comparing and Ordering Rational Numbers
Order the numbers from least to greatest.Try This: Example 3
35 0.84, and 0.7 ,
35 = 0.60
Graph the numbers on a number line.
0 0.2 0.4 0.6 0.8 1
0.84
Write as decimals with the same number of places.
0.84 = 0.84 0.7 = 0.70
Course 2
3-10 Comparing and Ordering Rational Numbers
Try This: Example 3 Continued
The values on a number line increase as we move from left to right.
0.60 < 0.70 < 0.84
35 , 0.7, 0.84
Place the decimals in order.
Order the numbers from least to greatest.35 0.84, and 0.7 ,
0 0.2 0.4 0.6 0.8 1
0.84
Course 2
3-10 Comparing and Ordering Rational Numbers
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
Insert Lesson Title Here
0.3, 0.312, 0.32
37 or 4
1058 or 2
32. 23
37
56 , 0.8, 0.826 0.8, 0.826, 5
64.
Course 2
3-10 Comparing and Ordering Rational Numbers
Lesson Quiz: Part 25. 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? Monday
Insert Lesson Title Here
3811
4
Course 2
3-10 Comparing and Ordering Rational Numbers
