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Comparing and Ordering Rational Numbers. 3-10. Course 2. Warm Up. Problem of the Day. Lesson Presentation. Comparing and Ordering Rational Numbers. 3-10. Course 2. Warm Up Write each mixed number as an improper fraction. 1. 1 3. 1 . 23 8. 3 4. 7 8. 7 4.

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Comparing and Ordering Rational Numbers

3-10

Course 2

Warm Up

Problem of the Day

Lesson Presentation

Comparing and Ordering Rational Numbers

3-10

Course 2

Warm Up

Write each mixed number as an improper fraction.

1.1

3. 1

23

8

3

4

7

8

7

4

2. 2

1

12

5

6

11

6

97

12

4. 8

Comparing and Ordering Rational Numbers

3-10

Course 2

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

Comparing and Ordering Rational Numbers

3-10

Course 2

Learn to compare and order fractions and decimals.

Comparing and Ordering Rational Numbers

3-10

Course 2

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

=

Comparing and Ordering Rational Numbers

3-10

7

9

7

9

7

9

5

8

5

8

5

8

56

72

7 · 8

9 · 8

45

72

5 · 9

8 · 9

56

72

45

72

, and so .

>

>

Course 2

Compare the fractions. Write < or >.

A.

Both fractions can be written with a denominator of 72.

Write as fractions with

common denominators.

=

=

=

=

Comparing and Ordering Rational Numbers

3-10

2

5

2

5

3

7

2

5

3

7

Course 2

Compare the fractions. Write < or >.

B.

Both fractions can be written with a denominator of 35.

Write as fractions with

common denominators.

Put the negative signs

in the numerators.

–2 · 7

5 · 7

–14

35

=

=

–3 · 5

7 · 5

–15

35

=

=

3

7

14

35

15

35

>

, and so – > .

Comparing and Ordering Rational Numbers

3-10

5

6

5

6

5

6

7

8

7

8

7

8

40

48

5 · 8

6 · 8

42

48

7 · 6

8 · 6

40

48

42

48

, and so .

<

<

Course 2

Try This: Example 1A

Compare the fractions. Write < or >.

A.

Both fractions can be written with a denominator of 48.

Write as fractions with

common denominators.

=

=

=

=

Comparing and Ordering Rational Numbers

3-10

6

8

6

8

6

8

5

7

5

7

Course 2

Try This: Example 1B

Compare the fractions. Write < or >.

B.

Both fractions can be written with a denominator of 56.

Write as fractions with

common denominators.

Put the negative signs

in the numerators.

–6 · 7

8 · 7

–42

56

=

=

–5 · 8

7 · 8

–40

56

=

=

5

7

42

56

40

56

<

, and so – < .

Comparing and Ordering Rational Numbers

3-10

Course 2

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.

Comparing and Ordering Rational Numbers

3-10

Course 2

Compare the decimals. Write < or >.

0.427

0.425

Line up the decimal points.

0.427

7

The tenths and hundredths are

the same.

0.425

5

Compare the thousandths:

7 > 5.

0.427 > 0.425

Comparing and Ordering Rational Numbers

3-10

Course 2

Try This: Example 2

Compare the decimals. Write < or >.

0.535

0.538

Line up the decimal points.

0.535

5

The tenths and hundredths are

the same.

0.538

8

Compare the thousandths:

5 < 8.

0.535 < 0.538

Comparing and Ordering Rational Numbers

3-10

0 0.2 0.4 0.6 0.8 1

Course 2

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

Comparing and Ordering Rational Numbers

3-10

0 0.2 0.4 0.6 0.8 1

Course 2

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

Comparing and Ordering Rational Numbers

3-10

0 0.2 0.4 0.6 0.8 1

Course 2

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

Comparing and Ordering Rational Numbers

3-10

0 0.2 0.4 0.6 0.8 1

Course 2

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

Comparing and Ordering Rational Numbers

3-10

3

7

2

3

5

6

0.8, 0.826,

Course 2

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

4

10

3

7

5

8

2

3

or

2.

or

0.3, 0.312, 0.32

5

6

4.

, 0.8, 0.826

Comparing and Ordering Rational Numbers

3-10

Course 2

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