6th Grade Math Textbook, Fundamentals

Update your skills. See page 413 XV.

Compare and Order Rational Numbers

Objective To compare and order rational numbers • To use the LCD to rename fractions

• To rename mixed numbers as fractions greater than 1 • To rename fractions greater than 1 as
  mixed numbers • To name a rational number between any two rational numbers • To use cross
  products to compare fractions

In a gymnastics competition, Gina scored 7 points, and

Mei scored 7 points. Who scored fewer points?

To find who scored fewer points, compare 7 and 7.

To compare mixed numbers, first compare the integer

parts. If needed, rename the fraction parts as equivalent

fractions using the LCD, and then compare the fractions.

• Compare the integer parts of the mixed numbers.
  7  7


• The integers are equal. Compare the fractions. Use the
  LCD to rename the fractions with like denominators.

Find the LCD of and.

Multiples of 4: 4, 8, 12, 16, 20, 24,...

Multiples of 10: 10, 20,...

The LCD of 4 and 10 is 20.

Rename 7 as a mixed number with Rename 7 as a mixed number with

a denominator of 20. a denominator of 20.

7   7 7   7

So 7 7. So 7 7.

Compare the numerators of the fractions: 5  6

Since 7 is less than 7 , Gina scored fewer points than Mei.

You can find a rational number between any two

rational numbers.

Name a number between 7 and 7.

7, , 7

• Rename the fractions as equivalent fractions in 7  7  7
  greater terms that have the same denominator.


• Look at the numerators, and write the integers 7  7  7
  between them.

11 is between 10 and 12, so 7 is between 7 and 7.

To compare and order fractions and decimals, first rename

the fractions as equivalent decimals. Then compare and order.

10

40

5 • 2

20 • 2

5

20

12

40

6 • 2

20 • 2

6

20

6

20

5

20

205? 206

3

10

1

4

3 • 2

10 • 2

1 • 5

4 • 5

3

10

1

4

5

20

5

20

6

20

6

20

3

10

1

4

3

10

1

4

3

10

1

4

11

40

3

10

1

4

3

10

1

4

 &KDSWHU

5-5

An infinite number of rational

numbers can be found between

any two rational numbers.

Density Property