Comparing Rational Numbers

Absent copy

11/14,15

A Rational number is any number (neg. or pos.)

that can be written as a fraction. But a fraction can also be written as a decimal.

Ex: 12 -3 7.2 -5.81 15

Make fraction 12 -3 7 2/10 -5 81/100 15 1

Example #1Which Rational number(fraction)is greater or are they equal.

5 78 12

12 • 5 7 • 8 12 • 8 12 • 8 60 56 96 96

60Solution

• In order to compare these fractions what do they both have to have?

• You have to get a common denominator.

• How do we get a common denominator?

• You cross multiply each denominator to the whole fraction.

• After cross multiplying what do we do?

• You re-write each fraction.

• What do we compare to see what fraction is greater?

• You compare the numerators on each fraction and see what one is greater or maybe they are equal.

58

Example #2Which Rational

number(fraction)is greater or are they equal.

6 215 5

5 • 6 2 • 15

5 • 15 5 • 15

30 30

75 75

30 = 30

Solution

• In order to compare these fractions what do they both have to have?

• You have to get a common denominator.

• How do we get a common denominator?

• You cross multiply each denominator to the whole fraction.

• After cross multiplying what do we do?

• You re-write each fraction.• What do we compare to

see what fraction is greater?

• You compare the numerators on each fraction and see what one is greater or maybe they are equal.

They are equal

Example #3Which Rational

number(fraction)is greater or are they equal.

-2 -5 3 7

7 • -2 -5 • 3 7 • 3 7 • 3 -14 -15 21 21

-14

Solution

• In order to compare these fractions what do they both have to have?

• You have to get a common denominator.

• How do we get a common denominator?

• You cross multiply each denominator to the whole fraction.

• After cross multiplying what do we do?

• You re-write each fraction.

• What do we compare to see what fraction is greater?

• You compare the numerators on each fraction and see what one is greater or maybe they are equal.

• What is the difference when looking at numerators that are Neg.?

• When both numerators are neg. the smaller number is really greater.

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Example #4Which Rational number(fraction)is greater or are they equal.

2¼ 2½

9 54 2

2 • 9 5 • 4 2 • 4 2 • 4

18 20 8 8

20

Solution

• In order to compare these fractions what do we have to do first? (2 steps)

• You have to change the mixed number into a fraction.

• You have to get a common denominator for both fractions.

• How do we get a common denominator?

• You cross multiply each denominator to the whole fraction.

• After cross multiplying what do we do?

• You re-write each fraction.• What do we compare to see

what fraction is greater?• You compare the numerators on

each fraction and see what one is greater or maybe they are equal.

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