7th Grade Math

134 Rational Numbers

A common denominator is a common multiple of the denominators

of two or more fractions. The least common denominator or LCD is

the LCM or least common multiple of the denominators. You can use

the LCD to compare fractions.

Compare Rational Numbers

Replace the ● with <, >, or = to make _ 127 ● _ 188 a true sentence.

The LCD of the denominators 2 and 3 is 6.

_ 127 = _ 127 × ×^33 _ 188 = _ 188 × ×^22

= ^2136 = ^1636

Since ^2136 > 3616 , 127 > 188.

Replace each ● with <, >, or = to make a true sentence.

b. _^56 ● _^7

9

c. _^15 ● _^7

50

d. - _^9

16

● - _^7

10

You can also compare fractions by writing each fraction as a decimal

and then comparing the decimals.

ROLLER SHOES In Mr. Huang’s math class, 20% of students own

roller shoes. In Mrs. Trevino’s math class, 5 out of 29 students

own roller shoes. In which class does a greater fraction of

students own roller shoes?

Express each number as a decimal and then compare.

20% = 0.2 _^5

29

= 5 ÷ 29

≈ 0.1724

Since 0.2 > 0.1724, 20% > _^5

29

.

A greater fraction of students in Mr. Huang’s class owns roller shoes.

e. BOWLING In a second period class, 37.5% of students like to

bowl. In a fifth period class, 12 out of 29 students like to bowl.

In which class does a greater fraction of the students like to bowl?

LCD

To fi nd the least common

denominator for _ 127 and

_ 188 , fi nd the LCM of 12

and 18.

12 = 2 × 2 × 3

18 = 2 × 3 × 3

LCM = 2 × 2 × 3 × 3

= 36

Percents as Decimals

To write a percent as a

decimal, remove the

percent sign and then

move the decimal point

two places to the left.

Add zeros if necessary.

20% = 20%

= 0.20

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