Warm Up

Problem of the Day

Lesson Presentation

Warm Up Write each mixed number as an improper

fraction. 1. 1 3. 1

23 8

7 4

3 4

7 8

2. 2

5 6

1 12

11 6

97 12

4. 8

Learn to compare and order fractions and

decimals.

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Vocabulary

rational number

7 9

2 9

Which is greater, or ?

When two fractions have the same denominator,

just compare the numerators.

7 9

2 9

gt

because 7 gt 2.

7 9

2 9

Additional Example 1A Comparing Fractions

Compare the fractions. Write lt or gt.

The LCM of the denominators 9 and 8 is 72.

Write equivalent fractions with 72 as the

denominator.

Compare the numbers.

Additional Example 1B Comparing Fractions

Compare the fractions. Write lt or gt.

Cross Multiply the denominator Of the first

fraction by the Numerator of the second

fraction Second, Cross multiply the Denominator

of the second fraction By the numerator of the

first fraction

Cross Multiply

-14 -15

-14 gt -15 So -2/5 gt -3/7

Check It Out Example 1A

Compare the fractions. Write lt or gt.

Check It Out Example 1B

Compare the fractions. Write lt or gt.

Both fractions can be written with a denominator

of 56.

Write equivalent 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

lt

, and so lt .

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.

Additional Example 2A Comparing Decimals

Compare the decimals. Write lt or gt.

0.427

0.425

0.427

Line up the decimal points.

7

The tenths and hundredths are the same.

0.425

5

Compare the thousandths

7 gt 5.

Since 0.007 gt 0.005, 0.427 gt 0.425.

Additional Example 2B Comparing Decimals

Compare the decimals. Write lt or gt.

0.73

0.734

0.733

Line up the decimal points.

3

The tenths and hundredths are the same.

0.734

4

Compare the thousandths

3 lt 4.

Check It Out Example 2A

Compare the decimals. Write lt or gt.

0.535

0.538

0.535

Line up the decimal points.

5

The tenths and hundredths are the same.

0.538

8

Compare the thousandths

5 lt 8.

Since 0.005 lt 0.008, 0.535 lt 0.538.

Check It Out Example 2B

Compare the decimals. Write lt or gt.

0.334

0.3333

Line up the decimal points.

3

The tenths and hundredths are the same.

0.334

4

Compare the thousandths

3 lt 4.

A rational number is a number that can be written

as a fraction with integers for its numerator and

denominator. When rational numbers are written in

a variety of forms, you can compare the numbers

by writing them all in the same form.

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Additional Example 3 Ordering Fractions and

Decimals

4 5

0.93, and 0.9 from least to greatest.

,

Order

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

0.80 lt 0.90 lt 0.93

Compare the decimals in order.

4 5

From least to greatest, the numbers are , 0.9,

0.93.

Check It Out Example 3

3 5

Order , 0.84, and 0.7 from least to greatest.

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

0.60 lt 0.70 lt 0.84

Compare the decimals in order.

3 5

From least to greatest, the numbers are , 0.7,

0.84.

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Lesson Practice

Compare the fractions. Write gt or lt. 1.

Compare the decimals. Write lt or gt. 3. 0.32

and 0.312

4 10

3 7

2 3

5 8

or

2.

or

gt

5 6

4. Order , 0.8, 0.826 from least to greatest.