ALGEBRA READINESS

LESSON 4-5Warm Up

ALGEBRA READINESS

LESSON 4-4Warm Up

ALGEBRA READINESS

“Comparing and Ordering Rational Numbers” (4-5)

How do you order rational numbers?

To order rational numbers, put them all into decimal form. Then, put the decimals in order by: 1. graphing them on a number line, or 2. changing them to decimal form and lining the numbers up vertically by the decimal points, adding zeroes in blank spaces, and comparing the place values from the left (largest place values) to the right (smallest place values) [In the result of a tie, go to the next largest place value until there is no longer a tie].

Example:

Write each fraction as a decimal by dividing the bottom into the top.

Graph each decimal on a

number line.

Change the decimals back to their original form.

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Order –0.175, , – , 1.7, –0.95 from least to greatest.23

58

Then graph each decimal on a number line.

The number line shows that –0.95 < –0.625 < –0.175 < 0.667 < 1.7

So, –0.95 < – < –0.175 < < 1.7.23

58

Write each fraction as a decimal.

23 0.667

58 = –0.625–

Comparing and Ordering Rational NumbersLESSON 4-5

Additional Examples

Turn the decimals that were changed back into fractions (original form).

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“Comparing and Ordering Rational Numbers” (4-5)

How do you compare fractions?

To compare fractions, you can compare the numerators (number of parts) if the denominator (size of the parts) are equal. So, if the denominators aren’t the same, you need to change one or more of the fractions into equivalent fractions with a common denominator.

Method 1: One way you find a common denominator is to multiply the two original denominators.

Example: Recipe A uses cups sugar and Recipe B uses cups sugar. Which recipe uses more sugar?

3 • 4 = 12 Multiply the denominators together to find a common denominator

Write equivalent fractions with a denominator of 12 (Hint: Notice that you multiply the each fraction by the other fractions denominator)

Since , then , so Recipe B uses more sugar.

2 3

3 4

2 • 4 = 8_ 3 • 4 = 12 3 • 3 = 9_ 4 • 3 = 12

9 12

8 12

3 4

2 3

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“Comparing and Ordering Rational Numbers” (4-5)

What is the “least common multiple” (LCM) and “least common denominator” (LCD)?

Method 2: Another way to find a common denominator is to use the Least Common Denominator (LCD). The advantage of this method is that you will not need to reduce the answer later.

Least Common Multiple (LCM): the smallest multiple shared by all of the numbers

Least Common Denominator (LCD): the LCM of two or more denominators (in other words, the smallest common denominator)

Example:

List the multiples of each denominator until you find a multiple that is shared by both numbers (LCM). LCM = 36

Rewrite the fractions into equivalent fractions with a denominator of 36 (The LCD is 36). Then, compare thenumerators.

Since , then , .16 36

15 36

4 9

5 12

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The Eagles won 7 out of 11 games, while the Seals

won 8 out of 12 games. Which team has the better record?

A common denominator of 11 and 12 is 11 • 12, or 132.

Write equivalent fractions with adenominator of 132.Seals:

812

711Eagles:

7 • 12 11 • 12= 84

132=

8 • 11 12 • 11= 88

132=

Because > , > . The Seals have the better record. 88 132

84 132

812

711

Comparing and Ordering Rational NumbersLESSON 4-5

Additional Examples

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718

512

The LCM of 18 and 12 is 36. So the LCD of the fractions is 36.

Multiples of 18: 18, 36

Multiples of 12: 12, 24, 36

Stop when you find a multiple thatis shared by both numbers.

Compare and using their LCD. Use <, =, >.

List multiples of each denominator to find their LCD.

5 • 312 • 3

Use the LCD to write equivalent fractions.

718

7 • 218 • 2=

1436=

512 = 15

36=

1436

1536 > , >

718.

512

so

Comparing and Ordering Rational NumbersLESSON 4-5

Additional Examples

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Compare. Use <, >, or =.

1. 2.

3. 4. 0.35

5. Order 0.17, , –0.3, 0, and – from least to greatest.

6. A survey found that 75 out of 125 men and 88 out of 136 women prefer comedy films over action films. Which group prefers comedy over action films more?

< >

= =

–0.3, – , 0, 0.17, 14

15

5 12

8 15

45

8 11

1550

36 120

7 20

15

14

women

Comparing and Ordering Rational NumbersLESSON 4-5

Lesson Quiz