Evaluating Algebraic Expressions

2-1 Rational Numbers

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Evaluating Algebraic Expressions

2-1 Rational Numbers

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12 24

34

16

1. 36 3 2. 144 6

3. 68 17 4. 345 115

5. 1024 64

Evaluating Algebraic Expressions

2-1 Rational Numbers

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Patricia works twice as many days as Laura works each month. Laura works 3 more days than Jaime. If Jaime works 10 days each month, how many days does Patricia work?

Evaluating Algebraic Expressions

2-1 Rational Numbers

rational numberterminating decimalrepeating decimal

Vocabulary

Evaluating Algebraic Expressions

2-1 Rational Numbers

A rational number is any number that can be written as a fraction , where n

and d are integers and d 0.

nd

Any fraction can be written as a decimal by dividing the numerator by the denominator. If the division ends or terminates, because the remainder is zero, then the decimal is a terminating decimal.

Evaluating Algebraic Expressions

2-1 Rational Numbers

If the division leads to a repeating block of one or more digits (where all digits are not zeros) after the decimal point, then the decimal is a repeating decimal. A repeating decimal can be written with a bar over the digits that repeat. So 0.13333… = 0.13 (bar notation)

Evaluating Algebraic Expressions

2-1 Rational Numbers

9 11 The pattern repeats.

1

–9

.2

2

0

.0

2

11 9

–1 8

Additional Example 1A: Writing Fractions as Decimals

Write the fraction as a decimal.

The fraction is equivalent to the decimal 1.211 9

This is a repeating decimal.

Evaluating Algebraic Expressions

2-1 Rational Numbers

This is a terminating decimal.20 7

.30 5

The remainder is 0.

7 20

–07

1 0

0

0

0

.0

0–6 0

–1 0 0

Additional Example 1B: Writing Fractions as Decimals

Write the fraction as a decimal.

The fraction is equivalent to the decimal 0.357 20

Evaluating Algebraic Expressions

2-1 Rational Numbers

9 15 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal.

1

–9

.6

6

0

.0

6

15 9

–5 4

Write the fraction as a decimal. Check your answer with a calculator.

Partner Share! Example 1A

The fraction is equivalent to the decimal 1.6.15 9

Evaluating Algebraic Expressions

2-1 Rational Numbers

40 9 This is a terminating decimal.

.20 2

The remainder is 0.

9 40

–09

1 0

0

0

.0

0–8 0

– 8 02 0

0

0

5

0– 2 00

Write the fraction as a decimal. Check youranswer with a calculator.

Partner Share! Example 1B

The fraction is equivalent to the decimal 0.225.9 40

Evaluating Algebraic Expressions

2-1 Rational Numbers

To write a terminating decimal as a fraction, identify the place value of the digit farthest to the right. Then write all of the digits after the decimal point as the numerator with the place value as the denominator.

Evaluating Algebraic Expressions

2-1 Rational Numbers

5.37

A. 5.377 is in the hundredths place, so write hundredths as the denominator.

37 100

= 5

Additional Example 2: Writing Terminating Decimals as Fractions

Write each decimal as a fraction in simplest form.

0.622

B. 0.6222 is in the thousandths place, so write thousandths as the denominator.

622 1000

=

= 311 500

Simplify by dividing by the greatest common divisor.

Evaluating Algebraic Expressions

2-1 Rational Numbers

A fraction is in reduced, or simplest, form when the numerator and the denominator have no common divisor other than 1.

Remember!

Evaluating Algebraic Expressions

2-1 Rational Numbers

8.75

A. 8.75 5 is in the hundredths place, so write hundredths as the denominator.

75 100

= 8

= 8 3 4

Simplify by dividing by the greatest common divisor.

Write each decimal as a fraction in simplest form.Partner Share! Example 2

0.2625

B. 0.26255 is in the ten-thousandths place.

2625 10,000

=

= 21 80

Simplify by dividing by the greatest common divisor.

Evaluating Algebraic Expressions

2-1 Rational Numbers

x = 0.44444… Let x represent the number.

Additional Example 3: Writing Repeating Decimals as Fractions

Write 0.4 as a fraction in simplest form.

10x = 10(0.44444…) Multiply both sides by 10 because 1 digit repeats.

Subtract x from both sides to eliminate the repeating part. Since x = 0.44444…, use 0.44444… for x on the right side of the equation.

_

10x = 4.444444…

x = 0.44444…

9x = 4

9x = 4 9 9

Since x is multiplied by 9, divide both sides by 9.

x = 4 9

Evaluating Algebraic Expressions

2-1 Rational Numbers

x = 0.363636… Let x represent the number.

Partner Share! Example 3

Write 0.36 as a fraction in simplest form.

100x = 100(0.363636…) Multiply both sides by 100 because 2 digits repeat.

Subtract x from both sides to eliminate the repeating part. Since x = 0.363636…, use 0.363636… for x on the right side of the equation.

__

100x = 36.363636…

x = 0.363636…

99x = 36

99x = 36 99 99

Since x is multiplied by 99, divide both sides by 99.

x = =36 99

4 11

Write in simplest form.

Evaluating Algebraic Expressions

2-1 Rational NumbersLesson Review!

Write each decimal as a fraction in simplest form.

1. 0.35 2. 0.600

3. Write as a decimal. 2.16

7 20

3 5

13 6

Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal.)

4.

0.325