Warm-up: Countdown to testing week #7 Homework: Page 70 #1-10 all and #29-38 all

and d are integers and d  0. A rational number is any number that can be written as a fraction , where n and d are integers and d  0. n d

The goal of simplifying fractions is to make the numerator and the denominator relatively prime. Relatively prime numbers have no common factors other than 1.

Example 1 = 12 15 4 5

Example 2 Simplify. 16 80 16 = 1 • 4 • 4 80 = 5 • 4 • 4 ;16 is a common factor. = 16 ÷ 16 80 ÷ 16 Divide the numerator and denominator by 16. 16 80 1 5 = = 0 for a ≠ 0 = 1 for a ≠ 0 = = – Remember! 0a aa –7 8 7 –8 7 8

Example 3 Simplify. –18 29 18 = 2 • 9 29 = 1 • 29 ;There are no common factors. –18 29 = –18 29 18 and 29 are relatively prime.

Example 4 Simplify. 18 27 18 = 3 • 3 • 2 27 = 3 • 3 • 3 ; 9 is a common factor. 18 27 = 18 ÷ 9 27 ÷ 9 Divide the numerator and denominator by 9. 2 3 =

Example 5 Simplify. 17 –35 17 = 1 • 17 35 = 5 • 7 ; There are no common factors. 17 –35 = – 17 35 17 and 35 are relatively prime.

Homework: Page 70 #11-18 all and #39-46 all Warm-up Homework: Page 70 #11-18 all and #39-46 all 24 30 Simplify 16 28 18 42 15 21

Decimals that terminate or repeat are 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.

= 5 = = 37 100 5.37 7 is in the hundredths place. 622 1000 Example 1 Write each decimal as a fraction in simplest form. A. 5.37 37 100 = 5 5.37 7 is in the hundredths place. B. 0.622 622 1000 = 2 is in the thousandths place. 0.622 Simplify by dividing by the common factor 2. = 311 500

= 8 = 8 = = 75 100 8.75 5 is in the hundredths place. Example 2 Write each decimal as a fraction in simplest form. A. 8.75 75 100 = 8 8.75 5 is in the hundredths place. Simplify by dividing by the common factor 25. = 8 3 4 B. 0.2625 2625 10,000 = 5 is in the ten-thousandths place. 0.2625 = 21 80 Simplify by dividing by the common factor 125.

Warm-up: 3. 0.875 4. 0.43 Homework: Page 70 #19-28 all and #47-56 all Write each decimal as a fraction in simplest form. 27 100 – 5 8 1. 0.27 2. –0.625 7 8 43 100

numerator denominator denominator numerator To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. numerator denominator denominator numerator

_ 11 9 1 .2 9 11 .0 The pattern repeats. –9 2 –1 8 2 Example 1 Write the fraction as a decimal. 11 9 1 .2 9 11 .0 The pattern repeats. –9 2 –1 8 A repeating decimal can be written with a bar over the digits that repeat. So 1.2222… = 1.2. Writing Math _ 2 The fraction is equivalent to the decimal 1.2. 11 9

This is a terminating decimal. 20 7 .0 –0 7 –6 0 1 0 –1 0 Example 2 Write the fraction as a decimal. 7 20 .3 5 This is a terminating decimal. 20 7 .0 –0 7 –6 0 1 0 –1 0 The remainder is 0. The fraction is equivalent to the decimal 0.35. 7 20

The fraction is equivalent to the decimal 1.6. 15 9 Example 3 Write the fraction as a decimal. 15 9 1 .6 9 15 .0 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. –9 6 –5 4 6 The fraction is equivalent to the decimal 1.6. 15 9

This is a terminating decimal. 40 9 .0 –0 9 –8 0 1 0 – 8 2 – 2 Example 4 Write the fraction as a decimal. 9 40 .2 2 5 This is a terminating decimal. 40 9 .0 –0 9 –8 0 1 0 – 8 2 – 2 The remainder is 0. The fraction is equivalent to the decimal 0.225. 9 40