Learn to write rational numbers in equivalent forms.

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.

Additional Example 1A: Simplifying Fractions 16 80

Additional Example 1B: Simplifying Fractions –18 29

Check It Out: Example 1A Simplify. 18 27

Check It Out: Example 1B Simplify. 17 –35

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.

Additional Example 2: Writing Decimals as Fractions 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. Check It Out: 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.

Additional Example 3A: Writing Fractions as Decimals 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

Additional Example 3B: Writing Fractions as Decimals 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 Check It Out: Example 3A 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