1. Equivalent Fractions and Decimals 2-6

2. * Write these in the “Vocabulary” section of your binder. Make sure to add an example! * Equivalent fractions are different expressions for the same nonzero number. * Relatively prime numbers have no common factors other than 1. * A rational number is a number that can be written as a fraction with an integer for its numerator and a nonzero integer for its denominator. * Terminating decimals are decimals that come to an end. * Repeating decimals are decimals that repeat a pattern forever.

3. In some recipes the amounts of ingredients are given as fractions, and sometimes those fractions do not equal the fractions on a measuring cup. Knowing how fractions relate to each other can be very helpful. Different fractions can name the same number. 3535 = = 15 25 6 10

4. = To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by the same number. In the diagram =. These are called equivalent fractions because they are different expressions for the same nonzero number. 3535 6 10 15 25

5. Check It Out: Example 1 Find two fractions equivalent to. 6 · 2 12 · 2 = 12 24 Multiply the numerator and denominator by 2. 6 ÷ 2 12 ÷ 2 = 3636 Divide the numerator and denominator by 2. 6 12

6. A fraction is in simplest form when the numerator and denominator are relatively prime. Relatively prime numbers have no common factors other than 1.

7. Write the fraction in simplest form. Check It Out: Example 2 15 45 Find the GCF of 15 and 45. The GCF is 3 5 = 15. = 15 45 Divide the numerator and denominator by 15. 15 = 3 5 45 = 3 3 5 15 ÷ 15 45 ÷ 15 = 1 3

8. 8585 = 1 3535 8585 is an improper fraction. Its numerator is greater than its denominator. 1 3535 is a mixed number. It contains both a whole number and a fraction. An improper fraction is a fraction where the numerator is than or equal to the denominator. Remember!

9. A. Write Additional Example 4: Converting Between Improper Fractions and Mixed Numbers 13 5 as a mixed number. First divide the numerator by the denominator. 13 5 = 2 3535 Use the quotient and remainder to write a mixed number. B. Write 7 2323 as an improper fraction. First multiply the denominator and whole number, and then add the numerator. 23  + = 3 · 7 + 2 3 = 23 3 Use the result to write the improper fraction.

10. A rational number is a number that can be written as a fraction with an integer for its numerator and a nonzero integer for its denominator. To write a rational number as a decimal, divide the numerator by the denominator.

11. Write each fraction as a decimal. Round to the nearest hundredth, if necessary. Additional Example 1: Writing Fractions as Decimals A. 1414 1.00 9.0 5.000 B. 9595 C. 5353 4 5 3 0.2 – 8 20 – 20 0 1414 = 0.25 5 1 – 5 40.8 – 40 0 9595 = 1.8 1 – 3 20.6 – 18 20 – 18 6 20 – 18 2 5353 ≈ 1.67 6

12. The decimals 0.75 and 1.2 in Example 1 are terminating decimals because the decimals comes to an end. The decimal 0.333…is a repeating decimal because the decimal repeats a pattern forever. You can also write a repeating decimal with a bar over the repeating part. 0.333… = 0.3 0.8333… = 0.83 0.727272… = 0.72

13. Write each fraction as a decimal. Additional Example 2A: Write Fractions as Terminating and Repeating Decimals A. 25 9 25 ______ ) 9.00 0. 3 –75 The remainder is 0. 150 6 –150 0 9 25 = 0.36 This is a terminating decimal.

14. Write each fraction as a decimal. Additional Example 2B: Write Fractions as Terminating and Repeating Decimals B. 18 17 18 ______ ) 17.00 0. 9 –162 The pattern repeats. 80 4 – 72 8 17 18 = 0.94 This is a repeating decimal.

15. Write each decimal as a fraction in simplest form. Additional Example 3: Writing Decimals as Fractions A. 0.018 B. 1.55 0.018 = 18 1,000 1.55 = 155 100 = 18 ÷ 2 1,000 ÷ 2 = 155 ÷ 5 100 ÷ 5 = 31 20 or 1 11 20 = 9 500 You read the decimal 0.018 as “eighteen thousandths.” Reading Math