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Equivalent Fractions and Decimals 2-6

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* 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.

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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

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= 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

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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

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

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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

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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!

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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.

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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.

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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

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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

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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.

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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.

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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

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