2 6 Equivalent Fractions and Decimals Do Now

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2 -6 Equivalent Fractions and Decimals Do Now Write the following number in words.

2 -6 Equivalent Fractions and Decimals Do Now Write the following number in words. 0. 125

2 -6 Equivalent Fractions and Decimals Learn to write fractions as decimals, and vice

2 -6 Equivalent Fractions and Decimals Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating.

2 -6 Equivalent Fractions and Decimals Fractions and decimals belong to the group of

2 -6 Equivalent Fractions and Decimals Fractions and decimals belong to the group of numbers called rational numbers. A fraction bar is a representation of division.

2 -6 Equivalent Fractions and Decimals • Terminating decimal is when the division ends

2 -6 Equivalent Fractions and Decimals • Terminating decimal is when the division ends because you obtain a final remainder of zero. • In a repeating decimal, a digit or block of digits in the quotient repeats without end.

2 -6 Equivalent Fractions and Decimals To change a fraction to a decimal, we

2 -6 Equivalent Fractions and Decimals To change a fraction to a decimal, we divide the numerator by the denominator, using long division when needed. numerator denominator numerator

2 -6 Equivalent Fractions and Decimals Example A Write the fraction as a decimal.

2 -6 Equivalent Fractions and Decimals Example A Write the fraction as a decimal. A. 11 9 The fraction 1. 2 9 11. 0 – 9 20 – 1 8 2 The pattern repeats, so draw a bar over the 2 to indicate that this is a repeating decimal. 11 is equivalent to the decimal 1. 2. 9

2 -6 Equivalent Fractions and Decimals Example A Write the fraction as a decimal.

2 -6 Equivalent Fractions and Decimals Example A Write the fraction as a decimal. 7 B. 20 0. 3 5 This is a terminating decimal. 20 7. 0 0 – 0 70 – 6 0 1 00 – 1 0 0 0 The remainder is 0. The fraction 7 is equivalent to the decimal 0. 35. 20

2 -6 Equivalent Fractions and Decimals Extra Examples Write each fraction as a decimal.

2 -6 Equivalent Fractions and Decimals Extra Examples Write each fraction as a decimal. Round to the nearest hundredth, if necessary. A. 3 4 0. 7 5 4 3. 00 – 28 20 – 20 0 3 = 0. 75 4 B. 6 5 1. 2 5 6. 0 – 5 10 – 10 0 6 = 1. 2 5 C. 7 3 2. 3 3 7. 000 – 6 10 – 9 7 10 3 ≈ 2. 33 – 9 1

2 -6 Equivalent Fractions and Decimals Extra Example: Using Mental Math to Write Fractions

2 -6 Equivalent Fractions and Decimals Extra Example: Using Mental Math to Write Fractions as Decimals Write each fraction as a decimal. 4 A. 5 4 x 2 = 8 5 2 10 37 B. 50 Multiply to get a power of ten in the denominator. = 0. 8 37 x 2 = 74 50 2 100 = 0. 74 Multiply to get a power of ten in the denominator.

2 -6 Equivalent Fractions and Decimals • To convert terminating decimals to fractions, we

2 -6 Equivalent Fractions and Decimals • To convert terminating decimals to fractions, we have to remember our place values.

2 -6 Equivalent Fractions and Decimals To convert Terminating Decimals to Fractions: – Write

2 -6 Equivalent Fractions and Decimals To convert Terminating Decimals to Fractions: – Write all of the digits in the decimal as the numerator – Identify the place value of the farthest digit to the right – Write the place value of the digit farthest to the right as the denominator

2 -6 Equivalent Fractions and Decimals To simplify our fractions, we divide the numerator

2 -6 Equivalent Fractions and Decimals To simplify our fractions, we divide the numerator and denominator by the same integer 4 by dividing • Example: Simplify 12 to 15 5 both the numerator and denominator by 3.

2 -6 Equivalent Fractions and Decimals Example B Write each decimal as a fraction

2 -6 Equivalent Fractions and Decimals Example B Write each decimal as a fraction in simplest form. A. 0. 018 18 1, 000 18 ÷ 2 = 1, 000 ÷ 2 9 = 500 0. 018 = B. 1. 55 = 100 = 155 ÷ 5 100 ÷ 5 31 or 1 11 = 20 20 Reading Math You read the decimal 0. 018 as “eighteen thousandths. ”

2 -6 Equivalent Fractions and Decimals Extra Examples Write each decimal as a fraction

2 -6 Equivalent Fractions and Decimals Extra Examples Write each decimal as a fraction in simplest form. A. 0. 015 = 15 1, 000 B. 1. 30 = 100 = 15 ÷ 5 1, 000 ÷ 5 = 130 ÷ 10 100 ÷ 10 = 3 200 3 13 or 1 = 10 10

2 -6 Equivalent Fractions and Decimals Example C Carl´s dog Scout responded to a

2 -6 Equivalent Fractions and Decimals Example C Carl´s dog Scout responded to a command 16 out of 21 times. What is Scout´s success rate? Write your answer as a decimal (round to the nearest thousandth).

2 -6 Equivalent Fractions and Decimals Lesson Quiz Write each fraction as a decimal.

2 -6 Equivalent Fractions and Decimals Lesson Quiz Write each fraction as a decimal. 1. 3. 16 5 7 10 3. 2 2. 0. 7 4. 21 8 11 20 2. 625 0. 55 Write each decimal as a fraction in simplest form. 69 or 8 5 21 6. 8. 625 5. 0. 42 8 50 8 7. If your soccer team wins 21 out of 30 games, what is your team’s winning rate? 0. 70

2 -6 Equivalent Fractions and Decimals Lesson Quiz 8. Which of the following represents

2 -6 Equivalent Fractions and Decimals Lesson Quiz 8. Which of the following represents the fraction 18 as a decimal? 5 A. 3. 4 B. 3. 5 C. 3. 6 D. 3. 7

2 -6 Equivalent Fractions and Decimals Lesson Quiz 9. Which of the following represents

2 -6 Equivalent Fractions and Decimals Lesson Quiz 9. Which of the following represents the fraction 13 as a decimal? 20 A. 0. 65 B. 0. 75 C. 0. 85 D. 0. 95

2 -6 Equivalent Fractions and Decimals Lesson Quiz 10. Which of the following represents

2 -6 Equivalent Fractions and Decimals Lesson Quiz 10. Which of the following represents the decimal 0. 32 as a fraction in simplest form? A. C. 8 25 6 25 B. D. 7 25 1 5

2 -6 Equivalent Fractions and Decimals Lesson Quiz 11. Which of the following represents

2 -6 Equivalent Fractions and Decimals Lesson Quiz 11. Which of the following represents the decimal 6. 125 as a fraction in simplest form? 1 A. 49 or 8 C. 37 or 6 1 6 6 B. 49 or 6 8 1 8 D. 31 or 6 1 5 5

2 -6 Equivalent Fractions and Decimals Lesson Quiz 12. If Rita scores 34 out

2 -6 Equivalent Fractions and Decimals Lesson Quiz 12. If Rita scores 34 out of 50 in a class test, what is Rita’s scoring rate? A. 0. 65 B. 0. 66 C. 0. 67 D. 0. 68