Thursday, Sept. 27

Fractions and Decimals LESSON 2-6 Problem of the Day (For help, go to Lesson 2-3.) 1. Vocabulary Review How can you tell whether fractions are equivalent fractions? Write two fractions equivalent to each fraction. 2. 3. 4. 5. 16 20 15 20 6 9 10 50 2-6

Fractions and Decimals LESSON 2-6 Solutions 1. In simplest form, they are the same. 2–5. Answers may vary. Samples are given. 3. 4. 5. 4 5 , 8 10 3 4 , 6 8 2 3 , 8 12 1 5 , 2 10 2-6

Fractions and Decimals LESSON 2-6 Additional Examples The total amount of rainfall yesterday was reported as in. Express the amount of rainfall as a decimal. 1 4 or 1 ÷ 4 = 4 1.00 1 4 0.25 –8 20 –20 quotient The remainder is 0. So, = 0.25. The total amount of rainfall was 0.25 in. 1 4 2-6

Fractions and Decimals LESSON 2-6 Additional Examples 7 15 Write as a decimal. The digit “6” repeats. There will always be a remainder. or 7 ÷ 15 = 15 7.0000 0.4666 –60 100 –90 7 15 10 7 15 So, = 0.46. 2-6

Fractions and Decimals LESSON 2-6 Additional Examples Write 4.105 as a fraction in simplest form. Since 0.105 = , 4.105 = 4 . 105 1,000 4 = 4 105 1,000 105 ÷ 5 1,000 ÷ 5 Use the GCF to write the fraction in simplest form. = 4 21 200 2-6

Fractions and Decimals LESSON 2-6 Additional Examples Order from least to greatest: . 3 4 7 10 3 , 2.897, 3 3 4 = 3.75 Convert fractions to decimals. 7 10 3 = 3.70 2.897, 3.70, 3.75 , 3 2.897, 7 10 4 Order from least to greatest. 2-6

Fractions and Decimals LESSON 2-6 Additional Examples In a survey of next year’s seventh-grade students, 0.25 said they will come to school by bus, said they will walk, 0.375 said they will come in a car, and said they will ride their bicycles. Order the means of transportation from most used to least used. 5 24 1 16 bicycles 1 16 = 0.0625 Change the fractions to decimals. walk 5 24 = 0.2083 Since 0.375 > 0.25 > 0.2083 > 0.0625, the means of transportation are car, bus, walking, and bicycle. 2-6

Fractions and Decimals LESSON 2-6 Practice Write each fraction as a decimal. 1. 2. 3. 4. 7 8 4 9 0.875 0.4 3 5 5 16 0.6 0.3125 2-6

Homework for Thursday, Sept. 27 Practice 2-6 Quiz on Saturday - Lessons 2-1 to 2-4

Friday, Sept. 28

Rational Numbers LESSON 2-7 Problem of the Day (For help, go to Lesson 2-6.) 1. Vocabulary Review Is 1.234 a repeating decimal or a terminating decimal? Explain. Write each fraction as a decimal. 2. 3. 4. 5. 3 4 7 9 1 3 12 48 – 2-7

1.Terminating decimal; the decimal stops. Rational Numbers LESSON 2-7 Solutions 1.Terminating decimal; the decimal stops. 2. 0.75 3. –0.7 4. 1.3 5. 0.25 2-7

Rational Numbers LESSON 2-7 Additional Examples Compare – and – . 1 4 3 8 Method 1 Since – is farther to the left on the number line, it is the lesser number. 3 8 So, – > – . 1 4 3 8 2-7

Rewrite – with a –1 in the numerator. Rational Numbers LESSON 2-7 Additional Examples (continued) Method 2 – = 1 4 –1 Rewrite – with a –1 in the numerator. The LCD is 8. Write an equivalent fraction. = –1  2 4  2 The fraction – is equivalent to . 2 8 = –2 = – Since – > – , then – > – . 2 8 3 1 4 2-7

Compare. Use <, >, or =. Rational Numbers LESSON 2-7 Additional Examples Compare. Use <, >, or =. a. 8.7 and 8.1 8.7 > 8.1 Both numbers are positive. Compare the digits. b. –8.7 and 8.1 –8.7 < 8.1 Any negative number is less than a positive number. c. –8.7 and –8.1 –8.7 < –8.1 Place the decimals on a number line and compare their locations. 2-7

Order these numbers from least to greatest: Rational Numbers LESSON 2-7 Additional Examples Order these numbers from least to greatest: – , 0.625, , –0.5 3 5 2 3 5 – = –3 ÷ 5 = –0.6 Write as a decimal. Write as a repeating decimal. 2 3 = 2 ÷ 3 = 0.6 Compare the decimals. –0.6 < –0.5 < 0.625 < 0.6 From least to greatest, the numbers are – , –0.5, 0.625, . 3 5 2 2-7

Practice Compare. Use <, >, or =. 1. – 2. – Rational Numbers LESSON 2-7 Practice Compare. Use <, >, or =. 1. – 2. – 3. 3.4 –3.4 4. –8.9 –8.6 3 4 4 7 1 8 3 8 < – > – > < 2-7

Homework for Friday, Sept. 28 (in HW Notebooks) Lesson 2-7, p. 104-105, #s 8-30 evens, #31 Quiz tomorrow - Lessons 2-1 to 2-4

Saturday, Sept. 29 Quiz on Lessons 2-1 to 2-4

Problem of the Day 1. Vocabulary Review An exponent tells you how many Scientific Notation LESSON 2-8 Problem of the Day (For help, go to Lesson 2-1.) 1. Vocabulary Review An exponent tells you how many times a number, or base, is used as a ? . Simplify. 2. 33 3. 42 4. 105 5. 24 2-8

Solutions 1. factor 2. 33 = 3 • 3 • 3 = 27 3. 42 = 4 • 4 = 16 Scientific Notation LESSON 2-8 Check Skills You’ll Need Solutions 1. factor 2. 33 = 3 • 3 • 3 = 27 3. 42 = 4 • 4 = 16 4. 105 = 10 • 10 • 10 • 10 • 10 = 100,000 5. 24 = 2 • 2 • 2 • 2 = 16 2-8

Write as a product of 2 factors. Scientific Notation LESSON 2-8 Additional Examples Quick Check The mean distance from Mars to the sun is about 141,750,000 mi. Write this number in scientific notation. Move the decimal point to get a factor greater than 1 but less than 10. 1. 41,750,000. 141,750,000 = 1.4175  100,000,000 Write as a product of 2 factors. = 1.4175  108 Write 100,000,000 as a power of 10. The mean distance from Mars to the sun is about 1.4175  108 mi. 2-8

Write as a product of 2 factors. Scientific Notation LESSON 2-8 Additional Examples Light from the sun reaches Earth in about 4.99012  102 s. Write this time in standard form. Method 1 4.99012  102 = 4.99012  100 Write as a product of 2 factors. = 499.012 Multiply the factors. Method 2 4.99012  102 = 4.99012 The exponent is 2. Move the decimal 2 places to the right. = 499.012 The time is about 499.012 s. 2-8

Practice Write in scientific notation. 1. 45,300 2. 714,900,000 LESSON 2-8 Practice Write in scientific notation. 1. 45,300 2. 714,900,000 Write in standard form. 3. 5.7  103 4. 6.034  106 4.53  104 7.149  108 5,700 6,034,000 2-8

Homework for Saturday, Sept. 29 (in HW Notebooks) Lesson 2-8, p. 108-109, #s 10-30 evens, #34