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C3 Ch02 01

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C3 Ch02 01

1. 1. Warm Up Problem of the Day Lesson Presentation 2-1 Rational Numbers Course 3
2. 2. Warm Up Divide. 12 24 3 4 16 1. 36  3 2. 144  6 3. 68  17 4. 345  115 5. 1024  64
3. 3. Problem of the Day An ice cream parlor has 6 flavors of ice cream. A dish with two scoops can have any two flavors, including the same flavor twice. How many different double-scoop combinations are possible? 21
4. 4. Learn to write rational numbers in equivalent forms.
5. 5. rational number relatively prime Vocabulary
6. 6. A rational number is any number that can be written as a fraction , where n and d are integers and d  0. n d
7. 7. 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.
8. 8. You can often simplify fractions by dividing both the numerator and denominator by the same nonzero integer. You can simplify the fraction to by dividing both the numerator and denominator by 3. The same total area is shaded. 4 5 12 of the 15 boxes are shaded. 4 of the 5 boxes are shaded. 12 15 = 12 15 4 5
9. 9. Additional Example 1A: Simplifying Fractions 16 80 16 = 1 • 16 80 = 5 • 16 Divide the numerator and denominator by 16. Simplify. ;16 is a common factor. 1 5 = 16 80 = 16 ÷ 16 80 ÷ 16 = 0 for a ≠ 0 = 1 for a ≠ 0 = = – Remember! 0 a a a – 7 8 7 –8 7 8
10. 10. – 18 29 18 = 2 • 9 29 = 1 • 29 – 18 and 29 are relatively prime. Simplify. Additional Example 1B: Simplifying Fractions = – 18 29 ;There are no common factors. – 18 29
11. 11. 18 27 ; 9 is a common factor. Divide the numerator and denominator by 9. Check It Out: Example 1A Simplify. 18 = 3 • 3 • 2 27 = 3 • 3 • 3 2 3 = 18 27 = 18 ÷ 9 27 ÷ 9
12. 12. 17 –35 17 = 1 • 17 35 = 5 • 7 ; There are no common factors. 17 and –35 are relatively prime. Check It Out: Example 1B Simplify. = – 17 35 17 –35
13. 13. 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.
14. 14. Repeating decimal 0.1 6 Terminating decimal – 3.2 Written as a Fraction Description Rational Number – 32 ___ 10 1 __ 6
15. 15. 5.37 A. 5.37 7 is in the hundredths place. Additional Example 2: Writing Decimals as Fractions Write each decimal as a fraction in simplest form. 0.622 B. 0.622 2 is in the thousandths place. Simplify by dividing by the common factor 2. 37 100 = 5 622 1000 = = 311 500
16. 16. 8.75 A. 8.75 5 is in the hundredths place. Simplify by dividing by the common factor 25. Write each decimal as a fraction in simplest form. Check It Out: Example 2 0.2625 B. 0.2625 5 is in the ten-thousandths place. Simplify by dividing by the common factor 125. 75 100 = 8 = 8 3 4 2625 10,000 = = 21 80
17. 17. numerator To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. numerator denominator denominator
18. 18. The pattern repeats. 1 .2 2 0 .0 2 11 9 Additional Example 3A: Writing Fractions as Decimals Write the fraction as a decimal. 9 11 – 9 – 1 8 The fraction is equivalent to the decimal 1.2. 11 9 A repeating decimal can be written with a bar over the digits that repeat. So 1.2222… = 1.2. Writing Math _
19. 19. This is a terminating decimal. .3 0 5 The remainder is 0. 7 20 7 1 0 0 0 0 .0 0 Additional Example 3B: Writing Fractions as Decimals Write the fraction as a decimal. 20 7 – 0 – 6 0 – 1 0 0 The fraction is equivalent to the decimal 0.35. 7 20
20. 20. The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 1 .6 6 .0 6 15 9 Write the fraction as a decimal. Check It Out: Example 3A 9 15 – 9 0 – 5 4 The fraction is equivalent to the decimal 1.6. 15 9
21. 21. This is a terminating decimal. .2 0 2 The remainder is 0. 9 40 9 1 0 0 0 .0 0 0 0 5 0 Write the fraction as a decimal. Check It Out: Example 3B 40 9 – 0 – 8 0 – 8 0 2 0 0 – 2 0 The fraction is equivalent to the decimal 0.225. 9 40
22. 22. Lesson Quiz: Part 1 Simplify. 1. 2. Write each decimal as a fraction in simplest form. 3. 0.27 4. –0.625 5. Write as a decimal 18 42 15 21 13 6 2.16 3 7 5 7 27 100 – 5 8
23. 23. Tommy had 13 hits in 40 at bats for his baseball team. What is his batting average? (Batting average is the number of hits divided by the number of at bats, expressed as a decimal.) Lesson Quiz: Part 2 6 . 0.325