1. Pre-Algebra 3-1 Rational Numbers 3-1 Rational Numbers Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Pre-Algebra 3-1 Rational Numbers Warm Up Divide. Pre-Algebra 3-1 Rational Numbers 12 24 3 4 16 1. 36  3 2. 144  6 3. 68  17 4. 345  115 5. 1024  64

3. Pre-Algebra 3-1 Rational Numbers 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. Pre-Algebra 3-1 Rational Numbers Learn to write rational numbers in equivalent forms.

5. Pre-Algebra 3-1 Rational Numbers rational number relatively prime Vocabulary

6. Pre-Algebra 3-1 Rational Numbers A rational number is any number that can be written as a fraction, where n and d are integers and d  0. n d Decimals that terminate or repeat are rational numbers.

7. Pre-Algebra 3-1 Rational Numbers Numerator n d Denominator

8. Pre-Algebra 3-1 Rational Numbers 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.

9. Pre-Algebra 3-1 Rational Numbers 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. 12 of the 15 boxes are shaded. 4 of the 5 boxes are shaded. The same total area is shaded. 12 15 4 5 = 12 15 4 5

10. Pre-Algebra 3-1 Rational Numbers Additional Example 1A: Simplifying Fractions 5 10 5 = 1 5 10 = 2 5 ; 5 is a common factor. Divide the numerator and denominator by 5. 1212 = 5 10 Simplify. = 5 ÷ 5 10 ÷ 5 A.

11. Pre-Algebra 3-1 Rational Numbers Additional Example 1B: Simplifying Fractions 16 80 16 = 1 16 80 = 5 16 ;16 is a common factor. 1515 = 16 80 Divide the numerator and denominator by 16. = 16 ÷ 16 80 ÷ 16 B. Simplify.

12. Pre-Algebra 3-1 Rational Numbers = –18 29 –18 29 18 = 2 9 29 = 1 29 ;There are no common factors. –18 and 29 are relatively prime. –18 29 C. Simplify. Additional Example 1C: Simplifying Fractions

13. Pre-Algebra 3-1 Rational Numbers Try This: Example 1A 6 30 6 = 1 6 30 = 5 6 ;6 is a common factor. Divide the numerator and denominator by 6. 1515 = 6 30 = 6 ÷ 6 30 ÷ 6 A. Simplify.

14. Pre-Algebra 3-1 Rational Numbers 18 27 ;9 is a common factor. 2323 = 18 27 = 18 ÷ 9 27 ÷ 9 B. Divide the numerator and denominator by 9. Try This: Example 1B Simplify. 18 = 3 3 2 27 = 3 3 3

15. Pre-Algebra 3-1 Rational Numbers = – 17 35 17 –35 17 = 1 17 35 = 5 7 ;There are no common factors. 17 and –35 are relatively prime. 17 –35 C. Try This: Example 1C Simplify.

16. Pre-Algebra 3-1 Rational Numbers To write a finite decimal as a fraction, identify the place value of the farthest digit to the right. Then write all of the digits after the decimal points as the numerator with the place value as the denominator.

17. Pre-Algebra 3-1 Rational Numbers –0.8 A. –0.8 –8 is in the tenths place. Simplify by dividing by the common factor 2. –8 10 = = – 4545 Additional Example 2A: Writing Decimals as Fractions Write the decimal as a fraction in simplest form.

18. Pre-Algebra 3-1 Rational Numbers 5.37 B. 5.37 7 is in the hundredths place. 37 100 = 5= 5 Additional Example 2B: Writing Decimals as Fractions Write the decimal as a fraction in simplest form.

19. Pre-Algebra 3-1 Rational Numbers 0.622 C. 0.622 2 is in the thousandths place. 622 1000 = = 311 500 Simplify by dividing by the common factor 2. Additional Example 2C: Writing Decimals as Fractions Write the decimal as a fraction in simplest form.

20. Pre-Algebra 3-1 Rational Numbers –0.4 A. –0.4 –4 is in the tenths place. Simplify by dividing by the common factor 2. –4 10 = Write the decimal as a fraction in simplest form. Try This: Example 2A = – 2525

21. Pre-Algebra 3-1 Rational Numbers 8.75 B. 8.75 5 is in the hundredths place. 75 100 = 8= 8 = 8= 8 3434 Simplify by dividing by the common factor 25. Write the decimal as a fraction in simplest form. Try This: Example 2B

22. Pre-Algebra 3-1 Rational Numbers 0.2625 5 is in the ten-thousandths place. 2625 10,000 = = 21 80 Simplify by dividing by the common factor 125. C. Write each decimal as a fraction in simplest form. Try This: Example 2C

23. Pre-Algebra 3-1 Rational Numbers denominator numerator To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. When writing a long division problem from a fraction, put the numerator inside the “box,” or division symbol. It may help to write the numerator first and then say “divided by” to yourself as you write the division symbol. numerator denominator

24. Pre-Algebra 3-1 Rational Numbers 9 11 The pattern repeats, so draw a bar over the 2 to indicate that this is a repeating decimal. 1 –9.2 2 0.0 2 11 9 –1 8 Additional Example 3A: Writing Fractions as Decimals A. Write the fraction as a decimal. The fraction is equivalent to the decimal 1.2. 11 9

25. Pre-Algebra 3-1 Rational Numbers This is a terminating decimal. 20 7.3 05 The remainder is 0. 7 20 –0 7 1 0 0 0 0.0 0 –6 0 –1 0 0 B. Additional Example 3B: Writing Fractions as Decimals Write the fraction as a decimal. The fraction is equivalent to the decimal 0.35. 7 20

26. Pre-Algebra 3-1 Rational Numbers 9 15 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 1 –9.6 6 0.0 6 15 9 –5 4 Write the fraction as a decimal. Try This: Example 3A A. The fraction is equivalent to the decimal 1.6. 15 9

27. Pre-Algebra 3-1 Rational Numbers 40 9 This is a terminating decimal..2 02 The remainder is 0. 9 40 –0 9 1 0 0 0.0 0 –8 0 – 8 0 2 0 0 0 5 0 – 2 0 0 B. Write the fraction as a decimal. Try This: Example 3B The fraction is equivalent to the decimal 0.225. 9 40

28. Pre-Algebra 3-1 Rational Numbers 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 2.16 18 42 3737 15 21 5757 27 100 – 5858 13 6

29. Pre-Algebra 3-1 Rational Numbers 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 6.6. 0.325