Student Learning Goal Chart

1. Student Learning Goal Chart Handout

2. Pre-Algebra Learning GoalStudent will understand rational and real numbers.

3. Students will understand rational and real numbers by being able to do the following: • Learn to write rational numbers in equivalent forms (3.1)

4. Today’s Learning Goal Assignment Learn to write rational numbers in equivalent forms.

5. Vocabulary rationalonumber relativelyoprime

6. A rational numberis 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. n Numerator d Denominator

8. 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. 12 15 12 of the 15 boxes are shaded. 4 of the 5 boxes are shaded. = 12 4 15 5 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. 4 5 The same total area is shaded.

11. 3 7 5 7 5 8 27100 – 2.16 Lesson Quiz: Part 1 Simplify. 18 42 15 21 1. 2. Write each decimal as a fraction in simplest form. 3. 0.27 4. –0.625 13 6 5. Write as a decimal

12. Lesson Quiz: Part 2 6. 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.) 0.325

13. Are you ready for the FAST Track?If YES, prepare for Ch. 3 Section 2 along with Ch. 3 Section 5!If NO, continue with the Ch. 3 Section 1 lesson!

14. Pre-Algebra HW: page ?? #?-?? Page ?? #?-??

15. 3-1 Rational Numbers Pre-Algebra Warm Up Problem of the Day Lesson Presentation

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

17. 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

18. Today’s Learning Goal Assignment Learn to write rational numbers in equivalent forms.

19. Vocabulary rationalonumber relativelyoprime

20. A rational numberis 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.

21. n Numerator d Denominator

22. 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.

23. 12 15 12 of the 15 boxes are shaded. 4 of the 5 boxes are shaded. = 12 4 15 5 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. 4 5 The same total area is shaded.

24. ;5 is a common factor. 5 ÷ 5 = 10 ÷ 5 1 2 5 = 10 Additional Example 1A: Simplifying Fractions Simplify. 5 = 1 • 5 10 = 2 • 5 5 10 A. Divide the numerator and denominator by 5.

25. ;16 is a common factor. 16 80 1 5 = 16 ÷ 16 = 80 ÷ 16 Additional Example 1B: Simplifying Fractions Simplify. 16 = 1 • 16 80 = 5 • 16 16 80 B. Divide the numerator and denominator by 16.

26. ;There are no common factors. –18 29 –18 29 = Additional Example 1C: Simplifying Fractions Simplify. –18 29 18 = 2 • 9 29 = 1 • 29 C. –18 and 29 are relatively prime.

27. 1 5 6 = = 30 Try This: Example 1A Simplify. 6 30 6 = 1 • 6 30 = 5 • 6 ;6 is a common factor. A. Divide the numerator and denominator by 6. 6 ÷ 6 30 ÷ 6

28. 18 ÷ 9 18 = 27 27 ÷ 9 2 3 = Try This: Example 1B Simplify. 18 = 3 • 3 • 2 27 = 3 • 3 • 3 18 27 ;9 is a common factor. B. Divide the numerator and denominator by 9.

29. 17 35 17 –35 = – Try This: Example 1C Simplify. 17 –35 ;There are no common factors. 17 = 1 • 17 35 = 5 • 7 C. 17 and –35 are relatively prime.

30. 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.

31. –8 10 = 4 5 = – Additional Example 2A: Writing Decimals as Fractions Write the decimal as a fraction in simplest form. A. –0.8 –8 is in the tenths place. Simplify by dividing by the common factor 2. –0.8

32. 37 100 =5 Additional Example 2B: Writing Decimals as Fractions Write the decimal as a fraction in simplest form. 7 is in the hundredths place. B. 5.37 5.37

33. 622 1000 = 311 500 = Additional Example 2C: Writing Decimals as Fractions Write the decimal as a fraction in simplest form. 2 is in the thousandths place. C. 0.622 Simplify by dividing by the common factor 2. 0.622

34. –4 10 = 2 5 = – Try This: Example 2A Write the decimal as a fraction in simplest form. –4 is in the tenths place. A. –0.4 Simplify by dividing by the common factor 2. –0.4

35. 75 100 =8 3 4 =8 Try This: Example 2B Write the decimal as a fraction in simplest form. B. 8.75 5 is in the hundredths place. Simplify by dividing by the common factor 25. 8.75

36. 2625 10,000 = 21 80 = Try This: Example 2C Write each decimal as a fraction in simplest form. 5 is in the ten-thousandths place. C. 0.2625 Simplify by dividing by the common factor 125. 0.2625

37. denominator To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. numerator denominator numerator 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.

38. 9 11 –9 –1 8 11 9 The fraction is equivalent to the decimal 1.2. Additional Example 3A: Writing Fractions as Decimals Write the fraction as a decimal. 11 9 1 .2 A. .0 The pattern repeats, so draw a bar over the 2 to indicate that this is a repeating decimal. 0 2 2

39. 20 7 –0 –6 0 0 –1 0 7 20 The fraction is equivalent to the decimal 0.35. Additional Example 3B: Writing Fractions as Decimals Write the fraction as a decimal. 7 20 .3 0 5 This is a terminating decimal. B. 0 .0 0 7 0 1 0 The remainder is 0. 0

40. 9 15 –9 0 –5 4 15 9 The fraction is equivalent to the decimal 1.6. Try This: Example 3A Write the fraction as a decimal. 15 9 1 .6 A. .0 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal. 6 6

41. 40 9 –0 –8 0 – 8 0 9 40 0 2 0 0 – 2 The fraction is equivalent to the decimal 0.225. Try This: Example 3B Write the fraction as a decimal. 9 40 .2 0 2 5 This is a terminating decimal. B. 0 0 .0 0 9 0 1 0 0 The remainder is 0. 0

42. 3 7 5 7 5 8 27100 – 2.16 Lesson Quiz: Part 1 Simplify. 18 42 15 21 1. 2. Write each decimal as a fraction in simplest form. 3. 0.27 4. –0.625 13 6 5. Write as a decimal

43. Lesson Quiz: Part 2 6. 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.) 0.325