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

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

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. Learn to write rational numbers in equivalent forms.

5. Vocabulary
rational number
relatively prime

6. Decimals that terminate or repeat are 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. Numerator n 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. The same total area is shaded.
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 15 4 5
12 of the 15 boxes are shaded.
4 of the 5 boxes are shaded. = 12 15 4 5
The same total area is shaded.

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

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

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

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

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

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

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

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

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

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

21. = 8 = 8 B. 8.75 75 100 8.75 5 is in the hundredths place. 3 4
Try This: Example 2B
Write the decimal as a fraction in simplest form.
B. 8.75
75 100
= 8
8.75
5 is in the hundredths place.
= 8
3 4
Simplify by dividing by the common factor 25.

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

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

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

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

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

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

28. 1. 2. – 3. 0.27 4. –0.625 5. Write as a decimal Simplify. 18 42 3 7
Lesson Quiz: Part 1
Simplify.
18 42
3 7
15 21
5 7 1. 2.
Write each decimal as a fraction in simplest form.
27 100 –
5 8
4. –0.625
13 6
5. Write as a decimal
2.16

29. 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