1. Warm-up: Countdown to testing week #7 Homework: Page 70 #1-10 all and #29-38 all

2. and d are integers and d  0.
A rational number is any number that can be written as a fraction , where n
and d are integers and d  0. n d

3. 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.

4. Example 1 = 12 15 4 5

5. Example 2
Simplify.
16 80
16 = 1 • 4 • 4
80 = 5 • 4 • 4
;16 is a common factor. =
16 ÷ 16
80 ÷ 16
Divide the numerator and denominator by 16. 16 80
1 5 =
= 0 for a ≠ = 1 for a ≠ 0
= = –
Remember! 0a aa
–7 8
7 –8
7 8

6. Example 3
Simplify.
–18 29
18 = 2 • 9
29 = 1 • 29
;There are no common factors.
–18 29 =
–18 29
18 and 29 are relatively prime.

7. Example 4
Simplify.
18 27
18 = 3 • 3 • 2
27 = 3 • 3 • 3
; 9 is a common factor. 18 27 =
18 ÷ 9
27 ÷ 9
Divide the numerator and denominator by 9.
2 3 =

8. Example 5
Simplify.
17 –35
17 = 1 • = 5 • 7
; There are no common factors.
17 –35
= –
17 and 35 are relatively prime.

9. Homework: Page 70 #11-18 all and #39-46 all
Warm-up
Homework: Page 70 #11-18 all and #39-46 all
Simplify
18 42
15 21

10. 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.

12. = 5 = = 37 100 5.37 7 is in the hundredths place. 622 1000
Example 1
Write each decimal as a fraction in simplest form.
A. 5.37
37 100
= 5
5.37
7 is in the hundredths place. B =
2 is in the thousandths place.
0.622
Simplify by dividing by the common factor 2. =

13. = 8 = 8 = = 75 100 8.75 5 is in the hundredths place.
Example 2
Write each decimal as a fraction in simplest form.
A. 8.75
75 100
= 8
8.75
5 is in the hundredths place.
Simplify by dividing by the common factor 25.
= 8
3 4 B
,000 =
5 is in the ten-thousandths place.
0.2625 =
21 80
Simplify by dividing by the common factor 125.

14. Warm-up: 3. 0.875 4. 0.43 Homework: Page 70 #19-28 all and #47-56 all
Write each decimal as a fraction in simplest form.
27 100 –
5 8
2. –0.625
7 8

15. 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

16. _ 11 9 1 .2 9 11 .0 The pattern repeats. –9 2 –1 8 2
Example 1
Write the fraction as a decimal.
11 9 1 .2
9 11 .0
The pattern repeats. –9 2 –1 8
A repeating decimal can be written with a bar over the digits that repeat. So … = 1.2.
Writing Math _ 2
The fraction is equivalent to the decimal 1.2.
11 9

17. This is a terminating decimal. 20 7 .0 –0 7 –6 0 1 0 –1 0
Example 2
Write the fraction as a decimal.
7 20 .3 5
This is a terminating decimal.
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

18. The fraction is equivalent to the decimal 1.6. 15 9
Example 3
Write the fraction as a decimal.
15 9 1 .6
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

19. This is a terminating decimal. 40 9 .0 –0 9 –8 0 1 0 – 8 2 – 2
Example 4
Write the fraction as a decimal.
9 40 .2 2 5
This is a terminating decimal.
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