1. Warm Up
Divide.
1. 36   6 12 24
3. 68   115 4 3
 64 16

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

3. 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.

4. Example 1: Simplifying Fractions
A. 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

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

6. Check It Out: Example 1
A. 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 =

7. Check It Out: Example 1
B. Simplify.
17 –35
17 = 1 • = 5 • 7
; There are no common factors.
17 –35
= –
17 and 35 are relatively prime.

8. 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.

9. Example 2: Writing Decimals as Fractions
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. =

10. = 8 = 8 = = 75 100 8.75 5 is in the hundredths place.
Check It Out: 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.

11. 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

12. Example 3: Writing Fractions as Decimals
A. 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

13. Example 3: Writing Fractions as Decimals
B. 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

14. The fraction is equivalent to the decimal 1.6. 15 9
Check It Out: Example 3
A. 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

15. This is a terminating decimal. 40 9 .0 –0 9 –8 0 1 0 – 8 2 – 2
Check It Out: Example 3
B. 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

16. 1. 2. – 3. 0.27 4. –0.625 5. Write as a decimal. 6. 0.325 Simplify.
Lesson Quiz
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
5. Write as a decimal.
2.16 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