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

2. 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

3. TB P
Learn to write rational numbers in equivalent forms.

4. Vocabulary
rational number
relatively prime

5. 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

6. 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.

7. 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.

8. Additional Example 1A: Simplifying Fractions
16 80
16 = 1 • = 5 • 16
;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

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

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.

11. Rational Number
Description
Written as a Fraction
–3.2
Terminating decimal
0.16
Repeating decimal
–32
___ 10 1 __ 6

12. Additional 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. =

13. 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

14. Additional Example 3A: Writing Fractions as Decimals
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

15. Additional Example 3B: Writing Fractions as Decimals
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

16. 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

17. 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