2-1 rational numbers warm up warm up lesson presentation lesson presentation problem of the day...
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2-1 Rational Numbers
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
2-1 Rational Numbers
Warm UpDivide.
12 24
34
16
1. 36 3 2. 144 6
3. 68 17 4. 345 115
5. 1024 64
2-1 Rational Numbers
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
2-1 Rational Numbers
Learn to write rational numbers in equivalent forms.
2-1 Rational Numbers
rational number
relatively prime
Vocabulary
2-1 Rational Numbers
A rational number is any number that can be written as a fraction , where n
and d are integers and d 0.
nd
2-1 Rational Numbers
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.
2-1 Rational Numbers
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 of the 15 boxes are shaded.
4 of the 5 boxes are
shaded.
The same total area is shaded.
1215
45
=1215
45
2-1 Rational Numbers
Additional Example 1A: Simplifying Fractions
16
80
16 = 1 • 4 • 480 = 5 • 4 • 4
;16 is a common factor.
1 5
=
1680
Divide the numerator and denominator by 16.= 16 ÷ 16
80 ÷ 16
Simplify.
= 0 for a ≠ 0 = 1 for a ≠ 0
= = –
Remember!
0a
aa
–7 8
7 –8
7 8
2-1 Rational Numbers
= –18 29
–18 29
18 = 2 • 9 29 = 1 • 29
;There are no common factors.
18 and 29 are relatively prime.–18 29
Simplify.
Additional Example 1B: Simplifying Fractions
2-1 Rational Numbers
18
27
; 9 is a common factor.
2 3
=
1827 =18 ÷ 9
27 ÷ 9Divide the numerator and denominator by 9.
Check It Out: Example 1A
Simplify.
18 = 3 • 3 • 227 = 3 • 3 • 3
2-1 Rational Numbers
= – 17 35
17 –35
17 = 1 • 17 35 = 5 • 7
; There are no common factors.
17 and 35 are relatively prime. 17 –35
Check It Out: Example 1B
Simplify.
2-1 Rational Numbers
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.
2-1 Rational Numbers
2-1 Rational Numbers
5.37
A. 5.37
7 is in the hundredths place.37 100
= 5
Additional Example 2: Writing Decimals as Fractions
Write each decimal as a fraction in simplest form.
0.622
B. 0.6222 is in the thousandths place.
622 1000
=
= 311 500
Simplify by dividing by the common factor 2.
2-1 Rational Numbers
8.75
A. 8.75
5 is in the hundredths place.75
100= 8
= 8 3 4
Simplify by dividing by the common factor 25.
Write each decimal as a fraction in simplest form.Check It Out: Example 2
0.2625
B. 0.26255 is in the ten-thousandths place.
2625 10,000
=
= 21 80
Simplify by dividing by the common factor 125.
2-1 Rational Numbers
denominator numerator
To write a fraction as a decimal, divide the numerator by the denominator. You can use long division.
numeratordenominator
2-1 Rational Numbers
9 11 The pattern repeats.
1
–9
.2
2
0
.0
2
11 9
–1 8
Additional Example 3A: Writing Fractions as Decimals
Write the fraction as a decimal.
The fraction is equivalent to the decimal 1.2.11 9
A repeating decimal can be written with a bar over the digits that repeat. So 1.2222… = 1.2.
Writing Math
_
2-1 Rational Numbers
This is a terminating decimal.20 7
.30 5
The remainder is 0.
7 20
–07
1 0
0
0
0
.0
0–6 0
–1 0 0
Additional Example 3B: Writing Fractions as Decimals
Write the fraction as a decimal.
The fraction is equivalent to the decimal 0.35.7 20
2-1 Rational Numbers
9 15 The pattern repeats, so draw a bar over the 6 to indicate that this is a repeating decimal.
1
–9
.6
6
0
.0
6
15 9
–5 4
Write the fraction as a decimal.
Check It Out: Example 3A
The fraction is equivalent to the decimal 1.6.15 9
2-1 Rational Numbers
40 9 This is a terminating decimal..20 2
The remainder is 0.
9 40
–09
1 0
0
0
.0
0–8 0
– 8 02 0
0
0
5
0– 2 00
Write the fraction as a decimal.
Check It Out: Example 3B
The fraction is equivalent to the decimal 0.225.9 40
2-1 Rational Numbers
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
2-1 Rational Numbers
Lesson Quiz: Part I
Simplify.
1. 2.
Write each decimal as a fraction in simplest form.
3. 0.27 4. –0.625
5. Write as a decimal 2.16
18 42
3 7
15 21
5 7
27 100
– 5 8
13 6
2-1 Rational Numbers
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.)
Lesson Quiz: Part II
6.
0.325
2-1 Rational Numbers
1. Simplify .
A. C.
B. D.
Lesson Quiz for Student Response Systems
3 7
4 7
5 7
6 7
16 28
2-1 Rational Numbers
2. Simplify .
A. C.
B. D.
Lesson Quiz for Student Response Systems
4 6
4 5
6 5
5 4
24 30
2-1 Rational Numbers
3. Which of the following represents the given decimal as a fraction in simplest form?
0.43
A. C.
B. D.
Lesson Quiz for Student Response Systems
43 100
100 43
43
10 43 1000
2-1 Rational Numbers
4. Which of the following represents the given decimal as a fraction in simplest form?
–0.875
A. – C. –
B. – D. –
Lesson Quiz for Student Response Systems
57
4 5
7 8
9 10
2-1 Rational Numbers
5. Which of the following represents the
given fraction as a decimal?
A. 4.3
B. 4.6
C. 5.6
D. 6.5
Lesson Quiz for Student Response Systems
51 9