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3-1
3-1 Rational
RationalNumbers
Numbers
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
3-1 Rational Numbers
Warm Up
Divide.
1. 36  3
3. 68  17
12
4
5. 1024  64 16
Pre-Algebra
2. 144  6
4. 345  115
24
3
3-1 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
Pre-Algebra
3-1 Rational Numbers
Learn to write rational numbers in
equivalent forms.
Pre-Algebra
3-1 Rational Numbers
Vocabulary
rational number
relatively prime
Pre-Algebra
3-1 Rational Numbers
A rational number is any number that can
n
be written as a fraction
, where n and d
d
are integers and d  0.
Decimals that terminate or repeat are
rational numbers.
Pre-Algebra
3-1 Rational Numbers
Numerator
Pre-Algebra
n
d
Denominator
3-1 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.
Pre-Algebra
3-1 Rational Numbers
You can often simplify fractions by dividing
both the numerator and denominator by
the same nonzero integer. You can simplify
12
4
the fraction
to
by
dividing
both the
15
5
numerator and denominator by 3.
12 of the 15 boxes
are shaded.
12
15
4 of the 5 boxes
are shaded.
=
4
5
The same total area is shaded.
Pre-Algebra
3-1 Rational Numbers
Additional Example 1A: Simplifying Fractions
Simplify.
5
A.
10
5 =1•5
10 = 2 • 5
5÷5
5
= 10 ÷ 5
10
1
=
2
Pre-Algebra
; 5 is a common factor.
Divide the numerator
and denominator by 5.
3-1 Rational Numbers
Additional Example 1B: Simplifying Fractions
Simplify.
B. 16
80
16 = 1 • 16 ;16 is a common factor.
80 = 5 • 16
16 ÷ 16
16
= 80 ÷ 16
80
1
=
5
Pre-Algebra
Divide the numerator
and denominator by 16.
3-1 Rational Numbers
Additional Example 1C: Simplifying Fractions
Simplify.
C. –18
29
18 = 2 • 9
29 = 1 • 29
–18
–18
=
29
29
Pre-Algebra
;There are no common
factors.
–18 and 29 are relatively prime.
3-1 Rational Numbers
Try This: Example 1A
Simplify.
A.
6
30
6 = 1 • 6 ;6 is a common factor.
30 = 5 • 6
6÷6
6
=
30 ÷ 6
30
1
=
5
Pre-Algebra
Divide the numerator
and denominator by 6.
3-1 Rational Numbers
Try This: Example 1B
Simplify.
18 = 3 • 3 • 2 ;9 is a common factor.
27 = 3 • 3 • 3
B. 18
27
18 = 18 ÷ 9
27 ÷ 9
27
=
Pre-Algebra
2
3
Divide the numerator
and denominator by 9.
3-1 Rational Numbers
Try This: Example 1C
Simplify.
C.
17
–35
17 = 1 • 17 ;There are no common
factors.
35 = 5 • 7
17
17 17 and –35 are
=–
–35
35 relatively prime.
Pre-Algebra
3-1 Rational Numbers
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.
Pre-Algebra
3-1 Rational Numbers
Additional Example 2A: Writing Decimals as Fractions
Write the decimal as a fraction in simplest form.
A. –0.8
–0.8 =
–8
10
4
=–
5
Pre-Algebra
–8 is in the tenths place.
Simplify by dividing by
the common factor 2.
3-1 Rational Numbers
Additional Example 2B: Writing Decimals as Fractions
Write the decimal as a fraction in simplest form.
B. 5.37
37 7 is in the hundredths place.
5.37 = 5
100
Pre-Algebra
3-1 Rational Numbers
Additional Example 2C: Writing Decimals as Fractions
Write the decimal as a fraction in simplest form.
C. 0.622
622
0.622 =
1000
311
=
500
Pre-Algebra
2 is in the thousandths
place.
Simplify by dividing by the
common factor 2.
3-1 Rational Numbers
Try This: Example 2A
Write the decimal as a fraction in simplest form.
A. –0.4
–4
–0.4 =
10
2
=–
5
Pre-Algebra
–4 is in the tenths place.
Simplify by dividing by
the common factor 2.
3-1 Rational Numbers
Try This: Example 2B
Write the decimal as a fraction in simplest form.
B. 8.75
75
5 is in the hundredths place.
8.75 = 8
100
3
= 8
4
Pre-Algebra
Simplify by dividing by the
common factor 25.
3-1 Rational Numbers
Try This: Example 2C
Write each decimal as a fraction in simplest form.
C. 0.2625
2625
0.2625 =
10,000
21
=
80
Pre-Algebra
5 is in the ten-thousandths
place.
Simplify by dividing by
the common factor 125.
3-1 Rational Numbers
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.
Pre-Algebra
3-1 Rational Numbers
Additional Example 3A: Writing Fractions as Decimals
Write the fraction as a decimal.
A. 11
9
The fraction
Pre-Algebra
1 .2
9 11 .0
–9
20
–1 8
2
The pattern repeats, so
draw a bar over the 2
to indicate that this is a
repeating decimal.
11
is equivalent to the decimal 1.2.
9
3-1 Rational Numbers
Additional Example 3B: Writing Fractions as Decimals
Write the fraction as a decimal.
7
B.
20
0.3 5 This is a terminating decimal.
20 7.0 0
–0
70
–6 0
1 00
–1 0 0
0 The remainder is 0.
The fraction
Pre-Algebra
7
is equivalent to the decimal 0.35.
20
3-1 Rational Numbers
Try This: Example 3A
Write the fraction as a decimal.
A. 15
9
The fraction
Pre-Algebra
1 .6
9 15 .0
–9
60
–5 4
6
The pattern repeats, so
draw a bar over the 6 to
indicate that this is a
repeating decimal.
15
is equivalent to the decimal 1.6.
9
3-1 Rational Numbers
Try This: Example 3B
Write the fraction as a decimal.
9
B.
40
0.2 2 5 This is a terminating decimal.
40 9.0 0 0
–0
90
–8 0
1 00
– 80
200
– 2 00
0 The remainder is 0.
9
The fraction
is equivalent to the decimal 0.225.
40
Pre-Algebra
3-1 Rational Numbers
Lesson Quiz: Part 1
Simplify.
18
1.
42
3
7
15
2.
21
5
7
Write each decimal as a fraction in
simplest form.
5
27
–
3. 0.27
4.
–0.625
8
100
13
5. Write
as a decimal
6
Pre-Algebra
2.16
3-1 Rational Numbers
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
Pre-Algebra