Download 1-1 Rational Numbers - Minidoka County Schools

1-1 Rational Numbers
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
1-1 Rational Numbers
Warm Up
Divide.
1. 36  3
3. 68  17
12
4
5. 1024  64 16
2. 144  6
4. 345  115
24
3
1-1 Rational Numbers
Learn to write rational numbers in
equivalent forms.
1-1 Rational Numbers
Vocabulary
rational number
relatively prime
1-1 Rational Numbers
A rational number is any number that can
n
be written as a fraction
, where n
d
and d are integers and d  0.
1-1 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.
1-1 Rational Numbers
You can often simplify fractions by dividing
both the numerator and denominator by
the same nonzero integer. You can
12
simplify the fraction 15
to 45 by dividing
both the 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.
1-1 Rational Numbers
Example 1: Simplifying Fractions
A. Simplify.
16
80
16 = 1 • 4 • 4 ;16 is a common
80 = 5 • 4 • 4 factor.
16 = 16 ÷ 16
80 ÷ 16
80
1
=
5
Divide the numerator
and denominator by 16.
Remember
a
0
= 1 for a ≠ 0
=0 for ≠ 0
a
a
7
7
7
=
=
8
8
8
1-1 Rational Numbers
Example 1: Simplifying Fractions
B. Simplify.
–18
29
18 = 2 • 9
29 = 1 • 29
–18
–18
=
29
29
;There are no common
factors.
18 and 29 are relatively prime.
1-1 Rational Numbers
Check It Out
C. Simplify.
18 = 3 • 3 • 2 ; 9 is a common factor.
27 = 3 • 3 • 3
18
27
18 = 18 ÷ 9
27 27 ÷ 9
=
2
3
Divide the numerator
and denominator by 9.
1-1 Rational Numbers
Check It Out
D. Simplify.
17
–35
17 = 1 • 17 ; There are no common
factors.
35 = 5 • 7
17
17
=–
17 and 35 are relatively prime.
35
–35
1-1 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.
1-1 Rational Numbers
1-1 Rational Numbers
Example 2: Writing Decimals as Fractions
Write each decimal as a fraction in simplest form.
A. 5.37
37
5.37 = 5
100
7 is in the hundredths place.
B. 0.622
0.622 =
622
1000
311
=
500
2 is in the thousandths
place.
Simplify by dividing by the
common factor 2.
1-1 Rational Numbers
Check It Out
Write each decimal as a fraction in simplest form.
C. 8.75
8.75 = 8
75
100
3
= 8
4
D. 0.2625
5 is in the hundredths place.
Simplify by dividing by the
common factor 25.
2625
0.2625 =
10,000
21
=
80
5 is in the
ten-thousandths place.
Simplify by dividing by
the common factor 125.
1-1 Rational Numbers
To write a fraction as a decimal, divide the
numerator by the denominator. You can
use long division.
numerator
denominator
denominator numerator
1-1 Rational Numbers
Example 3: Writing Fractions as Decimals
A. Write the fraction as a decimal.
11
9
The fraction
1 .2
9 11 .0
–9
20
–1 8
2
The pattern repeats.
Writing Math
A repeating decimal can be written
with a bar over the digits_that
repeat. So 1.2222… = 1.2.
11
is equivalent to the decimal 1.2.
9
1-1 Rational Numbers
Example 3: Writing Fractions as Decimals
B. Write the fraction as a decimal.
7
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
7
is equivalent to the decimal 0.35.
20
1-1 Rational Numbers
Check It Out
C. Write the fraction as a decimal.
15
9
The fraction
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
1-1 Rational Numbers
Check It Out
D. Write the fraction as a decimal.
9
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