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2-1 Rational Numbers
Learn to write rational numbers in equivalent forms.
Mr. Dixon
2-1 Rational Numbers
Rational number- Any number that can be written as a fraction, where n and d are integers and d 0.
Relatively prime- Numbers that
have no common factors other than
1. The goal of simplifying fractions
is to make the numerator and the
denominator relatively prime.
Vocabulary
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 1: 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
=–1829
–1829
18 = 2 • 929 = 1 • 29
;There are no common factors.
18 and 29 are relatively prime.–1829
Simplify.
Additional Example 2: Simplifying Fractions
2-1 Rational Numbers
18 27
; 9 is a common factor.
2 3
=
1827
=18 ÷ 9 27 ÷ 9
Divide the numerator and denominator by 9.
Check It Out: Example 3
Simplify.
18 = 3 • 3 • 227 = 3 • 3 • 3
2-1 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
8.75
A. 8.75
5 is in the hundredths place.75 100
= 8
= 83 4
Simplify by dividing by the common factor 25.
Write each decimal as a fraction in simplest form.
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.
numerator
denominator
2-1 Rational Numbers
9 11 The pattern repeats.
1
–9
.2
2
0
.0
2
11 9
–1 8
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
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.
The fraction is equivalent to the decimal 0.225.9 40
2-1 Rational Numbers
2.1 homework
Pg. 70 (24 – 56) Evens
Write down the problem from the book.
SHOW YOUR WORK!
