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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!