1. Pre-Algebra 3-1 Rational Numbers Learn to write rational numbers in equivalent forms.

2. Pre-Algebra 3-1 Rational Numbers A rational number is any number that can be written as a fraction where n and d are integers and d  0. n d Decimals that terminate or repeat are rational numbers.

3. Pre-Algebra 3-1 Rational Numbers Numerator n d Denominator

4. Pre-Algebra 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.

5. 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 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. 12 15 4 5 = 12 15 4 5

6. Pre-Algebra 3-1 Rational Numbers Example 1A 6 30 6 = 1 6 30 = 5 6 ;6 is a common factor. Divide the numerator and denominator by 6. 1515 = 6 30 = 6 ÷ 6 30 ÷ 6 A. Simplify.

7. Pre-Algebra 3-1 Rational Numbers Example 1B: Simplifying Fractions 16 80 16 = 1 16 80 = 5 16 ;16 is a common factor. 1515 = 16 80 Divide the numerator and denominator by 16. = 16 ÷ 16 80 ÷ 16 B. Simplify.

8. Pre-Algebra 3-1 Rational Numbers 18 27 ;9 is a common factor. 2323 = 18 27 = 18 ÷ 9 27 ÷ 9 B. Divide the numerator and denominator by 9. Example 1B Simplify. 18 = 3 3 2 27 = 3 3 3

9. Pre-Algebra 3-1 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 C. Simplify. Example 1C: Simplifying Fractions

10. 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.

11. Pre-Algebra 3-1 Rational Numbers –0.8 A. –0.8 –8 is in the tenths place. Simplify by dividing by the common factor 2. –8 10 = = – 4545 Example 2A: Writing Decimals as Fractions Write the decimal as a fraction in simplest form.

12. Pre-Algebra 3-1 Rational Numbers 5.37 B. 5.37 7 is in the hundredths place. 37 100 = 5= 5 Example 2B: Writing Decimals as Fractions Write the decimal as a fraction in simplest form.

13. Pre-Algebra 3-1 Rational Numbers 0.622 C. 0.622 2 is in the thousandths place. 622 1000 = = 311 500 Simplify by dividing by the common factor 2. Example 2C: Writing Decimals as Fractions Write the decimal as a fraction in simplest form.

14. Pre-Algebra 3-1 Rational Numbers A rational number is any number that can be written as a fraction where n and d are integers and d  0. n d Decimals that terminate or repeat are rational numbers.

15. Pre-Algebra 3-1 Rational Numbers Numerator n d Denominator

16. Pre-Algebra 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.

17. 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 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. 12 15 4 5 = 12 15 4 5

18. 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.

19. Pre-Algebra 3-1 Rational Numbers denominator numerator To write a fraction as a decimal, divide the numerator by the denominator. You can use long division. 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. numerator denominator

20. Pre-Algebra 3-1 Rational Numbers 9 11 The pattern repeats, so draw a bar over the 2 to indicate that this is a repeating decimal. 1 –9.2 2 0.0 2 11 9 –1 8 Example 3A: Writing Fractions as Decimals A. Write the fraction as a decimal. The fraction is equivalent to the decimal 1.2. 11 9

21. Pre-Algebra 3-1 Rational Numbers This is a terminating decimal. 20 7.3 05 The remainder is 0. 7 20 –0 7 1 0 0 0 0.0 0 –6 0 –1 0 0 B. Example 3B: Writing Fractions as Decimals Write the fraction as a decimal. The fraction is equivalent to the decimal 0.35. 7 20

22. Pre-Algebra 3-1 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. Example 3A A. The fraction is equivalent to the decimal 1.6. 15 9

23. Pre-Algebra 3-1 Rational Numbers 40 9 This is a terminating decimal..2 02 The remainder is 0. 9 40 –0 9 1 0 0 0.0 0 –8 0 – 8 0 2 0 0 0 5 0 – 2 0 0 B. Write the fraction as a decimal. Example 3B The fraction is equivalent to the decimal 0.225. 9 40