Section 2.3 Simplifying Fractions to Lowest Terms 117 Answers 63 1 3 9. 10. 11. 19 40 5 12. Four zeros; the numerator and denominator are both divisible by 10,000. Avoiding Mistakes Suppose that you do not recognize the greatest common factor in the numerator and denominator. You can still divide by any common factor. However, you will have to repeat this process more than once to simplify the fraction completely. For instance, consider the fraction from Example 3(c). Simplifying Fractions by 10, 100, and 1000 12 Example 4 Simplify each fraction to lowest terms by first reducing by 10, 100, or 1000. Write the answer as a fraction. a. b. c. Solution: a. 170 30 2500 7500 1 b. Both 2500 and 7500 are divisible by 100. “Strike through” two zeros. Simplify further. 5000 130,000 1 c. The numbers 5000 and 130,000 are both divisible by 1000. “Strike through” three zeros. Simplify further. 1 26 5 1 130 26 5000 130,000 1 3 25 75 3 2500 7500 17 10 3 10 1 17 3 5000 130,000 2500 7500 170 30 2 1 10 5 1 5 2 60 10 2 10 Dividing by the common factor of 6 leaves a fraction that can be simplified further. Divide again, this time by 2. The fraction is now simplified completely because there are no other common factors in the numerator and denominator. Notice that dividing numerator and denominator by 10 has the effect of eliminating the 0 in the ones place from each number: 170 30 Skill Practice Simplify to lowest terms by first reducing by 10, 100, or 1000. 9. 10. 11. 21,000 35,000 1300 52,000 630 190 Avoiding Mistakes The “strike through” method only works for the digit 0 at the end of the numerator and denominator. Concept Connections 12. How many zeros may be eliminated from the numerator and denominator of the fraction 430,000 154,000,000?
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