In the fractions problem, what is the sum of the numerators when rewriting 1/5 and 1/9 with denominator 45?

In the fractions problem, what is the sum of the numerators when rewriting 1/5 and 1/9 with denominator 45?

• A. 9
• B. 45
• C. 14
• D. 5

Answer: (C)

To compare or add fractions, you rewrite each fraction with a common denominator. The smallest common denominator for 1/5 and 1/9 is 45. So adjust each fraction: 1/5 becomes 9/45 (multiply top and bottom by 9), and 1/9 becomes 5/45 (multiply top and bottom by 5). The sum of the numerators then is 9 plus 5, which equals 14. Noting that if you actually added the fractions you’d get (9/45) + (5/45) = 14/45, but the question asks for the sum of the numerators, which is 14.

To compare or add fractions, you rewrite each fraction with a common denominator. The smallest common denominator for 1/5 and 1/9 is 45. So adjust each fraction: 1/5 becomes 9/45 (multiply top and bottom by 9), and 1/9 becomes 5/45 (multiply top and bottom by 5). The sum of the numerators then is 9 plus 5, which equals 14. Noting that if you actually added the fractions you’d get (9/45) + (5/45) = 14/45, but the question asks for the sum of the numerators, which is 14.