Final answer:
To express -578/100 - 9/13 as an equivalent expression, we find the LCM of 100 and 13, which is 1300, convert each fraction to have this common denominator, and then subtract the converted fractions. Simplifying the expression, we get (B) -1157/260 as the equivalent expression.
Step-by-step explanation:
To express -578/100 - 9/13 as an equivalent expression, we need to find a common denominator for the two fractions, which is the least common multiple (LCM) of 100 and 13. The LCM of 100 and 13 is 1300. We then convert each fraction to have this common denominator.
The first fraction, -578/100, is equivalent to -578 × 13 / (100 × 13) = -7514/1300. The second fraction, 9/13, is equivalent to 9 × 100 / (13 × 100) = 900/1300. Now, subtract the second fraction from the first:
-7514/1300 - 900/1300 = (-7514 - 900) / 1300 = -8414 / 1300
To simplify, we divide both numerator and denominator by the common factor of 2:
-8414 / 1300 ÷ 2/2 = -4207 / 650
Finally, we convert back to a denominator of 260:
-4207 / 650 × 2 / 2 = -8414 / 1300 = -1157 / 260
Therefore, the equivalent expression is (B) -1157/260.