QuestionJuly 15, 2025

43. -7 (3)/(5)+(-3 (5)/(6))

43. -7 (3)/(5)+(-3 (5)/(6))
43. -7 (3)/(5)+(-3 (5)/(6))

Solution
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Answer

\( -\frac{343}{30} \) Explanation 1. Convert Mixed Numbers to Improper Fractions Convert \( -7 \frac{3}{5} \) to an improper fraction: \( -\left(\frac{35}{5} + \frac{3}{5}\right) = -\frac{38}{5} \). Convert \( -3 \frac{5}{6} \) to an improper fraction: \( -\left(\frac{18}{6} + \frac{5}{6}\right) = -\frac{23}{6} \). 2. Find a Common Denominator The least common denominator of 5 and 6 is 30. 3. Convert Fractions to Common Denominator Convert \( -\frac{38}{5} \) to \( -\frac{228}{30} \). Convert \( -\frac{23}{6} \) to \( -\frac{115}{30} \). 4. Add the Fractions Add \( -\frac{228}{30} + (-\frac{115}{30}) = -\frac{343}{30} \).

Explanation

1. Convert Mixed Numbers to Improper Fractions<br /> Convert \( -7 \frac{3}{5} \) to an improper fraction: \( -\left(\frac{35}{5} + \frac{3}{5}\right) = -\frac{38}{5} \).<br /> Convert \( -3 \frac{5}{6} \) to an improper fraction: \( -\left(\frac{18}{6} + \frac{5}{6}\right) = -\frac{23}{6} \).<br /><br />2. Find a Common Denominator<br /> The least common denominator of 5 and 6 is 30.<br /><br />3. Convert Fractions to Common Denominator<br /> Convert \( -\frac{38}{5} \) to \( -\frac{228}{30} \).<br /> Convert \( -\frac{23}{6} \) to \( -\frac{115}{30} \).<br /><br />4. Add the Fractions<br /> Add \( -\frac{228}{30} + (-\frac{115}{30}) = -\frac{343}{30} \).
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