Question

add: (\frac{7}{10} + (-4\frac{1}{2}) =)

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \( 5\frac{7}{10} \) to an improper fraction: \( 5\frac{7}{10}=\frac{5\times10 + 7}{10}=\frac{57}{10} \)
Then, convert \( - 4\frac{1}{3} \) to an improper fraction: \( -4\frac{1}{3}=-\frac{4\times3+1}{3}=-\frac{13}{3} \)

Step2: Find a common denominator

The common denominator of 10 and 3 is 30.
Rewrite the fractions with the common denominator:
\( \frac{57}{10}=\frac{57\times3}{10\times3}=\frac{171}{30} \)
\( -\frac{13}{3}=-\frac{13\times10}{3\times10}=-\frac{130}{30} \)

Step3: Add the fractions

Now add the two fractions: \( \frac{171}{30}+(-\frac{130}{30})=\frac{171 - 130}{30}=\frac{41}{30} \)

Step4: Convert back to mixed number (optional)

\( \frac{41}{30}=1\frac{11}{30} \)

Answer:

\( 1\frac{11}{30} \) (or \( \frac{41}{30} \))