Question

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

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(-4\frac{1}{2}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(-4\frac{1}{2}\), we have \(a=-4\), \(b = 1\), \(c = 2\). Then \(-4\frac{1}{2}=-\frac{4\times2 + 1}{2}=-\frac{9}{2}\).

Step2: Find a common denominator

The denominators of \(\frac{-7}{10}\) and \(-\frac{9}{2}\) are 10 and 2. The least common denominator is 10. So we convert \(-\frac{9}{2}\) to a fraction with denominator 10. Multiply the numerator and denominator of \(-\frac{9}{2}\) by 5: \(-\frac{9\times5}{2\times5}=-\frac{45}{10}\).

Step3: Add the fractions

Now we add \(\frac{-7}{10}\) and \(-\frac{45}{10}\). When adding fractions with the same denominator, we add the numerators: \(\frac{-7+(-45)}{10}=\frac{-52}{10}\).

Step4: Simplify the fraction

Simplify \(\frac{-52}{10}\) by dividing both the numerator and denominator by 2: \(\frac{-52\div2}{10\div2}=-\frac{26}{5}\). We can also convert this to a mixed number: \(-5\frac{1}{5}\) (since \(26\div5 = 5\) with a remainder of 1).

Answer:

\(-\frac{26}{5}\) (or \(-5\frac{1}{5}\))