Question

subtract.
$-7\frac{7}{10} - 9\frac{3}{5} = \square$

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(-7\frac{7}{10}\) 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 \(-7\frac{7}{10}\), we have \(a = -7\), \(b = 7\), \(c = 10\). Then \(-7\frac{7}{10}=-\frac{7\times10 + 7}{10}=-\frac{70 + 7}{10}=-\frac{77}{10}\).

Next, convert \(9\frac{3}{5}\) to an improper fraction. Here, \(a = 9\), \(b = 3\), \(c = 5\). So \(9\frac{3}{5}=\frac{9\times5 + 3}{5}=\frac{45 + 3}{5}=\frac{48}{5}\).

Now the expression becomes \(-\frac{77}{10}-\frac{48}{5}\).

Step2: Find a common denominator

The denominators are 10 and 5. The least common denominator of 10 and 5 is 10. So we need to rewrite \(\frac{48}{5}\) with a denominator of 10. To do this, multiply the numerator and denominator by 2: \(\frac{48\times2}{5\times2}=\frac{96}{10}\).

Now the expression is \(-\frac{77}{10}-\frac{96}{10}\).

Step3: Subtract the fractions

When subtracting fractions with the same denominator, we subtract the numerators and keep the denominator the same. So \(-\frac{77}{10}-\frac{96}{10}=-\frac{77 + 96}{10}=-\frac{173}{10}\).

Step4: Convert back to a mixed number (optional, but often preferred)

To convert \(-\frac{173}{10}\) to a mixed number, divide 173 by 10. 10 times 17 is 170, so the quotient is 17 and the remainder is 3. So \(-\frac{173}{10}=-17\frac{3}{10}\).

Answer:

\(-17\frac{3}{10}\) (or \(-\frac{173}{10}\))