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$Evaluate the expression shown below and write your answer a mixed number or fraction in simplest form, or a decimal. (-7.2(2+8))/(0.8)+(4)/((-2.3+7.3))$

Evaluate the expression shown below and write your answer a mixed number or fraction in simplest form, or a decimal. $\newline$ $\frac{-7.2(2+8)}{0.8}+\frac{4}{(-2.3+7.3)}$

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Evaluate numerical expressions involving rational numbers

Full solution

Q. Evaluate the expression shown below and write your answer a mixed number or fraction in simplest form, or a decimal.

\newline

\frac{-7.2(2+8)}{0.8}+\frac{4}{(-2.3+7.3)}

Simplify inside parentheses: First, we need to simplify the expression inside the parentheses in the numerator and the denominator. $\newline$ $(-7.2(2+8))/(0.8) + (4)/((-2.3+7.3))$ $\newline$ = $(-7.2(10))/(0.8) + (4)/(5)$
Multiply and divide: Next, we multiply $-7.2$ by $10$ in the numerator. $\frac{-7.2 \times 10}{0.8} + \frac{4}{5}$ = $\frac{-72}{0.8} + \frac{4}{5}$
Add fractions: Now, we divide $-72$ by $0.8$ to simplify the first term. $\newline$ $(-72)/(0.8) = -90$ $\newline$ So the expression becomes: $\newline$ $-90 + (4)/(5)$
Find common denominator: We can now add the second term, which is $\frac{4}{5}$ , to $-90$ . $\newline$ $-90 + \frac{4}{5}$ $\newline$ Since $-90$ is the same as $\frac{-90}{1}$ , we can find a common denominator to add these two fractions.
Combine fractions: The common denominator for $1$ and $5$ is $5$ . We convert $-90/1$ to a fraction with a denominator of $5$ . $\newline$ $-90/1 = -450/5$ $\newline$ Now we can add the two fractions. $\newline$ $-450/5 + 4/5$ $\newline$ $= (-450 + 4)/5$ $\newline$ $= -446/5$
Convert to mixed number: Finally, we simplify $-446/5$ to a mixed number. $\newline$ $-446/5 = -89 \frac{1}{5}$ $\newline$ So the final answer is $-89 \frac{1}{5}.$

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