Simplify \(7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2}\)and correct your answer to the nearest whole number
Answer Details
To simplify the expression \(7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2}\), we need to perform the arithmetic operations in the following order: division, addition, and subtraction.
First, we need to simplify the expression inside the parentheses:
\begin{align*}
2\frac{1}{2}+3 &= \frac{5}{2} + 3 \\
&= \frac{5}{2} + \frac{6}{2} \\
&= \frac{11}{2}
\end{align*}
Next, we need to divide $\frac{11}{2}$ by $16\frac{1}{2}$:
\begin{align*}
\frac{11}{2} \div 16\frac{1}{2} &= \frac{\frac{11}{2}}{\frac{33}{2}} \\
&= \frac{11}{33} \\
&= \frac{1}{3}
\end{align*}
Substituting $\frac{1}{3}$ into the original expression, we have:
\begin{align*}
7\frac{1}{2}-\left(2\frac{1}{2}+3\right)\div16\frac{1}{2} &= 7\frac{1}{2}-\frac{1}{3} \\
&= \frac{22}{3}-\frac{1}{3} \\
&= \frac{21}{3} \\
&= 7
\end{align*}
Therefore, the answer is 7, corrected to the nearest whole number. Answer is correct.