Answered

Work from left to right through the addition and subtraction:



$\begin{aligned}

& \frac{6+12 \times 4}{15-11+2} \\

= & \frac{6+48}{15-11+2} \\

= & \frac{54}{15-11+2}

\end{aligned}$



$=\frac{54}{}$

Verified Answer :

  • Calculate the numerator: \(6 + 12 \times 4 = 6 + 48 = 54\).
  • Calculate the denominator working left to right: \(15 - 11 + 2 = 4 + 2 = 6\).
  • The expression simplifies to \(\frac{54}{6}\).
  • The missing number in the denominator is \(\boxed{6}\).

Explanation

  1. Analysis and Numerator Calculation

The objective is to simplify the arithmetic expression \(\frac{6 + 12 \times 4}{15 - 11 + 2}\) by following the order of operations. We analyze the components of the expression separately, starting with the numerator and the denominator. The numerator is \(6 + 12 \times 4\). According to the order of operations, we must perform the multiplication before the addition. Multiplying \(12\) by \(4\) yields \(48\), and adding \(6\) results in \(6 + 48 = 54\). This gives us the numerator as \(54\).

  1. Calculating the Denominator

Next, we focus on the denominator \(\frac{15 - 11 + 2}{1}\). The instructions specify that for the addition and subtraction operations in the denominator, we should work from left to right. Starting with the subtraction: \(15 - 11 = 4\). Then, we proceed with the addition: \(4 + 2 = 6\). Thus, the value of the denominator is \(6\).

  1. Conclusion and Final Result

Combining the results from the previous steps, we have the expression \(\frac{54}{6}\). The question asks for the missing number in the denominator sequence, which is the result of the calculation \(15 - 11 + 2\). We found this value to be \(6\). Dividing \(54\) by \(6\) gives \(9\). The required number to complete the expression is \(\boxed{6}\).

Examples

Understanding the order of operations is crucial in everyday life, such as when calculating shared expenses among friends or adjusting recipes. For example, if you are buying supplies for a group project where each of the 6 people needs 12 items at \$4 each, plus an initial setup fee of \$6, you would calculate the total cost as \(\frac{6 + 12 \times 4}{15 - 11 + 2} \times \text{something}\) or similar structures. Mastery of these rules ensures that your financial and logistical planning remains accurate and reliable.

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