Let's break down the expression [tex]\(\frac{1}{2} \times (734 - 246)\)[/tex] step by step to understand it and find the statement that best describes it.
1. Evaluate the inner expression: Calculate the difference between 734 and 246.
[tex]\[
734 - 246 = 488
\][/tex]
2. Multiply the result by [tex]\(\frac{1}{2}\)[/tex]: Now, take half of the difference we just calculated.
[tex]\[
\frac{1}{2} \times 488 = 244
\][/tex]
Thus, the expression [tex]\(\frac{1}{2} \times (734 - 246)\)[/tex] simplifies to 244.
Now let’s compare this with the statements given:
1. Half the sum of 734 and 246:
[tex]\[
\text{Sum: } 734 + 246 = 980
\][/tex]
[tex]\[
\text{Half the sum: } \frac{1}{2} \times 980 = 490
\][/tex]
This does not match our calculated result of 244.
2. [tex]\(\frac{1}{2}\)[/tex] the difference between 734 and 246:
[tex]\[
\text{Difference: } 734 - 246 = 488
\][/tex]
[tex]\[
\text{Half the difference: } \frac{1}{2} \times 488 = 244
\][/tex]
This matches our calculated result of 244.
3. [tex]\(\frac{1}{2}\)[/tex] the quotient of 734 and 246:
[tex]\[
\text{Quotient: } 734 / 246 \approx 2.9837
\][/tex]
[tex]\[
\text{Half the quotient: } \frac{1}{2} \times 2.9837 \approx 1.4918
\][/tex]
This does not match our calculated result of 244.
4. 2 times the difference between 734 and 246:
[tex]\[
\text{Difference: } 734 - 246 = 488
\][/tex]
[tex]\[
\text{2 times the difference: } 2 \times 488 = 976
\][/tex]
This does not match our calculated result of 244.
Therefore, the statement that best describes the expression [tex]\(\frac{1}{2} \times (734 - 246)\)[/tex] is:
[tex]\[
\boxed{\frac{1}{2} \text{ the difference between 734 and 246}}
\][/tex]
