Question

1. which two expressions can be used to model the statement below?

statement:
add four and six, then multiply the sum by eight.
divide the product by two, then triple the quotient.
a. $3(4 + 6 \times 8 \div 2)$
b. $8(4 + 6) \div (8 \times 3)$
c. $(4 + 6) \div (8 \times 2 \times 3)$
d. $8(4 + 6) \times \frac{1}{2} \times 3$
e. $8(4 + 6) \div 2 \times 3$

Explanation:

Step1: Analyze the statement

First, "Add four and six" is \(4 + 6\). Then "multiply the sum by eight" gives \(8\times(4 + 6)\) or \(8(4 + 6)\). Next, "Divide the product by two" can be written as \(\div2\) or \(\times\frac{1}{2}\). Finally, "triple the quotient" means \(\times3\).

Step2: Analyze each option

• Option A: \(3(4 + 6\times8\div2)\) – This multiplies 6 and 8 first, which is wrong. The sum of 4 and 6 should be calculated first.
• Option B: \(8(4 + 6)\div(8\times3)\) – The denominator \(8\times3\) is incorrect. We need to divide by 2 and then multiply by 3, not divide by \(8\times3\).
• Option C: \((4 + 6)\div(8\times2\times3)\) – This is completely wrong as it divides the sum by the product of 8, 2, and 3, which does not match the statement.
• Option D: \(8(4 + 6)\times\frac{1}{2}\times3\) – "Divide the product by two" is \(\times\frac{1}{2}\) and "triple the quotient" is \(\times3\), so this matches.
• Option E: \(8(4 + 6)\div2\times3\) – "Divide the product by two" is \(\div2\) and "triple the quotient" is \(\times3\), so this also matches.

Answer:

D. \( 8(4 + 6) \times \frac{1}{2} \times 3 \), E. \( 8(4 + 6) \div 2 \times 3 \)