Question

which of the following options verbally expresses the following numerical expression? 22 - 6 ÷ (2 · 3)

1. the difference of twenty - two and six plus the product of two and three
2. the difference of twenty - two and six divided by the sum of two and three
3. the difference of twenty - two and six divided by the product of two and three
4. the quotient of twenty - two and six divided by the sum of two and three

Explanation:

Step1: Analyze the order of operations

First, we look at the parentheses: \(2 \cdot 3\) is the product of 2 and 3. Then, \(6 \div (2 \cdot 3)\) is 6 divided by the product of 2 and 3. Finally, \(22 - 6 \div (2 \cdot 3)\) is the difference of 22 and (6 divided by the product of 2 and 3).

Step2: Match with the options

• Option 1: Talks about "six plus the product", which is incorrect as it's division, not addition.
• Option 2: Talks about "sum of two and three", but \(2 \cdot 3\) is product, not sum.
• Option 3: Says "the difference of twenty - two and six divided by the product of two and three", which matches the expression \(22-6\div(2\cdot3)\) (since \(2\cdot3\) is the product of 2 and 3, \(6\div(2\cdot3)\) is 6 divided by that product, and then we take the difference of 22 and that quotient).
• Option 4: Talks about "quotient of twenty - two and six", but the expression is 22 minus (6 divided by...), not (22 divided by 6) divided by....

Answer:

1. the difference of twenty - two and six divided by the product of two and three