Question

Translate the following verbal expressions into variable expressions

Four-fifths of the sum of w and ten


The quotient of five more than twice a number and the number



Seventeen less than the product of the negative two and n

Answer 1

1) (w + 10) * (4/5)

2) (2n + 5) / n

3) -2n - 17

Answer 2

Four-fifths of the sum of w and ten: 4/5 × (w + 10)

The quotient of five more than twice a number and the number: (5 + 2x) / x

Seventeen less than the product of the negative two and n: -2n - 17

Explanation:

Four-fifths of the sum of w and ten:**

• "Sum" means addition.
• "Four-fifths" means multiply by 4/5.

Therefore, the verbal expression "four-fifths of the sum of w and ten" can be translated into the variable expression 4/5 × (w + 10).

The quotient of five more than twice a number and the number:

• "Quotient" means division.
• "Five more than twice a number" means 2x + 5.

Therefore, the verbal expression "the quotient of five more than twice a number and the number" can be translated into the variable expression (5 + 2x) / x.

Seventeen less than the product of the negative two and n:

• "Product" means multiplication.

Therefore, the verbal expression "seventeen less than the product of the negative two and n" can be translated into the variable expression -2n - 17.