Question

which phrase represents the algebraic expression \\(\frac{3p + 6}{7p - 9}\\)?

• the sum of six times a number and three, multiplied by the difference of nine times the number and seven
• the sum of six times a number and three, divided by the difference of nine times the number and seven
• the sum of three times a number and six, multiplied by the difference of seven times the number and nine
• the sum of three times a number and six, divided by the difference of seven times the number and nine

Explanation:

1. Analyze the numerator \(3p + 6\): This can be described as "the sum of three times a number (\(3p\)) and six (\(6\))".
2. Analyze the denominator \(7p-9\): This can be described as "the difference of seven times a number (\(7p\)) and nine (\(9\))".
3. The overall expression is a fraction, so it is "the sum of three times a number and six, divided by the difference of seven times the number and nine".

• Check the first option: It has multiplication and incorrect coefficients (six times, nine times, seven) which do not match the expression.
• Check the second option: Incorrect coefficients (six times, nine times, seven) do not match the expression.
• Check the third option: It has multiplication which does not match the fraction (division) in the expression.
• Check the fourth option: Matches the description of numerator, denominator and the operation (division) in the expression.

Answer:

the sum of three times a number and six, divided by the difference of seven times the number and nine