The value of $x$ is decreased by $39 \%$ . Which expression does NOT represent this situation? $\newline$ $39 x$ $\newline$ $x-0.39 x$ $\newline$ $0.61 x$ $\newline$ $1 x-0.39 x$

Full solution

Q. The value of

x

is decreased by

39 \%

. Which expression does NOT represent this situation?

\newline

39 x

\newline

x-0.39 x

\newline

0.61 x

\newline

1 x-0.39 x

Understand the problem: Understand the problem. $\newline$ Decreasing a value by $39\%$ means that the new value is $100\% - 39\% = 61\%$ of the original value. Therefore, the correct expression should represent $61\%$ of $x$ .
Convert to decimal: Convert the percentage to a decimal to use in the expressions. $\newline$ $61\%$ as a decimal is $0.61$ . So, the correct expressions should be equivalent to multiplying $x$ by $0.61$ .
Evaluate first expression: Evaluate the given expressions to see which one does NOT represent $61\%$ of $x$ . The first expression is ＂ $39 \times x$ ＂. This represents $39$ times $x$ , not $61\%$ of $x$ .
Check second expression: Check the second expression $x - 0.39 x$ . This expression can be simplified to $0.61 x$ because $x - 0.39 x = 1x - 0.39x = 0.61x$ . This represents $61\%$ of $x$ .
Check third expression: Check the third expression ＂ $0.61 \times$ ＂. This expression directly represents $61\%$ of $x$ , which is the correct representation of the decrease.
Check fourth expression: Check the fourth expression $1x - 0.39 x$ . This expression simplifies to $0.61 x$ as well, because $1x - 0.39x = 0.61x$ . This also represents $61\%$ of $x$ .
Determine incorrect expression: Determine which expression does NOT represent the decrease of $x$ by $39\%$ . The expression ＂ $39x$ ＂ does not represent a $39\%$ decrease of $x$ . It represents $39$ times $x$ , which is not the same as $61\%$ of $x$ .