Answered

Jeremiah answers $90 \%$ of the questions on his test correctly. There are 40 questions on the test.




\multicolumn{10}{|c|}{Correct Test Questions}

10\%		10\%10\%10\%10\%10\%10\%10\%10\%10\%

$\frac{1}{10}$		$\frac{1}{10}$$\frac{1}{10}$$\frac{1}{10}$$\frac{1}{10}$$\frac{1}{10}$$\frac{1}{10}$$\frac{1}{10}$$\frac{1}{10}$$\frac{1}{10}$

4		444444444






Jeremiah writes the expression $40-\left(\frac{1}{10} \times 40\right)$ to determine the number of questions answered correctly. Which is an equivalent expression?


A$\frac{9}{10} \times 40$
B$40-36$
C$\left(\frac{1}{10} \times 40\right)-40$

Verified Answer :

  • Evaluate the original expression: \(40 - (\frac{1}{10} \times 40) = 40 - 4 = 36\).
  • Calculate the values of each option to find the match: \(\frac{9}{10} \times 40 = 36\), \(40 - 36 = 4\), and \((\frac{1}{10} \times 40) - 40 = -36\).
  • Compare the results to identify the equivalent expression.
  • The equivalent expression is \(\boxed{\frac{9}{10} \times 40}\).

Explanation

  1. Evaluating the Expression

Jeremiah answered 90% of 40 questions correctly. To find the number of questions he answered correctly, we can calculate 90% of 40:
\[\text{Number of correct answers} = 40 \times 0.9 = 40 \times \frac{9}{10} = 36\]
The expression Jeremiah wrote is \(40 - (\frac{1}{10} \times 40)\). Let's evaluate this expression:
\[40 - (\frac{1}{10} \times 40) = 40 - 4 = 36\]
We see that the original expression evaluates to 36, which is equal to the number of correct answers. We need to identify which of the provided options is equivalent to this expression.

  1. Comparing Options

Now, let's examine the three provided options to see which one evaluates to the same value (36):

  1. \(\frac{9}{10} \times 40\):

\[\frac{9}{10} \times 40 = 9 \times \frac{40}{10} = 9 \times 4 = 36\]
This expression matches our result.

  1. \(40 - 36\):

\[40 - 36 = 4\]
This does not match our result.

  1. \((\frac{1}{10} \times 40) - 40\):

\[(\frac{1}{10} \times 40) - 40 = 4 - 40 = -36\]
This does not match our result.

Thus, the only expression equivalent to Jeremiah's is \(\frac{9}{10} \times 40\).

  1. Conclusion

We have demonstrated that both Jeremiah's expression and the first option evaluate to 36. Therefore, the equivalent expression is \(\frac{9}{10} \times 40\). The final answer is \(\boxed{\frac{9}{10} \times 40}\).

Examples

When calculating discounts on items, you often subtract a fraction of the total price (like a 10% discount). For example, if a shirt costs \(\$40\) and you have a 10% discount, you pay \(40 - (\frac{1}{10} \times 40) = \$36\). Alternatively, you can calculate the price as \(\frac{9}{10} \times 40 = \$36\). Recognizing that these two expressions are mathematically equivalent helps in simplifying shopping calculations and understanding percentages more intuitively.

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