For homework, Ari had to find 5% of $900. Did he do the work correctly?

Question

A tape diagram. There are 5 parts out of a whole of 100. There are question mark parts out of a whole of 900.

StartFraction part Over whole EndFraction = StartFraction 100 times 180 Over 5 times 180 EndFraction = StartFraction 18,000 Over 900 EndFraction

Are Ari’s calculations correct?

No. Ari multiplied the denominators incorrectly.
No. Ari should have written the percent ratio as StartFraction 5 Over 100 EndFraction
No. Ari should have divided, not multiplied.
Yes. Ari’s work is correct.

Answer 1

To find 5% of $900, we can use the formula for percentage:

\[ \text{Percentage} = \frac{\text{part}}{\text{whole}} \times 100 \]

In this case, we want to find 5% of 900, so we can set it up as follows:

\[ \frac{x}{900} = \frac{5}{100} \]

To solve for \(x\), we can cross-multiply:

\[ x \cdot 100 = 5 \cdot 900 \]

This simplifies to:

\[ 100x = 4500 \]

Now, we divide both sides by 100:

\[ x = \frac{4500}{100} = 45 \]

Thus, 5% of $900 is $45.

Looking at Ari's approach, he incorrectly described his process and made errors in his calculations. Specifically, he should have set up the equation using the percent ratio as \(\frac{5}{100}\) rather than multiplying the denominators incorrectly.

So, the correct answer is:

No. Ari should have written the percent ratio as \(\frac{5}{100}\).