Question

what is 130% of 9?\
\\(\frac{x}{130} = \frac{9}{100}\\)\
\\(\frac{x}{9} = \frac{130}{100}\\)\
\\(\frac{9}{x} = \frac{130}{100}\\)

Explanation:

To find what a percentage of a number is, we can use the proportion method. The general idea is that the percentage (130%) over 100% is equal to the part (x) over the whole (9).

Step 1: Set up the proportion

We know that "of" means multiplication in percentage problems, but using proportions: if \( x \) is 130% of 9, then we set up the proportion \(\frac{x}{9}=\frac{130}{100}\). This is because \( x \) is to 9 as 130 is to 100 (since percentages are out of 100).

Step 2: Solve for \( x \)

Cross - multiply: \( 100x=9\times130 \)
\( 100x = 1170 \)
Divide both sides by 100: \( x=\frac{1170}{100}=11.7 \)

But for the purpose of choosing the correct proportion, the correct proportion is \(\frac{x}{9}=\frac{130}{100}\)

Answer:

The correct proportion is \(\boldsymbol{\frac{x}{9}=\frac{130}{100}}\) (the middle option). And the value of 130% of 9 is \( 11.7 \)