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------------------------------------------------ What percent of 40 is 32?

Set up the percent proportion. The part is 32, the whole is 40, and the percent is unknown.

Proportion:

[tex]\[
\frac{32}{40} = \frac{x}{100}
\][/tex]

To determine what percent 32 is of 40, we need to set up a proportion that compares the part (32), the whole (40), and the percent (unknown, which we'll call x). Here's a step-by-step solution:

1. Set up the proportion:
We know that a part (32) of a whole (40) can be expressed as a ratio. This ratio should be equal to the ratio of the percent (x) over 100, since percentages are simply a part of a whole expressed out of 100.

The proportion can be set up as follows:
[tex]\[
\frac{32}{40} = \frac{x}{100}
\][/tex]

2. Solve the proportion:
To solve for x, we can use cross-multiplication. Cross-multiplying the terms gives:
[tex]\[
32 \times 100 = 40 \times x
\][/tex]

3. Simplify the equation:
Simplifying the multiplication on the left side of the equation:
[tex]\[
3200 = 40x
\][/tex]

4. Solve for x:
To isolate x, divide both sides of the equation by 40:
[tex]\[
x = \frac{3200}{40}
\][/tex]

5. Calculate the result:
Performing the division gives:
[tex]\[
x = 80
\][/tex]

So, 32 is 80% of 40.