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A percent equation is very useful for solving problems where you need to find out what percentage one number is of another number. The basic idea is to compare a part of something to the whole, using a percent. The general form of the percent equation is:
\[\frac{part}{whole} = \frac{p}{100} \]
In this equation:

• 'part' represents the portion or piece you are interested in.


• 'whole' is the total amount or number.


• 'p' is the percent.

When solving percent problems, this equation helps you organize the information you know and what you need to find out. By substituting the known values, we set up a proportion that makes it easier to solve for the missing value.

Cross-multiplication is a mathematical technique used to solve proportions. A proportion is an equation where two ratios are set equal to each other. In percent problems, we can use cross-multiplication to find the unknown percentage. Given the proportion from the percent equation:
\[\frac{4}{12} = \frac{p}{100} \]
Cross-multiplication involves multiplying the numerator of one fraction by the denominator of the other. This results in:
\[4 \times 100 = 12 \times p \]
Simplify this to get:
\[\frac{400}{12} = p \]
To isolate p, which is our percent, divide both sides by 12:
\[\frac{400}{12} = p \]
Simplifying this gives us p ≈ 33.33.
By using cross-multiplication, we simplify the process of solving for the unknown in our percent equation.

Sometimes, solving percent problems involves simplifying fractions to make calculations easier. Fraction simplification means reducing a ratio to its simplest form, where the numerator and denominator have no common factors other than 1. For the example in the exercise, we start with the fraction:
\[\frac{4}{12} \]
To simplify this, we look for the greatest common divisor (GCD) of 4 and 12, which is 4. We then divide both the numerator and the denominator by 4:
\[\frac{4 \div 4}{12 \div 4} = \frac{1}{3} \]
By simplifying the fraction from \[\frac{4}{12} \] to \[\frac{1}{3} \], further calculations become more straightforward. With a simpler fraction, solving percent equations through cross-multiplication or other techniques will be easier and quicker.