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To solve percentage problems effectively, understanding the percentage formula is crucial. The percentage formula helps convert relationships between parts and wholes into meaningful and comparable figures. The fundamental formula for determining percentages is:
\(\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\).
Here, the 'Part' represents the amount you're interested in comparing, and the 'Whole' is the total amount from which the part is taken. Converting these into percentages makes it easier to interpret relationships and quantify changes. In our exercise, we need to find out what percentage 30 is of 20. Plugging the values into the formula:
\(\frac{30}{20} \times 100\), we can conclude that 30 is 150% of 20.

Basic algebra is the foundation for many mathematical concepts, including percentage calculations. It helps translate real-world situations into mathematical expressions. In our exercise, we set up an equation to identify the percentage. Here's how algebra comes into play:
We started with the question: '30 is what percent of 20?'
This naturally translates to the equation:
\(\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100\).
Here, you're setting up an algebraic equation that solves for the unknown percentage, using given numerical values. Basic algebra allows us to manipulate these values and understand the relationships between different quantities.

Fraction simplification is a process of reducing fractions to their simplest form. Simplifying fractions makes them easier to interpret and use in further calculations. In our example, we started with \(\frac{30}{20}\).
To simplify, we divided both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor, which is 10 in this case.
So, \(\frac{30}{20} = \frac{30 \div 10}{20 \div 10} = \frac{3}{2} = 1.5\).
Simplifying the fraction made it easier to multiply by 100 and convert to a percentage.

Mathematical translation involves converting word problems into mathematical equations. This skill is essential in solving real-life problems using mathematics. In the exercise, the problem '30 is what percent of 20?' needs to be translated into an equation before solving.
We start with the statement: '30 is what percent of 20?'
By recognizing keywords, we understand that 'is' translates to 'equals,' and 'what percent' indicates a fraction multiplied by 100.
The translation leads us to the equation:
\(\text{Percentage} = \frac{30}{20} \times 100\).
By translating the words into mathematical symbols and operations, we solve for the desired percentage: 150%.