Question

Multiple Choice 4 is what percent of 20 ? (Percent Review) (A) \(16 \%\) (B) \(18 \%\) (C) \(20 \%\) (D) \(22 \%\)

Short answer

20% (Option C).

Step-by-step solution

Understand the Problem

The problem asks us to find what percent the number 4 is of the number 20. In other words, we need to determine what percentage of 20 is equivalent to the number 4.

Set Up the Percentage Equation

Percentage can be calculated using the equation \( \text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\% \). Here, our 'Part' is 4 and the 'Whole' is 20.

Substitute Numbers into the Equation

Substitute the given numbers into the percentage formula: \( \text{Percentage} = \left(\frac{4}{20}\right) \times 100\% \).

Perform the Division

Calculate the division \( \frac{4}{20} \). This simplifies to \( 0.2 \), since dividing 4 by 20 gives 0.2.

Convert Decimal to Percentage

To convert the decimal 0.2 to a percentage, multiply it by 100. So, \( 0.2 \times 100 = 20 \percent \).

Finalize the Solution

Based on the calculation, 4 is 20% of 20. Thus, the correct answer is option (C) - 20%.

Key concepts

Percent calculation

Calculating percentages is a fundamental concept in mathematics. It involves finding out what portion one number is of another, expressed in terms of 100. The percentage formula is

• \( \text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\% \)

This equation helps to transition from a fraction to a percentage. Here, the 'Part' is the portion of the 'Whole' you are examining. In our example, 4 is the part, and 20 is the whole.
First, you divide the part by the whole, which gives you a decimal representing the ratio of the part to the whole. Then, by multiplying the resulting decimal by 100, you convert this ratio into a percentage. This operation effectively scales the ratio so it fits into the 0-100 range that we expect with percentages.
Understanding percent calculations allows you to interpret data meaningfully, be it in exams or real-world scenarios like sales discounts or population statistics.

Mathematical equations

Mathematical equations are a way to represent relationships between numbers and variables. They are structured like sentences in language: each component has its own role. In this context, we used the equation for percentage calculation. The formula we worked with is simple but powerful for comparing numbers.
To solve such equations, it's essential to correctly assign values to variables and perform arithmetic operations in the right order. Here, the equation \( \text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\% \) helps us transform a real-life question into a solvable mathematical problem.
By substituting our specific values of 4 and 20 into the equation, we have turned abstract labels into concrete numbers, making it possible to perform calculations. Practicing setting up and solving equations sharpens skills needed for more complex mathematical tasks and ensures accuracy in everyday calculations.

Basic arithmetic

Basic arithmetic is the fundamental cornerstone of math, necessary for performing calculations like the one in our problem. Arithmetic involves operations such as addition, subtraction, multiplication, and division. In the context of percentage calculations, division and multiplication are particularly crucial.
First, you use division to determine what fraction one number is of another. For example, \( \frac{4}{20} \) tells us that 4 is 0.2 of 20. Next, multiplication transforms this fraction into a percentage, \( 0.2 \times 100 \% = 20 \% \). Understanding when and how to use these operations is critical.
Proficient arithmetic skills can help simplify complex problems into manageable parts, giving clarity and confidence. Over time, quick mental arithmetic also speeds up your problem-solving ability, which is handy not just in tests, but throughout various aspects of daily life.