Question

Translate to an equation and solve. What percent is 29 of \(30 ?\)

Short answer

Answer: Approximately 96.67%.

Step-by-step solution

Write down the percentage formula.

Write down the formula, which is Percentage = (Part / Whole) × 100%.

Identify the given values.

In this problem, the part is 29, and the whole is 30.

Plug the values into the formula.

Replace the variables in the formula with the given values: P = (29 / 30) × 100%

Divide the part by the whole.

Divide 29 by 30: \(\frac{29}{30}\) \(\approx\) 0.9667

Multiply by 100% to convert to a percentage.

Multiply the decimal (0.9667) by 100%: 0.9667 × 100% = 96.67%

Write the final answer.

29 is approximately 96.67% of 30.

Key concepts

Percentage Formula

The percentage formula is a fundamental mathematical concept used to express a number as a fraction of 100. It is the backbone of many operations in prealgebra and plays a crucial role in solving percentage problems.

The formula is given by: \[ \text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100\text{%} \]
Understanding this formula is essential for interpreting and solving real-world problems involving discounts, interest rates, statistics, and more. By breaking down the problem into 'part' and 'whole' and applying this formula, you can swiftly convert fractions and decimals into percentages.

Solving Percentages

To solve percentage problems, you first need to clearly understand what the 'part' and the 'whole' refer to in a given context. The 'whole' is the total amount or the reference point, while the 'part' is the portion of the whole you're looking to find the percentage of.

Once clear about the problem's context:

1. Identify the part and whole in the problem.
2. Use the percentage formula to set up an equation.
3. Perform the division to calculate the part divided by the whole.
4. Multiply this result by 100% to find the percentage.

With these steps, solving percentages can be made more approachable and manageable.

Prealgebra

Prealgebra serves as the foundation for all future math studies. It introduces students to basic mathematical concepts and operations that are used throughout algebra and other advanced math subjects. Topics in prealgebra usually include whole numbers, fractions, decimals, percentages, and simple equations.

A solid understanding of prealgebra is necessary to not only tackle percentage problems but also to succeed in more complex mathematical scenarios. The ability to manipulate numbers and understand their relationships is a critical skill developed in this phase of a student's mathematical education.

Mathematical Equations

Mathematical equations are statements that assert the equality of two expressions. In the context of percentage problems, equations allow us to solve for unknown values with precision. Learning to set up and solve equations is a crucial skill in math which allows students to unlock answers to both simple and complex problems alike.

In the case of the given exercise, the equation \[ P = \left(\frac{29}{30}\right) \times 100\text{%} \]is straightforward, but mastering equations can help in numerous situations, such as figuring out quantities in recipes or determining the rate of growth in populations. A thorough comprehension of equations is indispensable for anyone looking to excel in mathematics and related fields.