Question

Perform the indicated operations. 100 is what percentage of \(750 ?\)

Short answer

100 is 13% of 750.

Step-by-step solution

Understand the Problem

We need to find what percentage 100 is of 750. In mathematical terms, we want to find the value of \( x \) in the equation \( \frac{100}{750} \times 100 = x \).

Set Up the Percentage Equation

To determine what percentage one number is of another, use the formula \( \frac{\text{Part}}{\text{Whole}} \times 100 = \text{Percentage} \). Here, 100 is the part, and 750 is the whole, so the equation becomes \( \frac{100}{750} \times 100 \).

Perform the Division

First, divide the part by the whole: \( \frac{100}{750} = \frac{2}{15} \).

Convert to Percentage

Multiply the result by 100 to get the percentage: \( \frac{2}{15} \times 100 = 13.33\ldots \).

Round if Necessary

Since percentages are usually rounded to the nearest whole number, we can round 13.33 to 13%.

Key concepts

Basic Math Operations

Math is a language made up of numbers and operations. It's like learning the alphabet before reading. In this exercise, we perform basic math operations like division and multiplication, which help us express one quantity as a part of another.

• Division: We divide to find how many times a number fits into another. For example, when we divide 100 by 750, we see how much of 750 is taken up by 100.
• Multiplication: We multiply to scale our results. After finding what fraction 100 is of 750, we multiply by 100 to convert that fraction into a percentage.

Understanding these operations helps in solving real-world problems, like finding discounts or comparing quantities. Math might seem tricky, but with practice, these operations open the doors to more advanced calculations.

Fraction to Percentage Conversion

Turning a fraction into a percentage is a handy trick used in everyday math. Imagine a fraction as a slice of pie; converting it to a percentage shows how big your slice is compared to the whole pie.

• Identify the Fraction: In our example, the fraction is \( \frac{100}{750} \).
• Perform the Division: Divide 100 by 750 to obtain the decimal equivalent, \( \frac{2}{15} \).
• Multiply by 100: To convert the decimal into a percentage, multiply by 100. This gives us \( \frac{2}{15} \times 100 = 13.33 \ldots \).

This process shows the part-whole relationship clearly, making calculations easier to understand and quicker to perform. You often use this in statistics, finance, and many other fields.

Understanding Percentages

Percentages might seem like a mystery, but they are just another way to express fractions out of 100. This makes comparisons straightforward, whether in exams, shopping, or analyzing data.

• Origin of Percentages: A percentage is a fraction where the whole is always 100. It expresses how large one quantity is relative to another.
• Everyday Use: You often see percentages in discounts: "20% off" means you save 20 parts out of every 100.
• Mathematical Representation: Writing percentages as equations, 50% becomes \( \frac{50}{100} \) or simply 0.5 in decimal form. This helps connect percentages to fractions and decimals, enhancing understanding.

Using percentages helps make sense of data and everyday decisions. The simplicity of expressing anything in hundreds makes it a universal tool for comparison.