91Ó°ÊÓ

The percent equation is a handy tool whenever you are dealing with percentages in word problems. It helps you convert a percentage problem into a mathematical equation that you can solve. The basic form of the percent equation is: \[ \text{Part} = \text{Percent} \times \text{Whole} \] In our exercise, we're trying to find what percent (let's call it \(x\)) of 600 is 3. Here's how you can set it up:

• You know the "part" is 3, because that's your starting value.
• The "whole" is 600, because you are comparing to this total.
• The "percent" is your unknown \(x\), which you need to find.

By substituting into the percent equation, it becomes \( \frac{3}{600} = \frac{x}{100} \). This equation essentially states that the ratio of the part to the whole is the same as the ratio of the percent to 100.

Once you've set up your percent equation, cross-multiplication is used to solve it. This technique helps eliminate fractions and make it easier to find the answer. Let's delve into how cross-multiplication works with our example. Given the equation \( \frac{3}{600} = \frac{x}{100} \), you're dealing with two fractions set equal to each other. When cross-multiplying:

• Multiply the numerator of one fraction by the denominator of the other.
• Do the same in reverse for the other fraction.

So, you'll calculate: \[ 3 \times 100 = 600 \times x \] This simplifies to the equation \(100 = 600x\). Cross-multiplication transforms the proportions into an equation where any variable can be easily isolated.

Fraction simplification is the process of making a fraction as simple as possible without changing its value. It involves reducing the fraction to its smallest form. It's a crucial skill when dealing with percent problems to make calculations easier. For the problem "What percent of 600 is 3?", you start with the fraction \( \frac{3}{600} \). Simplifying this fraction requires finding the greatest common divisor (GCD) of 3 and 600, which is 3, and dividing both the numerator and the denominator by this number. So, you would have:

• \( \frac{3}{600} \) simplifies to \( \frac{1}{200} \)

The simplified fraction, \( \frac{1}{200} \), makes it much easier to work with and paves the way for the next steps of solving for the unknown variable \(x\). It reduces computation complexity, leading to quicker solutions.