Solve For X: Fractions, Percentages, And Ratios

Hey everyone! Today, we're diving into a fun mathematical problem where we need to calculate the value of x. This involves dealing with percentages, fractions, and ratios. Don't worry, we'll break it down step-by-step so it's super easy to follow. We'll also make sure to reduce our final answer to its lowest terms and express it as a fraction. Let's get started!

Understanding the Equation

First, let's take a close look at the equation we're working with:

$$\frac{1 \%}{2}=2 \frac{3}{8}:=x=\frac{2}{7}$$

Okay, so this looks a little complex at first glance, but trust me, it's manageable. The equation essentially presents a relationship between different values, and our goal is to isolate 'x' and find its numerical value. We're dealing with a percentage, a mixed number, a ratio denoted by the colons, and finally, a fraction that 'x' is supposedly equal to. Our job is to verify and properly compute 'x'. To do this, we need to understand what each part of the equation means and how they relate to each other. Let's break it down bit by bit. The left-hand side of the equation involves a percentage divided by a whole number. We need to convert the percentage to a fraction and then perform the division. Remember, percentages are just fractions out of 100, so 1% is the same as 1/100. Then, we need to consider the mixed number, 2 3/8. A mixed number is a whole number combined with a fraction. To work with it effectively, we'll need to convert it into an improper fraction. This means expressing it as a single fraction where the numerator is greater than the denominator. Next, we have the ratio, indicated by the colons. Ratios are used to compare two quantities. In this case, it's showing a relationship between the result of the left-hand side and 'x'. The presence of the colons implies a proportion, suggesting that the ratio of the first two terms should be equal to the ratio involving 'x'. Finally, we have 2/7 on the right side of the equation, which the equation claims is the value of 'x'. Our task is to perform the calculations on the left side and the middle terms to see if they indeed lead to x = 2/7. If not, we will determine the correct value of 'x' based on the proportion established in the equation. This careful step-by-step approach will help us unravel the equation and solve for 'x' accurately. So, let's dive into the calculations and see what we get!

Step 1: Convert 1% to a Fraction

The very first thing we need to do is convert 1% into its fractional form. Remember, the percent symbol (%) means