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Converting fractions to percentages is a common mathematical operation that translates the fraction into a more familiar format—percentages. A fraction like \(\frac{3}{5}\) is essentially saying that for every 5 parts of a whole, 3 are being considered. But how do we express that in terms of 100, which is what a percentage is—parts per 100?Let's start with a simple step-by-step :

• The goal is to represent the fraction as a number out of 100.
• The fraction's denominator is transformed to 100, making the numerator our percentage.

Think of percentages as a way to say "how many if there were 100 parts instead of 5 parts." By setting up an equation with the fraction on one side and \( \frac{x}{100} \) on the other side (where \( x \) is the sought-after percent), you're ready to solve for \( x \). This is where cross multiplication comes in—and it's a powerful tool when working with proportion problems.

Cross multiplication is one of those handy techniques in mathematics that helps solve equations involving fractions. When you set up your fraction equation \( \frac{3}{5} = \frac{x}{100} \), cross multiplication helps you find the unknown percentage \( x \) with ease.Here's a simple breakdown:

• First, multiply the numerator of the first fraction by the denominator of the second fraction.
• Then, multiply the numerator of the second fraction by the denominator of the first fraction.
• Set these two products equal.

So, applying this technique to our example gives us:Multiply 3 (from the fraction \( \frac{3}{5} \)) by 100 (the percent denominator), equaling 300.Simultaneously, multiply x by 5, giving \( 5x \).Since these two are equal, \( 5x = 300 \), solving for \( x \) becomes straightforward.

Now that we have our equation from cross multiplication, it's time to use basic arithmetic operations to solve for \( x \). This step is all about performing multiplication and division to find the missing number in our percentage equation.In our example, post cross multiplication, we have \( 5x = 300 \). The task now is to solve for \( x \), which involves a simple division:

• Divide both sides of the equation by 5 to isolate \( x \).
• This operation gives us \( x = \frac{300}{5} \).

Perform the division, and you'll find that \( x = 60 \).So, using these basic operations, we've converted the fraction \( \frac{3}{5} \) to 60%, demonstrating the beauty of basic math when unraveling fractions into percentages! Don't be shy to practice more with other fractions, as this technique holds strong universally.