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The concept of ratio is a way to compare two quantities. In this context, a ratio tells you how many times one number contains another. For instance, if you are trying to find what percent 8 is of 64, you can set up a ratio to help you.
Think of a ratio as a fraction, such as \(\frac{8}{64}\). This fraction shows the relationship between the two numbers. You read it as \(8\) out of \(64\). Ratios are versatile and can help you solve problems in different contexts.
When converting ratios to a percentage, you are essentially scaling the relationship between numbers to a base of 100. This makes it easier to understand and compare. Let's delve deeper into simplifying fractions and converting them to percentages.

Simplifying fractions means reducing them to their simplest form where the numerator and denominator are as small as possible.
For example, to simplify the fraction \(\frac{8}{64}\), you can divide both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). The GCD of 8 and 64 is 8.

• Divide the numerator by 8: \(8 \-\div 8 = 1\)
• Divide the denominator by 8: \(64 \-\div 8 = 8\)

Thus, \(\frac{8}{64}\) simplifies to \(\frac{1}{8}\).
This reduced fraction \(\frac{1}{8}\) is easier to work with when performing further calculations like converting to a percentage.

Converting a fraction to a percentage involves multiplying the fraction by 100.
In the simplified fraction \(\frac{1}{8}\), you multiply by 100 to convert it to a percentage.

• Perform the multiplication: \(\frac{1}{8} \-\times 100 = 12.5\)

Therefore, \(\frac{1}{8} \times 100 = 12.5\text{\%}\).
So, 8 is 12.5% of 64. This process shows how you can easily convert any fraction into a percentage by using multiplication.
Understanding these steps helps you analyze and solve percentage problems efficiently. Remember to always simplify fractions first to make your calculations smoother and more accurate.