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Fractions are numerical quantities that are not whole numbers. They represent a part of a whole. A fraction consists of a numerator and a denominator. The numerator is the top number and shows how many parts we have. The denominator is the bottom number and shows how many parts the whole is divided into.

A basic example is the fraction \( \frac{1}{2} \). Here, the numerator '1' means we have one part, and the denominator '2' means the whole is divided into two parts. This represents half of the whole. Others may include fractions like \( \frac{3}{4} \) and \( \frac{5}{8} \).

Understanding fractions is essential in many areas of math, such as ratio simplification. When dealing with fractions, we often need to simplify them by reducing them to their lowest terms.

The greatest common divisor (GCD) is the largest number that divides evenly into two or more numbers without leaving a remainder. In other words, it’s the biggest number that both the numerator and the denominator in a fraction can be divided by.

For instance, in the ratio simplification problem given, we first convert decimals to fractions: \( \frac{48}{64} \). To simplify, we find the GCD of 48 and 64, which is 16. Now, dividing both by 16:

• \( 48 \div 16 = 3 \)
• \( 64 \div 16 = 4 \)

So, \( \frac{48}{64} \) simplifies to \( \frac{3}{4} \).

Knowing how to find the GCD makes fraction simplification much easier, allowing you to reduce fractions to their simplest form quickly.

Decimal to fraction conversion is a crucial skill in mathematics. It's about transforming a decimal number into a fraction. Let's take our example of conversion for 0.48 and 0.64.

To convert 0.48 and 0.64 to fractions, follow these steps:

• First, count the number of decimal places. Both have 2 decimal places.
• Next, multiply both by 100 (since we have 2 decimal places).

This gives us \( 0.48 \times 100 = 48 \) and \( 0.64 \times 100 = 64 \). Now, we have the fraction \( \frac{48}{64} \).

Once converted to fractions, you can simplify as shown in the above steps. This process helps in working with ratios, proportions, and other math problems that involve fractions.