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Chapter 2: Problem 15

Simplify. $$ \frac{6}{8} $$

Short Answer

Expert verified
\frac{3}{4}

Step by step solution

01

Identify the greatest common divisor (GCD)

Find the greatest common divisor of 6 and 8.
02

Divide both numerator and denominator by the GCD

Divide 6 and 8 by their GCD to simplify the fraction.
03

Simplify the fraction

Using the GCD found in Step 1, divide both the numerator and denominator to get the simplest form.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

greatest common divisor
To simplify a fraction, we first need to find a special number called the greatest common divisor (GCD). The GCD of two numbers is the largest number that can evenly divide both of them without leaving a remainder. For instance, to simplify \(\frac{6}{8}\), we need to find the GCD of 6 and 8. Here's a simple way to do this:

  • List the factors of each number.
  • 6: 1, 2, 3, 6
  • 8: 1, 2, 4, 8
In this case, you can see that 2 is the largest number that appears in both lists. So, the GCD of 6 and 8 is 2. We will use this number in the next steps to simplify our fraction.
numerator and denominator
A fraction consists of two parts: the numerator and the denominator. The top number is called the numerator, while the bottom number is the denominator.

In our example, for \(\frac{6}{8}\),
  • 6 is the numerator.
  • 8 is the denominator.
To simplify a fraction, both the numerator and the denominator must be divided by their GCD. This helps transform the fraction into its simplest form.
simplified fraction
A simplified fraction means the numerator and the denominator do not have any common factors other than 1. Using the GCD we found earlier, let's simplify \(\frac{6}{8}\). We'll divide both the numerator and the denominator by the GCD, which is 2, like this:

  • Divide the numerator (6) by 2: 6 梅 2 = 3
  • Divide the denominator (8) by 2: 8 梅 2 = 4


After simplifying, we get \(\frac{3}{4}\). This is the simplest form. This simplified fraction means we've reduced the fraction \(\frac{6}{8}\) to its lowest terms. It's often easier to understand and use fractions when they are in their simplest form!

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