Question

Rewrite each fraction or mixed number in lowest terms. $$\frac{12}{3}$$

Short answer

4

Step-by-step solution

Understand the Problem

The task is to simplify the fraction \(\frac{12}{3}\) to its lowest terms.

Find the Greatest Common Divisor (GCD)

Identify the largest number that divides both the numerator (12) and the denominator (3) without leaving a remainder. The GCD of 12 and 3 is 3.

Divide the Numerator and Denominator by the GCD

Divide the numerator and the denominator by the GCD to simplify the fraction: \(\frac{12 ÷ 3}{3 ÷ 3} = \frac{4}{1}\).

Write the Simplified Fraction

The fraction \(\frac{4}{1}\) can be further simplified to 4 since any number divided by 1 is the number itself.

Key concepts

greatest common divisor

When simplifying fractions, one useful tool is the greatest common divisor (GCD). The GCD is the largest number that can evenly divide both the numerator and the denominator of a fraction. For instance, in the fraction \(\frac{12}{3}\), the GCD of 12 and 3 is 3.

To find the GCD:

• List the factors of each number.
• Identify the largest factor common to both lists.

Here, the factors of 12 are 1, 2, 3, 4, 6, and 12, while the factors of 3 are 1 and 3. The greatest common factor is 3. Knowing the GCD helps in reducing the fraction to its simplest form.

fraction simplification

Simplifying fractions means expressing a fraction in its lowest terms, where no number other than 1 can divide both the numerator and denominator. After finding the GCD, you divide both parts of the fraction by this number.

For \(\frac{12}{3}\):

• The GCD is 3.
• Divide 12 by 3 to get 4.
• Divide 3 by 3 to get 1.

So, \(\frac{12}{3}\) simplifies to \(\frac{4}{1}\), which is simply 4.

numerator and denominator

To work effectively with fractions, it’s essential to understand the concepts of numerator and denominator. The numerator is the top number, representing how many parts we have. The denominator is the bottom number, showing into how many parts the whole is divided.

In the fraction \(\frac{12}{3}\):

• 12 is the numerator.
• 3 is the denominator.

When simplifying, you'll often use the greatest common divisor to reduce both the numerator and the denominator by dividing them by this common factor. This process ensures the fraction is expressed in the simplest form possible. For example, since the GCD of 12 and 3 is 3, dividing both by 3 gives us \(\frac{4}{1}\), or simply 4.