What is \(\frac { 4} { 20} \) simplified?

Step 1: 
Find the greatest common divisor (GCD) of 4 and 20, which is 4. 
 

Step 2:

Divide both the numerator and the denominator by their GCD: 
\(\frac { 4 \div 4} { 20 \div 4} = \frac { 1} { 5} \).

Step 3:

Simplifying \(\frac { 4} { 20} \) by dividing both the numerator and the denominator by their GCD (4) gives \(\frac { 1} { 5} \).

Supplementary Knowledge:

1. Understanding Fractions: 
A fraction represents a part of a whole. The numerator (top number) indicates how many parts you have, while the denominator (bottom number) indicates how many equal parts the whole is divided into.

2. Greatest Common Divisor (GCD): 
The GCD of two numbers is the largest number that divides both of them without leaving a remainder. Finding the GCD is essential for simplifying fractions.

3. Equivalent Fractions: 
Fractions that represent the same value but have different numerators and denominators are called equivalent fractions. For example, \(\frac { 4} { 20} \) and \(\frac { 1} { 5} \) are equivalent because they represent the same part of a whole.

4. Simplifying Fractions: 
Simplifying a fraction means reducing it to its simplest form where the numerator and denominator are as small as possible. This is done by dividing both by their GCD.

Real-Life Connections:

Imagine you are organizing a community event and need to distribute tasks among volunteers. If you have 20 tasks and 4 volunteers, each volunteer will handle \(\frac { 4} { 20} \) of the tasks. Simplifying this fraction to \(\frac { 1} { 5} \) means each volunteer will handle \(\frac { 1} { 5} \) (or 20%) of the total tasks, making it easier to understand and manage the workload.

By mastering the skill of simplifying fractions, you can make calculations simpler and more intuitive in various real-life situations.

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