A Lowest Term Calculator is a mathematical tool designed to simplify fractions to their most reduced form. It works by dividing both the numerator and denominator of a fraction by their greatest common divisor (GCD).
Lowest Term Calculation Chart
| Original Fraction | Steps | Simplified Fraction |
|---|---|---|
| 24/36 | 1. Find GCD: 12. Divide numerator by GCD: 24 ÷ 12 = 2. Divide denominator by GCD: 36 ÷ 12 = 3 | 2/3 |
| 50/75 | 1. Find GCD: 25. Divide numerator by GCD: 50 ÷ 25 = 2. Divide denominator by GCD: 75 ÷ 25 = 3 | 2/3 |
| 18/24 | 1. Find GCD: 6. Divide numerator by GCD: 18 ÷ 6 = 3. Divide denominator by GCD: 24 ÷ 6 = 4 | 3/4 |
| 100/400 | 1. Find GCD: 100. Divide numerator by GCD: 100 ÷ 100 = 1. Divide denominator by GCD: 400 ÷ 100 = 4 | 1/4 |
Lowest Term Calculation Formula
The formula for calculating the lowest term of a fraction is:
Lowest Term = (Numerator ÷ GCD) / (Denominator ÷ GCD)Where GCD is the Greatest Common Divisor of the numerator and denominator.
To use this formula, let’s consider the fraction 48/72:
First, we need to find the GCD of 48 and 72. Using the Euclidean algorithm or factor trees, we determine that the GCD is 24.
Now, we apply the formula:
Numerator ÷ GCD = 48 ÷ 24 = 2
Denominator ÷ GCD = 72 ÷ 24 = 3
Therefore, the lowest term is 2/3.
How can you find the lowest term?
Finding the lowest term of a fraction involves a systematic approach:
- Identify the fraction: Start with the given fraction, for example, 56/84.
- Find the GCD: Determine the greatest common divisor of the numerator and denominator. For 56 and 84, the GCD is 28.
- Divide both parts by the GCD: Divide both the numerator and denominator by the GCD.
- Numerator: 56 ÷ 28 = 2
- Denominator: 84 ÷ 28 = 3
- Write the new fraction: The resulting fraction after division is the lowest term. In this case, 2/3.
- Verify: Ensure that the new fraction cannot be reduced further. If it can, repeat steps 2-4.
What is 5% in its lowest term?
To express 5% in its lowest term, we need to convert it to a fraction and then simplify:
Convert 5% to a fraction: 5% = 5/100
Simplify the fraction:
The GCD of 5 and 100 is 5
Divide both numerator and denominator by 5:
5 ÷ 5 = 1100 ÷ 5 = 20The simplified fraction is 1/20
Therefore, 5% in its lowest term is 1/20.