15 12 Simplified Calculator
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Reviewed by Calculator Editorial Team
Simplifying fractions is a fundamental math skill that helps make calculations easier and fractions more understandable. This guide explains how to simplify the fraction 15/12, including the step-by-step process and why simplification is important.
What is a simplified fraction?
A simplified fraction, also known as a reduced fraction, is a fraction where the numerator and denominator have no common factors other than 1. In other words, the fraction is in its simplest form when you can't divide both the numerator and denominator by any number except 1.
For example, 3/6 is not a simplified fraction because both 3 and 6 can be divided by 3. The simplified form of 3/6 is 1/2.
Simplified fractions are easier to work with in calculations and comparisons. They provide a clear representation of the relationship between the numerator and denominator.
How to simplify 15/12
To simplify the fraction 15/12, follow these steps:
- Find the greatest common divisor (GCD) of 15 and 12.
- Divide both the numerator and denominator by the GCD.
- Write the simplified fraction.
Step 1: Find the GCD of 15 and 12
The factors of 15 are: 1, 3, 5, 15
The factors of 12 are: 1, 2, 3, 4, 6, 12
The greatest common factor of 15 and 12 is 3.
Step 2: Divide numerator and denominator by GCD
15 ÷ 3 = 5
12 ÷ 3 = 4
Step 3: Write the simplified fraction
The simplified form of 15/12 is 5/4.
Remember that 5/4 is an improper fraction because the numerator is larger than the denominator. It can also be expressed as a mixed number: 1 1/4.
Simplified fraction examples
Here are some examples of fractions and their simplified forms:
| Original Fraction | Simplified Fraction | Explanation |
|---|---|---|
| 8/12 | 2/3 | GCD of 8 and 12 is 4 |
| 18/24 | 3/4 | GCD of 18 and 24 is 6 |
| 20/30 | 2/3 | GCD of 20 and 30 is 10 |
Why simplify fractions?
Simplifying fractions offers several benefits:
- Easier calculations: Simplified fractions are easier to work with in addition, subtraction, multiplication, and division.
- Clearer understanding: Simplified fractions provide a clearer representation of the relationship between the numerator and denominator.
- Consistent representation: Simplified fractions make it easier to compare different fractions.
- Standard practice: In most mathematical contexts, fractions are presented in their simplest form.
For example, when adding 1/4 and 1/2, it's easier to work with 1/4 and 2/4 (simplified form of 1/2) than with the original fractions.
FAQ
What is the simplified form of 15/12?
The simplified form of 15/12 is 5/4.
How do you simplify a fraction?
To simplify a fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD.
What is an improper fraction?
An improper fraction is a fraction where the numerator is larger than the denominator, such as 5/4.
Can all fractions be simplified?
Yes, all fractions can be simplified to their simplest form, which is when the numerator and denominator have no common factors other than 1.