What is 30/100 simplified?
The Correct Answer and Explanation is:
The fraction ( \frac{30}{100} ) can be simplified to ( \frac{3}{10} ).
Explanation:
To simplify a fraction, the goal is to express it in its lowest terms. This is done by finding the greatest common divisor (GCD) of the numerator and the denominator and then dividing both by this number.
- Identify the GCD: The first step is to find the GCD of the numerator (30) and the denominator (100). The GCD is the largest number that divides both numbers without leaving a remainder.
- The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30.
- The factors of 100 are: 1, 2, 4, 5, 10, 20, 25, 50, 100.
- The common factors are: 1, 2, 5, and 10. The largest of these is 10.
- Divide by the GCD: Next, we divide both the numerator and the denominator by their GCD (10). [
\frac{30 \div 10}{100 \div 10} = \frac{3}{10}
] - Final Fraction: The fraction ( \frac{3}{10} ) is now in its simplest form because 3 and 10 have no common factors other than 1. This means they cannot be simplified any further.
Understanding Fractions:
Fractions represent parts of a whole. In this case, ( \frac{30}{100} ) can be interpreted as 30 out of 100 parts, which is equivalent to 30%. Simplifying fractions is essential in mathematics as it makes calculations easier and clearer. For example, when comparing fractions or performing arithmetic operations like addition or subtraction, simplified fractions can prevent unnecessary complexity.
In practical applications, simplifying fractions is also helpful in real-life situations, such as cooking, budgeting, or any scenario where parts of a whole are involved. By simplifying, we achieve clearer understanding and more efficient problem-solving. Thus, the simplified form of ( \frac{30}{100} ) is ( \frac{3}{10} ).