simplify 30/72
Understand the Problem
The question is asking for the simplification of the fraction 30/72. To solve this, we need to find the greatest common divisor (GCD) of both the numerator and the denominator and then divide both by that number.
Answer
The simplified fraction is $\frac{5}{12}$.
Answer for screen readers
The simplified form of the fraction $\frac{30}{72}$ is $\frac{5}{12}$.
Steps to Solve
- Find the GCD of 30 and 72
To simplify the fraction $\frac{30}{72}$, we first need to find the greatest common divisor (GCD) of the numbers 30 and 72.
The prime factorization of 30 is: $$ 30 = 2 \times 3 \times 5 $$
The prime factorization of 72 is: $$ 72 = 2^3 \times 3^2 $$
The GCD is found by taking the lowest powers of all common prime factors. Here, the common factors are 2 and 3:
- For 2: the lowest power is $2^1$
- For 3: the lowest power is $3^1$
Thus, $$ \text{GCD}(30, 72) = 2^1 \times 3^1 = 2 \times 3 = 6 $$
- Divide both numerator and denominator by the GCD
Now, we divide both the numerator and the denominator of the fraction by the GCD we found:
$$ \frac{30 \div 6}{72 \div 6} = \frac{5}{12} $$
- Final Simplified Fraction
We have now simplified the initial fraction to its lowest terms, so the final answer is $\frac{5}{12}$.
The simplified form of the fraction $\frac{30}{72}$ is $\frac{5}{12}$.
More Information
This fraction, $\frac{5}{12}$, cannot be simplified any further because 5 and 12 do not have any common factors other than 1. Simplifying fractions is an important skill in mathematics that helps in reducing complexity in calculations and comparisons.
Tips
- Not finding the GCD correctly: Ensure to find the correct prime factorization or use the Euclidean algorithm to find the GCD accurately.
- Forgetting to simplify both parts of the fraction by the GCD: Always remember to divide both the numerator and denominator by the same number to maintain the equivalence of the fraction.
AI-generated content may contain errors. Please verify critical information
