30/21 simplified
Understand the Problem
The question is asking to simplify the fraction 30/21, which involves finding the greatest common divisor and reducing the fraction to its simplest form.
Answer
The simplified form of the fraction is \( \frac{10}{7} \).
Answer for screen readers
The simplified form of the fraction ( \frac{30}{21} ) is ( \frac{10}{7} ).
Steps to Solve
- Find the Greatest Common Divisor (GCD)
To simplify the fraction ( \frac{30}{21} ), we first need to find the GCD of the numerator (30) and the denominator (21).
The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30
The factors of 21 are: 1, 3, 7, 21
The largest common factor is 3, so ( \text{GCD}(30, 21) = 3 ).
- Divide the numerator and the denominator by the GCD
Now, we will divide both the numerator and the denominator by the GCD we found:
[ \frac{30 \div 3}{21 \div 3} = \frac{10}{7} ]
- Write the simplified fraction
Now that we have divided both parts, the simplified form of the fraction ( \frac{30}{21} ) is:
[ \frac{10}{7} ]
The simplified form of the fraction ( \frac{30}{21} ) is ( \frac{10}{7} ).
More Information
The fraction ( \frac{10}{7} ) cannot be simplified further, as 10 and 7 do not have any common factors other than 1. This means ( \frac{10}{7} ) is in its simplest form. This fraction is also an improper fraction because the numerator (10) is larger than the denominator (7).
Tips
- A common mistake is to stop after finding the GCD and not performing the division. It's important to divide both the numerator and denominator by the GCD to simplify the fraction correctly.
- Another mistake is to incorrectly identify the GCD. Always double-check the factors of both numbers.