20/35 simplified
Understand the Problem
The question is asking to simplify the fraction 20/35 to its lowest terms. To do this, we will find the greatest common divisor (GCD) of the numerator and denominator and divide both by that number.
Answer
The simplified fraction is \( \frac{4}{7} \).
Answer for screen readers
The simplified fraction of ( \frac{20}{35} ) is ( \frac{4}{7} ).
Steps to Solve
- Find the GCD of 20 and 35
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator (20) and the denominator (35). The GCD can be found using the prime factorization or the Euclidean algorithm.
The prime factorization of 20 is ( 2^2 \times 5^1 ), and for 35, it is ( 5^1 \times 7^1 ). The common factor here is 5.
Thus, the GCD is 5.
- Divide both the numerator and denominator by the GCD
Now that we have the GCD, we need to divide both the numerator and the denominator by 5.
[ \text{Numerator: } \frac{20}{5} = 4 ] [ \text{Denominator: } \frac{35}{5} = 7 ]
- Write the simplified fraction
The simplified form of the fraction is:
$$ \frac{4}{7} $$
The simplified fraction of ( \frac{20}{35} ) is ( \frac{4}{7} ).
More Information
When simplifying fractions, identifying the greatest common divisor (GCD) is essential as it allows us to reduce the fraction to its simplest form. This process ensures clearer communication of ratios and comparisons.
Tips
- Forgetting to find the GCD correctly may lead to incorrect simplification. To avoid this, always double-check your factorization or the use of the Euclidean algorithm.
- Not dividing both the numerator and denominator, which results in incorrect fractions. Always apply the GCD to both parts to get the simplified version.
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