Write the fraction 20/45 in simplest form.
Understand the Problem
The question asks to simplify the fraction 20/45 to its simplest form, which means finding the greatest common divisor (GCD) of 20 and 45 and then dividing both the numerator and denominator by that GCD.
Answer
$\frac{4}{9}$
Answer for screen readers
$\frac{4}{9}$
Steps to Solve
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Find the prime factorization of the numerator and denominator
The numerator is 20. Its prime factorization is $20 = 2 \times 2 \times 5 = 2^2 \times 5$. The denominator is 45. Its prime factorization is $45 = 3 \times 3 \times 5 = 3^2 \times 5$.
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Identify the greatest common divisor (GCD)
The common prime factor between 20 and 45 is 5. Therefore, the GCD(20, 45) = 5.
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Divide both the numerator and the denominator by the GCD
Divide the numerator (20) by 5: $20 \div 5 = 4$. Divide the denominator (45) by 5: $45 \div 5 = 9$.
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Write the simplified fraction
The simplified fraction is $\frac{4}{9}$.
$\frac{4}{9}$
More Information
Simplifying a fraction means reducing it to its lowest terms. This is achieved by finding the greatest common divisor (GCD) of the numerator and the denominator and then dividing both by that value.
Tips
A common mistake is not finding the greatest common divisor but just a common divisor. For example, improperly simplifying 20/45 by dividing the numerator and denominator by just noting that they are both divisible by $5$ which gives you $4/9$, which luckily arrives at the simplest form. But if you had a fraction like $36/48$ and simplified by only dividing by $2$, you would get $18/24$, where simplification is still possible.
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