Write the fraction 81/72 in simplest form.
Understand the Problem
The question asks to simplify the fraction 81/72 into its simplest form. This involves finding the greatest common divisor (GCD) of 81 and 72 and dividing both the numerator and the denominator by the GCD to reduce the fraction.
Answer
$\frac{9}{8}$
Answer for screen readers
$\frac{9}{8}$
Steps to Solve
- Find the prime factorization of 81 and 72
To simplify the fraction, we first need to find the prime factors of the numerator (81) and the denominator (72).
Prime factorization of 81: $81 = 3 \times 3 \times 3 \times 3 = 3^4$
Prime factorization of 72: $72 = 2 \times 2 \times 2 \times 3 \times 3 = 2^3 \times 3^2$
- Identify the greatest common divisor (GCD)
The greatest common divisor (GCD) is the largest number that divides both 81 and 72 without leaving a remainder. We can find it by identifying the common prime factors and their lowest powers.
Common prime factor: 3
Lowest power of 3 in both factorizations: $3^2 = 9$ So, the GCD of 81 and 72 is 9.
- Divide both the numerator and the denominator by the GCD
Now, divide both the numerator (81) and the denominator (72) by their GCD, which is 9.
New numerator: $81 \div 9 = 9$ New denominator: $72 \div 9 = 8$
- Write the simplified fraction
Therefore, the simplified fraction is $\frac{9}{8}$.
$\frac{9}{8}$
More Information
The fraction $\frac{81}{72}$ simplifies to $\frac{9}{8}$. Since the numerator is greater than the denominator, this is an improper fraction. It can be expressed as a mixed number: $1\frac{1}{8}$.
Tips
A common mistake is to stop simplifying the fraction before it is in its simplest form. For example, one might divide both 81 and 72 by 3 to get $\frac {27}{24}$, but then forget to divide by 3 again. Always make sure that there are no common factors between the numerator and denominator other than 1.
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