### Instruction: Simplify $\frac{91}{26}.$.### Response: To simplify a fraction, I need to find the greatest common factor of the numerator and denominator and divide both by it.
A common factor is a number that divides evenly into both the numerator and denominator.
To find the greatest common factor, I can use the prime factorization method, which means breaking down both numbers into products of prime factors.
A prime number is a number that has only two factors: itself and 1.
The prime factorization of 91 is 7 times 13, since both 7 and 13 are prime.
The prime factorization of 26 is 2 times 13, since both 2 and 13 are prime.
Now I can write the fraction as a product of prime factors: $\frac{91}{26} = \frac{7 \times 13}{2 \times 13}.$
I can see that 13 is a common factor of both the numerator and denominator, so I can divide both by 13.
This gives me $\frac{7}{2}.$
This is the simplest form of the fraction, since 7 and 2 have no common factors other than 1.
I can also write this as a mixed number, which means a whole number plus a fraction.
To do that, I need to divide 7 by 2 and write the quotient as the whole number and the remainder as the numerator of the fraction.
7 divided by 2 is 3 with a remainder of 1, so I can write $\frac{7}{2} = 3 \frac{1}{2}.$