3 1/2 times 6 1/2 as a Fraction
To evaluate the expression 3 1/2 times 6 1/2, we need to follow the order of operations (PEMDAS) and convert the mixed numbers to improper fractions.
Converting Mixed Numbers to Improper Fractions
3 1/2 as an Improper Fraction
3 1/2 can be written as an improper fraction by multiplying the whole number part (3) by the denominator (2) and then adding the numerator (1):
3 1/2 = (3 × 2) + 1 / 2 = 7 / 2
6 1/2 as an Improper Fraction
6 1/2 can be written as an improper fraction by multiplying the whole number part (6) by the denominator (2) and then adding the numerator (1):
6 1/2 = (6 × 2) + 1 / 2 = 13 / 2
Multiplying the Fractions
Now that we have the improper fractions, we can multiply them:
(7 / 2) × (13 / 2) = ?
To multiply fractions, we multiply the numerators and multiply the denominators:
(7 × 13) / (2 × 2) = 91 / 4
Simplifying the Fraction
The resulting fraction can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 91 and 4 is 1, so the fraction is already in its simplest form:
91 / 4
Therefore, 3 1/2 times 6 1/2 as a fraction is 91 / 4.
