7 1/2 x 2/3 as a Fraction
To evaluate the expression 7 1/2 × 2/3, we need to follow the order of operations (PEMDAS) and multiply the two fractions. But before we do that, let's convert the mixed number 7 1/2 to an improper fraction.
Converting the Mixed Number to an Improper Fraction
The mixed number 7 1/2 can be written as:
7 1/2 = (7 × 2) + 1 / 2 = 14 + 1 / 2 = 15 / 2
So, the improper fraction equivalent to 7 1/2 is 15/2.
Multiplying the Fractions
Now that we have the improper fraction, we can multiply it with 2/3:
(15/2) × (2/3) = (15 × 2) / (2 × 3) = 30 / 6
Simplifying the Fraction
The resulting fraction 30/6 can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 30 and 6 is 6, so we can divide both numbers by 6:
30 ÷ 6 = 5 6 ÷ 6 = 1
Therefore, the simplified fraction is:
30/6 = 5/1
Final Answer
So, 7 1/2 × 2/3 as a fraction is equal to:
7 1/2 × 2/3 = 15/2 × 2/3 = 30/6 = 5/1 = 5
