Divide and express the answer in simplest form:
6 2/3
divided by
4 1/2
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To divide the mixed numbers and express the answer in simplest form, follow these steps:
Step 1: Convert the mixed numbers into improper fractions.
The mixed number "6 2/3" can be converted to an improper fraction as follows:
6 2/3 = (6 x 3 + 2) / 3 = 20/3
Similarly, the mixed number "4 1/2" can be converted to an improper fraction as follows:
4 1/2 = (4 x 2 + 1) / 2 = 9/2
Step 2: Divide the two fractions.
Dividing fractions is as simple as multiplying the first fraction by the reciprocal of the second fraction. Therefore, we can divide 20/3 by 9/2 by multiplying 20/3 by 2/9:
(20/3) * (2/9) = (20 * 2) / (3 * 9) = 40/27
Step 3: Simplify the resulting fraction.
To simplify the fraction 40/27, find the greatest common divisor (GCD) of both the numerator and denominator. The GCD of 40 and 27 is 1. Divide both the numerator and denominator by 1:
40/27 ÷ 1/1 = 40/27
Since there is no common factor between 40 and 27 other than 1, the fraction 40/27 is already in simplest form.
Therefore, the quotient of 6 2/3 divided by 4 1/2 is 40/27.