Find the quotient of 9/10 and 2/3
A. 20/27
B. 30/18
C. 18/30
D. 27/20
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of 2/3 is 3/2.
So, 9/10 ÷ 2/3 = 9/10 * 3/2 = 27/20.
The quotient of 9/10 and 2/3 is 27/20.
Therefore, the correct answer is (D) 27/20.
To find the quotient of two fractions, we can multiply the first fraction by the reciprocal of the second fraction.
Reciprocal of a fraction is obtained by swapping the numerator and the denominator.
So, the reciprocal of 2/3 is 3/2.
Now, we can multiply 9/10 by 3/2.
(9/10) * (3/2) = (9 * 3) / (10 * 2) = 27/20
Therefore, the quotient of 9/10 and 2/3 is 27/20.
Therefore, the correct option is D. 27/20.
To find the quotient of two fractions, you need to divide the numerator of the first fraction by the numerator of the second fraction and divide the denominator of the first fraction by the denominator of the second fraction.
In this case, the first fraction is 9/10 and the second fraction is 2/3.
Dividing the numerators, we have 9 ÷ 2 = 4.5.
Dividing the denominators, we have 10 ÷ 3 = 3.33.
So the quotient of 9/10 and 2/3 is 4.5/3.33.
Let's simplify the fraction:
To simplify the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator.
The GCD of 4.5 and 3.33 is 0.01.
Dividing both the numerator and denominator by 0.01, we get:
4.5 ÷ 0.01 = 450
3.33 ÷ 0.01 = 333
So the simplified fraction is 450/333.
Now let's check which answer choice matches the simplified fraction:
A. 20/27
B. 30/18
C. 18/30
D. 27/20
Comparing the fraction 450/333 with the given answer choices:
A. 20/27 - The simplified fraction does not match.
B. 30/18 - The simplified fraction does not match.
C. 18/30 - The simplified fraction does not match.
D. 27/20 - The simplified fraction does not match.
None of the answer choices match the quotient of 9/10 and 2/3, which means none of the answer choices are correct.