Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
start fraction, 2, divided by, 3, end fraction, divided by, start fraction, 6, divided by, 7, end fraction
3
2
÷
7
6
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
The reciprocal of a fraction is obtained by swapping the numerator and denominator.
So, the reciprocal of the second fraction is start fraction 7, divided by 6, end fraction.
Now, we can multiply the two fractions:
start fraction 2, divided by 3, end fraction × start fraction 7, divided by 6, end fraction
= (2/3) × (7/6)
To simplify this expression, we can cancel common factors.
The numerator 2 has no common factors with the denominator 6, so it remains the same.
The numerator 7 has no common factors with the denominator 3, so it remains the same.
Therefore, the simplified fraction is:
start fraction 2, divided by 3, end fraction × start fraction 7, divided by 6, end fraction = (2/3) × (7/6) = 14/18
The simplified answer is start fraction 14, divided by 18, end fraction.
To simplify the expression
(2/3) ÷ (6/7),
we first invert and multiply:
(2/3) * (7/6).
Next, we multiply the numerators (2 * 7 = 14) and the denominators (3 * 6 = 18) together:
14/18.
To simplify this fraction further, we find the greatest common divisor (GCD) of the numerator and denominator, which in this case is 2. We divide both the numerator and denominator by 2:
14/18 = 7/9.
Therefore, the simplified fraction is 7/9.
what is the answer
The answer is 7/9.
To perform the given operation and reduce the answer fully, we can follow these steps:
Step 1: Divide the numerator of the first fraction (2) by the denominator of the second fraction (7):
2 ÷ 7 = 2/7
Step 2: Divide the numerator of the second fraction (3) by the denominator of the first fraction (6):
3 ÷ 6 = 1/2
Step 3: Divide the result from step 1 by the result from step 2:
(2/7) ÷ (1/2)
To divide fractions, we need to multiply the first fraction by the reciprocal of the second fraction:
(2/7) x (2/1)
Step 4: Multiply the numerators and denominators:
(2 x 2) / (7 x 1) = 4/7
So, the answer to the given operation, expressed as a simplified fraction, is 4/7.