Find the quotient. 5/6 divided by 1/6
The Correct Answer and Explanation is:
To solve 56÷16\frac{5}{6} \div \frac{1}{6}65÷61, follow these steps:
Step 1: Rewrite the division as multiplication
Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of 16\frac{1}{6}61 is 61\frac{6}{1}16. So, the expression becomes:56÷16=56×61\frac{5}{6} \div \frac{1}{6} = \frac{5}{6} \times \frac{6}{1}65÷61=65×16
Step 2: Multiply the fractions
Now, multiply the numerators and denominators. The numerators are 5×6=305 \times 6 = 305×6=30, and the denominators are 6×1=66 \times 1 = 66×1=6. So, the result is:56×61=306\frac{5}{6} \times \frac{6}{1} = \frac{30}{6}65×16=630
Step 3: Simplify the fraction
Now, simplify the fraction 306\frac{30}{6}630. Divide the numerator (30) by the denominator (6):306=5\frac{30}{6} = 5630=5
Final Answer:
So, 56÷16=5\frac{5}{6} \div \frac{1}{6} = 565÷61=5.
Explanation:
When you divide one fraction by another, you multiply the first fraction by the reciprocal of the second fraction. In this case, since the divisor is 16\frac{1}{6}61, we multiply by 61\frac{6}{1}16, which is just 6. The multiplication of 56\frac{5}{6}65 by 6 simplifies directly to 5, because the 6 in the numerator and denominator cancel out. Thus, the quotient of 56÷16\frac{5}{6} \div \frac{1}{6}65÷61 is 5.
