5/6 divided by 1/3 as a fraction
Understand the Problem
The question is asking us to divide the fraction 5/6 by the fraction 1/3. To solve this, we will multiply 5/6 by the reciprocal of 1/3, which is 3/1, and then simplify the resulting fraction if necessary.
Answer
The answer is \( \frac{5}{2} \).
Answer for screen readers
The final answer is ( \frac{5}{2} ).
Steps to Solve
-
Identify the fractions to divide
We are given the fractions ( \frac{5}{6} ) and ( \frac{1}{3} ). -
Find the reciprocal of the second fraction
The reciprocal of ( \frac{1}{3} ) is ( \frac{3}{1} ). -
Multiply the first fraction by the reciprocal
Now we multiply ( \frac{5}{6} ) by ( \frac{3}{1} ):
$$ \frac{5}{6} \times \frac{3}{1} $$ -
Perform the multiplication
To multiply fractions, multiply the numerators together and the denominators together:
$$ \frac{5 \times 3}{6 \times 1} $$
This simplifies to
$$ \frac{15}{6} $$ -
Simplify the resulting fraction
Now, simplify ( \frac{15}{6} ) by finding the greatest common divisor (GCD) of 15 and 6, which is 3. This gives:
$$ \frac{15 \div 3}{6 \div 3} = \frac{5}{2} $$
The final answer is ( \frac{5}{2} ).
More Information
When dividing fractions, multiplying by the reciprocal is a key step. The result, ( \frac{5}{2} ), is an improper fraction that can also be expressed as 2.5 in decimal form.
Tips
- A common mistake is to forget to take the reciprocal of the second fraction.
- Another mistake is multiplying the denominators and numerators incorrectly; ensure to keep track of which numbers are being multiplied together.
