1/3 divided by 5/6 as a fraction
Understand the Problem
The question is asking to find the result of the division of the fraction 1/3 by the fraction 5/6. To solve this, we need to multiply 1/3 by the reciprocal of 5/6, which is 6/5.
Answer
The final answer is \( \frac{2}{5} \).
Answer for screen readers
The final result of dividing ( \frac{1}{3} ) by ( \frac{5}{6} ) is ( \frac{2}{5} ).
Steps to Solve
- Identify the fractions to divide
We are given the fractions ( \frac{1}{3} ) and ( \frac{5}{6} ). We need to divide ( \frac{1}{3} ) by ( \frac{5}{6} ).
- Find the reciprocal of the second fraction
To divide by a fraction, we multiply by its reciprocal. The reciprocal of ( \frac{5}{6} ) is ( \frac{6}{5} ).
- Set up the multiplication of the fractions
Now we can rewrite the problem:
$$ \frac{1}{3} \div \frac{5}{6} = \frac{1}{3} \times \frac{6}{5} $$
- Multiply the fractions
Next, we perform the multiplication of the two fractions:
$$ \frac{1 \times 6}{3 \times 5} $$
- Calculate the numerator and the denominator
Calculating both gives us:
$$ \frac{6}{15} $$
- Simplify the fraction
Now we simplify ( \frac{6}{15} ). Both the numerator and the denominator can be divided by their greatest common divisor, which is 3:
$$ \frac{6 \div 3}{15 \div 3} = \frac{2}{5} $$
The final result of dividing ( \frac{1}{3} ) by ( \frac{5}{6} ) is ( \frac{2}{5} ).
More Information
When dividing fractions, multiplying by the reciprocal is a foundational concept in fraction operations. This method of simplifying operations is essential in arithmetic.
Tips
- Forgetting to use the reciprocal: Some may forget to switch to the reciprocal and just try to divide directly.
- Not simplifying the final result: Remembering to simplify the fraction is crucial after performing the multiplication.
