4/5 divided by 2/5
Understand the Problem
The question is asking us to perform a division operation between two fractions, 4/5 and 2/5. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
Answer
2
Answer for screen readers
The final answer is 2
Steps to Solve
- Reciprocal of the second fraction
To divide fractions, we first find the reciprocal of the second fraction. The reciprocal of ( \frac{2}{5} ) is ( \frac{5}{2} ).
- Multiplication of fractions
Now, multiply the first fraction by the reciprocal of the second fraction:
$$ \frac{4}{5} \times \frac{5}{2} $$
- Simplify the multiplication
Multiply the numerators and the denominators:
$$ \frac{4 \times 5}{5 \times 2} = \frac{20}{10} $$
- Simplify the result
Simplify the fraction ( \frac{20}{10} ) by dividing both the numerator and the denominator by their greatest common divisor:
$$ \frac{20}{10} = 2 $$
The final answer is 2
More Information
Division of fractions is often simplified by multiplying by the reciprocal. This approach maintains the equivalence of the mathematical operation and simplifies the problem.
Tips
A common mistake is to multiply the fractions directly without taking the reciprocal of the second fraction. Always remember to flip the second fraction before multiplying.