4/5 divided by 2
How to Divide Fractions: What is 4/5 divided by 2?
To divide the fraction \frac{4}{5} by 2, follow these detailed steps:
Step 1: Understand Division of Fractions
When you divide a fraction by a whole number, you can convert the whole number to a fraction by expressing it as a fraction over 1. So, dividing by 2 is the same as dividing by \frac{2}{1}.
Step 2: Apply the Multiplicative Inverse
The division of fractions can be performed using the multiplicative inverse (or reciprocal) of the second fraction. The multiplicative inverse of \frac{2}{1} is \frac{1}{2}.
Step 3: Convert the Division into Multiplication
Instead of dividing by \frac{2}{1}, multiply by its reciprocal \frac{1}{2}:
\frac{4}{5} \div \frac{2}{1} = \frac{4}{5} \times \frac{1}{2}
Step 4: Multiply the Fractions
To multiply fractions, multiply the numerators together and the denominators together:
\frac{4}{5} \times \frac{1}{2} = \frac{4 \times 1}{5 \times 2} = \frac{4}{10}
Step 5: Simplify the Resulting Fraction
Next, simplify the fraction \frac{4}{10}. The greatest common divisor (GCD) of 4 and 10 is 2. Divide both the numerator and the denominator by 2:
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
Final Answer:
So, \frac{4}{5} \div 2 simplifies to \frac{2}{5}.
Thus, \boxed{\frac{2}{5}} is the simplified result.