4/5 divided by 2 in fraction form
The Correct Answer and Explanation is:
To divide two fractions, including a whole number (in this case, 2), you follow the rule of multiplying the first fraction by the reciprocal of the second number.
The problem is ( \frac{4}{5} \div 2 ).
Step-by-Step Solution:
- Convert the whole number into a fraction: Any whole number can be expressed as a fraction by putting it over 1. So, 2 becomes ( \frac{2}{1} ).
- Reciprocal of the second fraction: The reciprocal of a fraction is created by swapping its numerator and denominator. So, the reciprocal of ( \frac{2}{1} ) is ( \frac{1}{2} ).
- Multiply the first fraction by the reciprocal of the second:
[
\frac{4}{5} \times \frac{1}{2}
] - Multiply the numerators: Multiply the numerators of the two fractions:
[
4 \times 1 = 4
] - Multiply the denominators: Multiply the denominators of the two fractions:
[
5 \times 2 = 10
] - Final answer: The result is:
[
\frac{4}{10}
] - Simplify the fraction: To simplify ( \frac{4}{10} ), divide both the numerator and the denominator by their greatest common divisor, which is 2:
[
\frac{4 \div 2}{10 \div 2} = \frac{2}{5}
]
Therefore, ( \frac{4}{5} \div 2 = \frac{2}{5} ).
Explanation:
Dividing fractions involves a method known as multiplying by the reciprocal. Instead of dividing directly, you convert the division into multiplication by flipping the second fraction. This works because division is the inverse of multiplication, so when you multiply by the reciprocal, you’re essentially reversing the division operation.
In this case, ( \frac{4}{5} ) is multiplied by ( \frac{1}{2} ), which simplifies to ( \frac{2}{5} ). Simplifying fractions ensures that the answer is expressed in its lowest terms, making it easier to interpret and work with in future calculations.
This method is crucial in math, and it applies to many practical scenarios like dividing portions of a recipe, dividing time, or sharing resources equally among groups. Understanding how to manipulate fractions helps in everyday life and higher-level math concepts.