What fraction is equivalent to 4/10
The Correct Answer and Explanation is:
The fraction 4/10 can be simplified by dividing both the numerator (4) and the denominator (10) by their greatest common divisor (GCD).
Step 1: Find the greatest common divisor (GCD)
The GCD of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCD of 4 and 10, we list their divisors:
- Divisors of 4: 1, 2, 4
- Divisors of 10: 1, 2, 5, 10
The greatest number common to both lists is 2, so the GCD of 4 and 10 is 2.
Step 2: Simplify the fraction
To simplify the fraction 4/10, we divide both the numerator and the denominator by their GCD (which is 2):
[
\frac{4}{10} = \frac{4 \div 2}{10 \div 2} = \frac{2}{5}
]
So, the fraction 4/10 is equivalent to 2/5.
Step 3: Verify the result
We can verify this by converting both fractions into decimal form.
- 4/10 = 0.4
- 2/5 = 0.4
Since both fractions yield the same decimal value, we can confirm that 4/10 is indeed equivalent to 2/5.
Step 4: General Concept of Simplification
In general, simplifying a fraction involves dividing both the numerator and denominator by their greatest common divisor (GCD). This process ensures that the fraction is in its simplest form. In this case, 4/10 simplifies to 2/5 because 4 and 10 have a GCD of 2.
By understanding how to simplify fractions, you can easily reduce any fraction to its simplest form, which makes it easier to work with in mathematical operations such as addition, subtraction, multiplication, and division.