What is the simplified form of the fraction below?
14/49
The Correct Answer and Explanation is:
The simplified form of the fraction 14/49 is 2/7.
Explanation:
To simplify a fraction, you divide both the numerator (top number) and the denominator (bottom number) by their greatest common divisor (GCD). The GCD is the largest number that divides both numbers evenly, without leaving a remainder.
Step 1: Identify the numerator and denominator
In the fraction 14/49:
- The numerator is 14.
- The denominator is 49.
Step 2: Find the greatest common divisor (GCD)
To find the GCD of 14 and 49, you need to look for the largest number that divides both of them evenly. The easiest way to find the GCD is by listing the factors of both numbers and finding the largest one they have in common.
- Factors of 14: 1, 2, 7, 14
- Factors of 49: 1, 7, 49
From these lists, you can see that the largest common factor is 7.
Step 3: Divide both the numerator and denominator by the GCD
Now, divide both 14 (the numerator) and 49 (the denominator) by their GCD, which is 7.
- ( \frac{14}{7} = 2 )
- ( \frac{49}{7} = 7 )
So, the simplified fraction is 2/7.
Step 4: Verify the result
To ensure that 2/7 is correct, you can reverse the simplification process. Multiply both the numerator and denominator by 7:
- ( 2 \times 7 = 14 )
- ( 7 \times 7 = 49 )
This brings you back to the original fraction, 14/49, confirming that 2/7 is indeed the correct simplified form.
Importance of Simplification:
Simplifying fractions makes them easier to work with, especially in calculations or comparisons. It reduces complexity and presents the fraction in its most basic form, allowing you to better understand the ratio between the two numbers.