Write the fraction 28/40 in simplest form.
The Correct Answer and Explanation is :
To simplify the fraction 28/40, we need to find the greatest common divisor (GCD) of both the numerator (28) and the denominator (40) and divide both by that number.
- The prime factorization of 28 is:
- 28 = 2 × 2 × 7
- The prime factorization of 40 is:
- 40 = 2 × 2 × 2 × 5
Now, identify the common factors. Both 28 and 40 share two factors of 2. So, the GCD is 2 × 2 = 4.
Next, divide both the numerator and denominator by 4:
- ( \frac{28}{4} = 7 )
- ( \frac{40}{4} = 10 )
So, the simplest form of 28/40 is 7/10.
Explanation (300 words):
Simplifying fractions is about reducing them to their lowest terms by removing common factors in the numerator and denominator. Fractions represent a part of a whole, and simplifying helps to express that part in its most concise and clear form.
To begin, we look at the fraction 28/40. This means 28 parts of something that is divided into 40 equal parts. However, we want to see if we can express this ratio using smaller numbers while keeping the same value. This is done by finding a common factor shared by both 28 and 40.
The method involves prime factorization. Prime numbers are those that have no divisors other than 1 and themselves (like 2, 3, 5, 7, 11, etc.). By breaking 28 and 40 into their prime components, we find that 28 is 2 × 2 × 7, and 40 is 2 × 2 × 2 × 5. Both 28 and 40 share two factors of 2, which means the greatest common divisor (GCD) is 4.
By dividing both the numerator (28) and denominator (40) by this GCD, we reduce the fraction to 7/10. This simplified fraction represents the same value as 28/40 but in a more efficient and easily understandable way.