Understanding Fractions: Simplifying 7/8
What is a Fraction?
A fraction is a way to express a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). The numerator tells us how many equal parts we have, and the denominator tells us how many parts the whole is divided into.
Simplifying a Fraction
Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator have no common factors other than 1. This is also known as finding the equivalent fraction.
How to Simplify a Fraction
To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD is the largest number that divides both numbers without leaving a remainder.
The Greatest Common Divisor (GCD)
The GCD of two numbers can be found using the Euclidean algorithm or by listing the factors of each number. In this case, we need to find the GCD of 7 and 8.
Factors of 7 and 8
The factors of 7 are 1 and 7. The factors of 8 are 1, 2, 4, and 8.
Find the Greatest Common Divisor
The greatest common divisor of 7 and 8 is 1, since 1 is the only common factor.
Simplifying 7/8
Since the GCD of 7 and 8 is 1, the fraction 7/8 is already in its simplest form. Therefore, the simplified fraction is still 7/8.
Conclusion
In conclusion, simplifying a fraction involves finding the greatest common divisor of the numerator and denominator. In the case of 7/8, the GCD is 1, which means the fraction is already in its simplest form. Therefore, the simplified fraction is still 7/8.
What is a fraction?
+A fraction is a way to express a part of a whole as a ratio of two numbers.
How do I simplify a fraction?
+To simplify a fraction, find the greatest common divisor of the numerator and denominator, and divide both numbers by the GCD.
What is the greatest common divisor?
+The greatest common divisor is the largest number that divides both numbers without leaving a remainder.