Reduce this fraction to its simplest form: [tex]$\frac{6}{18}=?$\[/tex]
Answer (2)
Find the greatest common divisor (GCD) of 6 and 18, which is 6.
Divide both the numerator and the denominator by the GCD: 18 ÷ 6 6 ÷ 6 .
Simplify the fraction: 3 1 .
The simplest form of the fraction is 3 1 .
Explanation
Problem Analysis We are asked to reduce the fraction 18 6 to its simplest form. This means we need to find a fraction that is equivalent to 18 6 but has the smallest possible numerator and denominator. To do this, we need to find the greatest common divisor (GCD) of the numerator and the denominator.
Finding the Greatest Common Divisor The greatest common divisor (GCD) of two numbers is the largest number that divides both of them without leaving a remainder. In this case, we need to find the GCD of 6 and 18. The GCD of 6 and 18 is 6, since 6 divides both 6 and 18.
Simplifying the Fraction Now we divide both the numerator and the denominator by their GCD, which is 6. 18 ÷ 6 6 ÷ 6 = 3 1 So, the simplified fraction is 3 1 .
Final Answer Therefore, the simplest form of the fraction 18 6 is 3 1 .
Examples
Imagine you have 6 slices of pizza and want to share them equally among 18 people. The fraction 18 6 represents this situation. Simplifying the fraction to 3 1 tells you that each person gets the equivalent of one-third of a pizza slice. This concept of simplifying fractions is useful in everyday situations where you need to divide quantities or understand proportions, such as sharing food, measuring ingredients for a recipe, or understanding discounts at a store.
The simplest form of the fraction 18 6 is 3 1 after dividing both the numerator and numerator by their greatest common divisor, which is 6. This process highlights how to reduce fractions to their most basic form. Understanding how to simplify fractions is an essential skill in mathematics.
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