What's $15 / 45$ written as a fraction in simplest form?
A) $1 / 3$
B) $15 / 3$
C) $3 / 15$
D) $5 / 3$
Answer (1)
Find the greatest common divisor (GCD) of 15 and 45, which is 15.
Divide both the numerator and the denominator by the GCD: 45 ÷ 15 15 ÷ 15 .
Simplify the fraction: 3 1 .
The simplest form of 45 15 is 3 1 .
Explanation
Understanding the Problem We are asked to simplify the fraction 45 15 to its simplest form. This means we need to find the greatest common divisor (GCD) of the numerator (15) and the denominator (45) and then divide both by that GCD.
Finding the Greatest Common Divisor (GCD) To find the GCD of 15 and 45, we can use the Euclidean algorithm or simply recognize that 15 divides 45. Since 45 = 15 × 3 , the GCD of 15 and 45 is 15.
Simplifying the Fraction Now, we divide both the numerator and the denominator by their GCD, which is 15: 45 15 = 45 ÷ 15 15 ÷ 15 = 3 1
Final Answer The simplified fraction is 3 1 , which corresponds to option A.
Examples
Imagine you're baking a cake and the recipe calls for 45 15 of a cup of sugar. To make it easier to measure, you simplify the fraction to 3 1 of a cup. This way, you're using the same proportion of sugar but with a simpler measurement, making your baking process more straightforward and less prone to errors. Simplifying fractions is a practical skill that helps in everyday situations where proportions and ratios are involved.
