A ratio of 2:3 expressed as a fraction in its simplest form is
The Correct Answer and Explanation is:
The ratio 2:3 can be expressed as the fraction ( \frac{2}{3} ).
Explanation:
A ratio is a way of comparing two quantities, often expressed in the form “a:b,” where “a” and “b” are two numbers. When you have a ratio, it tells you how much of one quantity there is compared to another.
In this case, the ratio 2:3 tells you that for every 2 parts of one quantity, there are 3 parts of another quantity. This comparison can be represented as a fraction:
[
\frac{2}{3}
]
Here, 2 is the numerator (the part of the first quantity), and 3 is the denominator (the part of the second quantity). The fraction ( \frac{2}{3} ) is already in its simplest form because the greatest common divisor (GCD) of 2 and 3 is 1. The GCD is the largest number that divides both 2 and 3 without leaving a remainder. Since 2 and 3 do not share any common factors other than 1, the fraction is already in its simplest form.
Simplifying a Fraction:
To simplify a fraction, you divide both the numerator and the denominator by their greatest common divisor (GCD). If the numerator and denominator have a common factor greater than 1, you would divide both by that number to reduce the fraction to its simplest form. For example, if you had a ratio like 4:6, you would divide both by 2 (the GCD of 4 and 6) to get the simplified fraction ( \frac{2}{3} ).
Key Points:
- A ratio like 2:3 represents a relationship between two quantities.
- Expressing a ratio as a fraction is a common way to illustrate the comparison.
- The fraction ( \frac{2}{3} ) is already in its simplest form because 2 and 3 have no common divisors other than 1.
Therefore, the ratio 2:3 expressed as a fraction in its simplest form is ( \frac{2}{3} ).