Question

If the numerator of a fraction is odd and the denominator of a fraction is even, can you write an equivalent fraction with a smaller numerator and denominator? Explain.

Answer 1

Answer:

Possible, depending on whether the numerator and the denominator share a common factor.

For example, the fraction $(3/6)$ is equivalent to $(1/2)$ where the numerator and denominator are both smaller.

Step-by-step explanation:

If the numerator and the denominator of a fraction are divisible with the same factor, the fraction can be simplified to have a smaller numerator and denominator.

In this question, it is given that the numerator is odd, while the denominator is even. In other words, the numerator is not divisible by $2$, but the denominator is. Hence, neither $2\!$ nor multiples of $\!\! 2$ can be the common divisor of the numerator and the denominator.

However, the numerator and the denominator might share some divisors that are not multiples of $2$. For example, consider an example where both the numerator and the denominator are divisible by $3$:

• Numerator: $3 = 1 \times 3$, which is odd as requested.
• Denominator: $6 = 2 \times 3$, which is even as requested.

The resulting fraction $(3 / 6)$ can be simplified as $(1/2)$.