Question

Reduce the fractions. 60/90 and 27/45. PLZ help me and send work

Answer 1

60/90 = 2/3

27/45 = 3/5

Answer 2

Remember that to reduce fractions, you want to find common terms in the numerator and the denominator.

First, let's look at $\frac{60}{90}$. Let's find all the factors of the numerator and the denominator (you can do this by continuously dividing the numerator/denominator until you get to a prime number, where you can't divide any more)

$\dfrac{60}{90} = \dfrac{2 \cdot 30}{2 \cdot 45} = \dfrac{2 \cdot 3 \cdot 10}{2 \cdot 3 \cdot 15} = \dfrac{2 \cdot 3 \cdot 5 \cdot 2}{2 \cdot 3 \cdot 5 \cdot 3} = \dfrac{2^2 \cdot 3 \cdot 5}{2 \cdot 3^2 \cdot 5}$

We can see that both the numerator and the denominator have factors of 2, 3, and 5. Thus, let's divide both the numerator and denominator by these numbers (you can multiply them together first or just divide each one one-by-one).

$\dfrac{60}{90} = \dfrac{\frac{60}{2 \cdot 3 \cdot 5}}{\frac{90}{2 \cdot 3 \cdot 5}} = \dfrac{2}{3}$

Now, let's look at $\frac{27}{45}$. It's the same process as the fraction above, so I am going to complete it without explanation.

$\dfrac{27}{45} = \dfrac{3 \cdot 9}{3 \cdot 15} = \dfrac{3 \cdot 3 \cdot 3}{3 \cdot 3 \cdot 5} = \dfrac{3^3}{3^2 \cdot 5}$

We can see that both the numerator and denominator have a factor of $3^2$.

$\dfrac{27}{45} = \dfrac{\frac{27}{3^2}}{\frac{45}{3^2}} = \dfrac{3}{5}$

Our answers are 2/3 and 3/5, respectively.