Question

Algebra Help! I appreciate any assistance.

Answer 1

Hello!

Given the integer in form of fraction, we should know the denominator. We know the denominator n is 3^x * 5^y.

We should know the greatest divisor of 90.

You have to prime factorize 90.

90|2
45|3
15|3
5|5
1

So 90 = 2 × 3^2 × 5^1

We take the greatest numbers with highest exponents.

That means 3^2 × 5 = 45 <- answer

Answer 2

90 = 2 · 3 · 3 · 5 = 2 · 3² · 5¹

If n has the form  $3^x5^y$  and  $\frac{90}{n}$  is an integer, then greatest possible value of n = 3² · 5¹ = 45