Question

I'm trying to solve the problem shown in the picture above

If you could solve this, and explain how you got your answer, step by step

So I can learn how to do this on my own

I was able to get to
1 1
_ _
3 • 5 = 15

At first, I got 1/17 but that's incorrect

Extra help for a thorough explanation

Answer 1

`2(1)/(15)`

Explanation:

Problem:
`(1)/(3*5) +2`

First lets solve, 3 × 5 = 15

We have solved the denominator. Making a new fraction:
`(1)/(15)` + 2

=
`2(1)/(15)`

Thus,
`2(1)/(15)` is the answer.

Answer 2

`(31)/(15)`

Explanation:

Given expression:

`(1)/(3 \cdot 5)+2`

To evaluate the given expression, first carry out the multiplication in the denominator of the fraction. As 3 × 5 = 15, then:

`(1)/(15)+2`

Now, we need to convert the whole number into a fraction with the same denominator as the first fraction.

To do this, we multiply the whole number (2) by the desired denominator (15) and place the result over the denominator (15):

`(1)/(15)+(2 \cdot 15)/(15)`

Carry out the multiplication in the numerator:

`(1)/(15)+(30)/(15)`

When adding fractions with the same denominator, we simply add the numerators:

`(1+30)/(15)`

Carry out the addition in the numerator:

`(31)/(15)`

As 31 is a prime number (meaning that its only factors are one and itself), the fraction 31/15 cannot be simplified any further.

Therefore, the evaluation of the given expression is:

`(1)/(3 \cdot 5)+2=\boxed{(31)/(15)}`

`\hrulefill`

As one calculation:

`\begin{aligned}(1)/(3 \cdot 5)+2&=(1)/(15)+2\\\\&=(1)/(15)+(2 \cdot 15)/(15)\\\\&=(1)/(15)+(30)/(15)\\\\&=(1+30)/(15)\\\\&=(31)/(15)\end{aligned}`