Question

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

Please explain thoroughly on how I can solve this myself, please show the explanation, step by step, without a calculator
So I know how to solve it on my own from now on

I was able solve the exponent 3^2 to get to
5 - 9/2

How do I further complete this?
I'm not sure how to calculate the difference of 5 - 9/2

Answer 1

`(1)/(2)`

Explanation:

Given expression:

`5 - (3^2)/(2)`

To evaluate the given expression, first, we need to convert the whole number into a fraction with the same denominator as the fraction 3²/2.

To do this, we multiply 5 by the desired denominator (2) and place the result over 2:

`(5 * 2)/(2) - (3^2)/(2)`

`(10)/(2) - (3^2)/(2)`

When subtracting fractions with the same denominator, we simply subtract the numerators:

`(10 - 3^2)/(2)`

Now, we can evaluate 3². The exponent indicates how many times to multiply the base by itself. So, 3² = 3 × 3 = 9.

Therefore:

`(10 - 9)/(2)`

Finally, we perform 10 - 9 in the numerator:

`(1)/(2)`

Therefore, the evaluation of the given expression is:

`5 - (3^2)/(2) = \boxed{(1)/(2)}`

`\hrulefill`

As one calculation:

`\begin{aligned}5 - (3^2)/(2)&=(5 * 2)/(2) - (3^2)/(2)\\\\&=(10)/(2) - (3^2)/(2)\\\\&=(10 - 3^2)/(2)\\\\&=(10 - 9)/(2)\\\\&=(1)/(2)\end{aligned}`