Question

Maria solved the equation -5 1/8 n = -9 3/4. Here answer was n = 1 37/41. She is fairly confindent about her answer, but wants to do a quick check of her solution using estimation.

Answer 1

Answer: -5(2) = -10

Explanation:

You wanted a rounded answer so just round the numbers and simplify

Hope this helps!

Answer 2

Yes, she is correct.

Explanation:

Given equation,

`-5(1)/(8)n = -9(3)/(4)`

`(-5-(1)/(8))n=-9-(3)/(4)`

`((-40-1)n)/(8)=(-36-3)/(4)`

`-(41)/(8)n =-(39)/(4)`

`-41* 4n = -39* 8`

`\implies n =(39* 2)/(41)=(78)/(41)=1(37)/(41)`

By estimation :

Since, 1/8 = 0.125 ≈ 0, while, 3/4 = 0.75 ≈ 1

⇒
`-5(1)/(8)\approx -5`

And,
`-9(3)/(4)\approx -10`

`-5n = -10\implies n =(-10)/(-5)=2`

Since,
`1(37)/(41)` is near to 2.

Hence, she is correct.