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:

Yes, she is correct.

Step-by-step explanation:

Given equation,

$-5\frac{1}{8}n = -9\frac{3}{4}$

$(-5-\frac{1}{8})n=-9-\frac{3}{4}$

$\frac{(-40-1)n}{8}=\frac{-36-3}{4}$

$-\frac{41}{8}n =-\frac{39}{4}$

$-41\times 4n = -39\times 8$

$\implies n =\frac{39\times 2}{41}=\frac{78}{41}=1\frac{37}{41}$

By estimation :

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

⇒ $-5\frac{1}{8}\approx -5$

And, $-9\frac{3}{4}\approx -10$

$-5n = -10\implies n =\frac{-10}{-5}=2$

Since, $1\frac{37}{41}$ is near to 2.

Hence, she is correct.