Question

Solve 10 over 8=n over 10

Answer 1

10/8 = n/10

First, we need to simplify 10/8 into the lowest terms it can go down into. To do so, we need to find the greatest common factor (GCF) of both the numerator and denominator (10 and 8).

Factors of 10: 1, 2, 5, 10
Factors of 8: 1, 2, 4, 8

Looking at the listed factors above for our two numbers, we can see that the greatest common factor is 2. The GCF is 2.

Second, our next step for simplifying 10/8 down is to divide the numerator (10) and denominator (8) by our GCF we recently found which was 2.

$10 \div 2 = 5 \\ 8 \div 2 = 4$

We can now rewrite our fraction in the simplified form which is 5/4.

Third, our goal from the start is to get the variable (n) to one side of the problem by itself. This means we have to do everything else on the other side of the problem. We can start out by multiplying each side by 10.
$\frac{5}{4} \times 10 = n$

Fourth, we now need to simplify 5/4 times 10. To do this, we take the numerator and multiply it by 10. Since the numerator is 5, our problem should look like: 5 × 10. The answer is 50.
$\frac{50}{4} = n$

Fifth, since 50/4 can be simplified as well into lower terms. Let's do the same thing we did earlier when we simplified the earlier fraction. List the factors of the numerator (50) and denominator (4). 

Factors of 50: 1, 2, 5, 10, 25, 50
Factors of 4: 1, 2, 4

Out of the factors for both of the numbers, which are common? 1 and 2 are the common factors and 2 is the greatest, meaning that 2 is our GCF.

Sixth, like we did earlier as well, we now have to divide our numerator and denominator by our recently found GCF which is 2.

$50 \div 2 = 25 \\ 4 \div 2 = 2$

We now have our simplified fraction, which is also our answer. The simplified fraction is 25/2.

Answer in fraction form: $\fbox {n = 25/2}$
Answer in decimal form: $\fbox {x = 12.5}$