Solve u + (4520 / 1200) = 0.01 for u, giving an exact answer.

Step-by-step solution

1. 1

   Reduce the division to lowest terms. Both $4520$ and $1200$ are divisible by $40$:

   $\frac{4520}{1200}=\frac{113}{30}$

   Since $113$ is prime and does not divide $30$, this is fully reduced — and it is $3.7\overline{6}$, a repeating decimal, which is why staying in fractions matters here.

2. 2

   Put the right-hand side in fraction form too. Mixing a fraction with a decimal invites rounding error, so write

   $0.01=\frac{1}{100}$

   and the equation becomes $u+\dfrac{113}{30}=\dfrac{1}{100}$.

3. 3

   Isolate $u$.

   $u=\frac{1}{100}-\frac{113}{30}$

4. 4

   Use the least common denominator. $\operatorname{lcm}(100,30)=300$, so

   $\frac{1}{100}=\frac{3}{300},\qquad \frac{113}{30}=\frac{1130}{300}$

   and

   $u=\frac{3-1130}{300}=-\frac{1127}{300}$

5. 5

   Report and check. $\gcd(1127,300)=1$, so the fraction is final; as a decimal $u=-3.75\overline{6}$. Adding back, $-\dfrac{1127}{300}+\dfrac{1130}{300}=\dfrac{3}{300}=0.01\ \checkmark$.