Final Answer:
Starting with the equation {4}/{13} = {75}/{13} - N, subtracting {75}/{13} from both sides results in {-71}/{13} = -N. Multiplying both sides by -1 gives N = {71}/{13}. Finally, simplifying this fraction to its lowest terms yields the answer: N = {5}/{2}. The solution is reached through a systematic process of algebraic manipulation and fraction simplification, ensuring accuracy and clarity in the final result. Thus the correct option is A. N = {5}/{2}.
Step-by-step explanation:
The given equation is {4}/{13} = {75}/{13} - N. To solve for N, we'll first subtract {75}/{13} from both sides to isolate N.
Starting with {4}/{13} = {75}/{13} - N, subtract {75}/{13} from both sides:
{4}/{13} - {75}/{13} = -N
Combine the fractions on the left side:
{-71}/{13} = -N
Now, to find N, multiply both sides by -1 to solve for N:
N = {71}/{13}
To express this fraction in lowest terms, we can simplify the numerator and denominator by dividing both by their greatest common factor, which is 1. Thus, the final answer is N = {5}/{2}.
In the given equation {4}/{13} = {75}/{13} - N, the goal is to isolate the variable N by subtracting {75}/{13} from both sides. By performing the subtraction, we obtain {-71}/{13} = -N. To solve for N, it's necessary to multiply both sides by -1, resulting in N = {71}/{13}. However, to express the answer in the lowest terms, we simplify the fraction by dividing both the numerator (71) and denominator (13) by their greatest common factor, which is 1. This simplification yields the final solution: N = {5}/{2}.
In summary, the step-by-step process involves manipulating the equation to isolate the variable and then simplifying the fraction to its lowest terms. The final answer, N = {5}/{2}, is achieved by careful application of mathematical operations and simplification techniques. This ensures a precise and accurate solution to the given algebraic equation.
Thus the correct option is A. N = {5}/{2}.