In a fraction word problem, the denominator of a fraction is 3 more than its numerator. If both the numerator and the denominator are increased by 4, the value of the fraction becomes 4/5. What was the original fraction before this change?

Introduction:This question tests basic algebra with fractions and focuses on how changing numerator and denominator together affects the value of the fraction. You are given a relationship between the numerator and denominator, and then a new fraction formed after both parts are increased by the same amount. The aim is to form a simple equation in one variable and solve it to recover the original fraction.

Given Data / Assumptions:

• Let the original numerator be n.
• The denominator is 3 more than the numerator, so denominator = n + 3.
• Both numerator and denominator are increased by 4.
• The new fraction after this increase is 4/5.
• We must find the original fraction n/(n + 3).

Concept / Approach:Convert the description into an algebraic equation. After increasing numerator and denominator by the same number, we obtain a new fraction. Set this equal to 4/5 and solve for the unknown numerator. Once n is known, substitute back to get the denominator and hence the original fraction.

Step-by-Step Solution:Let original fraction = n/(n + 3).After increasing both by 4, new fraction = (n + 4)/(n + 3 + 4) = (n + 4)/(n + 7).Given (n + 4)/(n + 7) = 4/5.Cross-multiply: 5(n + 4) = 4(n + 7).5n + 20 = 4n + 28.5n - 4n = 28 - 20 => n = 8.Denominator = n + 3 = 8 + 3 = 11.Original fraction = 8/11.

Verification / Alternative check:If the original fraction is 8/11, then increasing numerator and denominator by 4 gives 12/15. Now 12/15 simplifies to 4/5, which matches the condition in the problem. So the solution is consistent.

Why Other Options Are Wrong:7/11: After adding 4 to numerator and denominator we get 11/15, which is not 4/5.9/11: Leads to 13/15, still not equal to 4/5.5/8 and 3/7: Their transformed fractions do not simplify to 4/5 and do not satisfy the relation “denominator is 3 more than numerator”.

Common Pitfalls:Forgetting that the denominator is 3 more than the numerator and instead assuming some random values.Adding 4 only to the numerator or only to the denominator, instead of both.Not simplifying or checking the resulting fraction after solving the equation.

Final Answer:8/11