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Percentage problems are all about understanding how a part relates to a whole in terms of 100. The concept is widely used in everyday situations, such as finding discounts, calculating interest rates, and determining growth rates. In this specific exercise, we need to find a number that, when 30% is taken, equals 14. Understanding the wording of the problem is crucial. We often represent the percentage as a decimal when we set up our equations. For example, 30% becomes 0.30. This transformation makes the math more straightforward. You'll often use the formula: part = (percentage as a decimal) * whole. To find the whole, you rearrange the formula to: whole = part ÷ (percentage as a decimal), which is exactly what we did in this problem.

Algebraic equations help us represent problems symbolically and solve for unknowns. In this problem, the unknown we need to find is the number, which we call x. Setting up the equation correctly is an important step. We use the information given—14 is 30% of x—and translate it into an equation: 14 = 0.30x. This equation represents the relationship between 14 (the part) and our unknown x (the whole) through the percentage 0.30. Solving this equation involves isolating the unknown variable, x, on one side of the equation. This is done through algebraic manipulation, which often includes operations like addition, subtraction, multiplication, and division.

Division in algebra is a method used to solve equations where the variable is multiplied by a coefficient. In our problem, to isolate x on one side of the equation from 14 = 0.30x, we need to divide both sides by 0.30. This operation gives us: \ \[x = \frac{14}{0.30} \]. The division operation simplifies the equation and isolates the variable, x. Make sure to perform the division accurately to get the correct value. In our exercise, dividing 14 by 0.30 yields approximately 46.67. Thus, 14 is 30% of 46.67. Division in algebra can simplify complex problems and is a fundamental tool for solving for unknown variables.