Problem 61 - Basic College Mathematics

Question

If \(\frac{1}{3}\) of a number is \(\frac{1}{4}\), what is \(\frac{1}{2}\) of the number?

Step-by-Step Solution

Answer

The answer is \(\frac{3}{8}\).

Step 1 - Understand the given information

We are given that \(\frac{1}{3}\) of a number is \(\frac{1}{4}\). Let's denote the unknown number by \(x\). Therefore, we can write the equation: \[ \frac{1}{3}x = \frac{1}{4} \]

Step 2 - Solve for the unknown number

To find the value of \(x\), we need to solve the equation from Step 1. Multiply both sides of \( \frac{1}{3}x = \frac{1}{4} \) by 3 to isolate \(x\): \[ x = 3 \times \frac{1}{4} \] \[ x = \frac{3}{4} \] So, the unknown number \(x\) is \( \frac{3}{4} \).

Step 3 - Find \(\frac{1}{2}\) of the number

We need to find \(\frac{1}{2}\) of the number we just calculated. Using \(x = \frac{3}{4}\), calculate \(\frac{1}{2}\) of \(x\): \[ \frac{1}{2} \times \frac{3}{4} = \frac{3}{8} \] Therefore, \(\frac{1}{2}\) of the number is \(\frac{3}{8}\).

Key Concepts

Fraction Multiplication

When multiplying fractions, you multiply the numerators (top numbers) together and the denominators (bottom numbers) together.
For example, to multiply \(\frac{1}{2}\) by \(\frac{3}{4}\):
To get the numerator, you multiply 1 by 3, which gives you 3.
For the denominator, you multiply 2 by 4, which results in 8. So, \(\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}\).
This rule is very useful in solving problems involving fractions, like the exercise where we need to find \(\frac{1}{2}\) of the number. It helps to break the process into simple steps.

Algebraic Equations

An algebraic equation is a mathematical statement where two expressions are set equal to each other. In the given exercise, the equation is \(\frac{1}{3}x = \frac{1}{4}\).
To solve for the unknown variable \