Problem 6 - Basic College Mathematics

Question

Find the reciprocal of each number. \(\frac{1}{4}\)

Step-by-Step Solution

Answer

The reciprocal of \(\frac{1}{4}\) is 4.

Step 1: Understand the Reciprocal

The reciprocal of a number is what you multiply by that number to get 1. For any fraction \(\frac{a}{b}\), the reciprocal is \(\frac{b}{a}\).

Step 2: Identify the Numerator and Denominator

In the given fraction \(\frac{1}{4}\), the numerator (the number on top) is 1 and the denominator (the number on the bottom) is 4.

Step 3: Swap the Numerator and Denominator

To find the reciprocal, swap the positions of the numerator and the denominator. So, the reciprocal of \(\frac{1}{4}\) is \(\frac{4}{1}\).

Step 4: Simplify the Reciprocal

Simplify the fraction if possible. \(\frac{4}{1}\) simplifies to 4.

Key Concepts

Basic Fractions

A fraction represents a part of a whole. It looks like two numbers separated by a line or a slash. For example, in the fraction \(\frac{1}{4}\), the '1' is the top part and the '4' is the bottom part.
This slash (or line) means that you are dividing the top number by the bottom number.
Imagine you have a pizza cut into 4 pieces. If you eat 1 piece, you've eaten \(\frac{1}{4}\) of the pizza.

Numerator and Denominator

In a fraction, the top number is called the numerator and the bottom number is called the denominator.
They help show what part of a whole you have.

• The numerator (top number) represents how many parts you are considering.
• The denominator (bottom number) represents the total number of equal parts the whole is divided into.

For example, in the fraction \(\frac{1}{4}\), the numerator is 1, which means we are considering 1 part, and the denominator is 4, which means the whole is divided into 4 equal parts.

Simplifying Fractions

Simplifying fractions means to make the fraction as simple as possible.
This involves making sure the numerator and the denominator have no common factors other than 1.
For example, if you have the fraction \(\frac{4}{8}\), it can be simplified because both 4 and 8 can be divided by 4.
So, \(\frac{4}{8}\) simplifies to \(\frac{1}{2}\). Often, simplified fractions are easier to work with and understand.
Let's not forget the main exercise: Finding the reciprocal is all about flipping the numerator and the denominator.
Once you flip, make sure your fraction is as simplified as possible to get your final answer.