Problem 98 - Algebra 1

Question

RECIPROCALS Find the reciprocal. $$ \frac{1}{121} $$

Step-by-Step Solution

Answer

The reciprocal of \( \frac{1}{121} \) is \( 121 \).

Step 1: Understand Reciprocal

A reciprocal of a number or a fraction is determined by dividing the number into 1. If a number is given in a fraction form, the reciprocal is found by inverting the fraction, that is, swapping the numerator and the denominator.

Step 2: Identify the Fraction to Invert

The fraction given to find the reciprocal is \(\frac{1}{121}\).

Step 3: Find the Reciprocal

The Reciprocal of the fraction \(\frac{1}{121}\) is found by swapping the numerator and the denominator. Hence, the reciprocal is \(121\).

Key Concepts

Fractions

A fraction is a way of representing a part of a whole. It consists of two parts: a numerator and a denominator, separated by a line or a slash. Think of a fraction as a sliced pizza. If you have a pizza cut into equal slices, and you eat some of them, those slices eaten can be represented as a fraction.

Some key points about fractions:

• The top number, called the numerator, tells us how many pieces or parts we are considering.
• The bottom number, the denominator, tells us into how many equal parts the whole is divided.
• Fractions can be used to compare amounts and can also represent ratios or divisions.
• Every fraction can have a reciprocal, which is found by swapping the numerator and the denominator.

Recognizing and working with fractions is an essential mathematical skill, necessary for understanding more advanced mathematical concepts.

Numerator

The numerator is the number found above the line in a fraction. It signifies the number of parts out of the whole we are focusing on. In our given exercise with the fraction \( \frac{1}{121} \), the numerator is 1.

Consider these elements of a numerator:

• The numerator shows the number of parts we have from the whole set defined by the denominator.
• If the numerator is smaller than the denominator, the fraction indicates a quantity less than one whole unit.
• A change in the numerator alters the size of the fraction, indicating either more or fewer parts of the whole.

Understanding the numerator is crucial because it is the variable in a fraction that defines the quantity. Without it, a fraction would merely describe a set without specifying how many pieces or parts of that set we have.

Denominator

The denominator is the part of the fraction located below the line. It indicates into how many parts the whole is divided. For instance, in the fraction \( \frac{1}{121} \), the denominator is 121. This tells us that the whole is divided into 121 equal parts.

The denominator is important because:

• It sets the standard unit of measure for the fraction, determining the size of each part.
• If the denominator changes, the size of each part changes as well.
• Having a larger denominator means smaller individual parts of the whole.

Inverting a fraction to find its reciprocal involves the denominator and the numerator swapping places. Thus, knowing the role of the denominator is crucial when working with reciprocals.