Problem 56 - Fundamentals of Mathematics

Question

State the numerator and denominator and write in words each of the fractions appearing in the statements for the following 10 problems. A contractor is selling houses on \(\frac{1}{4}\) acre lots.

Step-by-Step Solution

Answer

The fraction is \( \frac{1}{4} \) which is 'one-fourth'. Numerator: 1, Denominator: 4.

Step 1: Identifying the fraction

The fraction given in the problem is \( \frac{1}{4} \). This fraction represents the part of an acre that each lot contains on which the contractor is building and selling houses.

Step 2: Numerator

The numerator of the fraction \( \frac{1}{4} \) is 1. The numerator signifies the number of equal parts being considered, in this case, one part.

Step 3: Denominator

The denominator of the fraction \( \frac{1}{4} \) is 4. The denominator indicates the total number of equal parts into which the whole is divided, in this case, that the acre is divided into four parts.

Step 4: Writing the Fraction in Words

The fraction \( \frac{1}{4} \) is written in words as 'one-fourth'. This means each lot is one of four equal parts of an acre.

Key Concepts

Numerator

In fractions, the numerator is the top number, which indicates how many parts of the whole are being considered. Think of it as "what you have." For instance, in the fraction \( \frac{1}{4} \), the numerator is 1. This tells us we have one out of a possible number of parts.
When you look at a situation described by a fraction, the numerator is essential because it lets us know precisely what portion of the whole we're referring to:

• For \( \frac{1}{4} \), it signifies a single part of an acre.

This understanding helps in both visualizing fractions and performing mathematical operations with them, as the numerator is a guide to how much of something you're discussing.

Denominator

The denominator is the bottom number in a fraction, showing us into how many equal parts the whole is split. Consider it as the "total number of parts." In \( \frac{1}{4} \), the denominator is 4, meaning an acre is split into four equal parts.
The denominator is crucial because it helps determine the scale or size of each part:

• The larger the denominator, the more pieces the whole is divided into, which makes each piece smaller.
• Conversely, a smaller denominator means fewer parts and larger pieces.

Thus, understanding the denominator provides insight into the fraction's structure, making comparisons and calculations easier.

Writing Fractions in Words

Expressing fractions in words is a useful skill that helps in both communication and comprehension. By translating a fraction like \( \frac{1}{4} \) into words, you can easily convey its meaning. In this case, \( \frac{1}{4} \) is read as 'one-fourth'.
Here’s a simple way to follow:

• Start with the numerator, read it as a cardinal number (like "one").
• Then, the denominator is read as an ordinal number (like "fourth").

So, the fraction \( \frac{1}{4} \) becomes "one-fourth." This method is helpful in many real-life situations and makes fractions more relatable and less intimidating.