Problem 28 - Fundamentals of Mathematics

Question

For the following 10 problems, write the fractions using whole numbers. four fifths

Step-by-Step Solution

Answer

The fraction is \( \frac{4}{5} \).

Step 1: Understanding the Fraction

The phrase 'four fifths' represents a fraction composed of two parts: the numerator and the denominator. Here, 'four' is the numerator and 'fifths' indicates a denominator of five.

Step 2: Writing the Fraction

Convert the words into numbers to form the fraction. 'Four fifths' is written as the fraction \( \frac{4}{5} \).

Step 3: Simplifying the Fraction

Check if the fraction \( \frac{4}{5} \) can be simplified. Since 4 and 5 have no common factors other than 1, the fraction is already in its simplest form.

Key Concepts

Numerator

In a fraction, the numerator is the number that sits above the fraction bar. It's an essential part of any fraction and tells us how many parts we are considering. For instance, in the fraction \( \frac{4}{5} \), the number 4 is the numerator. When you hear someone say "four fifths," the "four" is indicating that we are looking at four equal parts of something.

• The role of the numerator is to specify how many parts of the whole or group we have.
• It is always the top number in the fraction.
• In terms of word problems, the numerator often comes from translating phrases like "four parts" or "three pieces."

Understanding the numerator helps you visualize what portion of the whole is considered, which is vital to grasping the concept of fractions fully.

Denominator

The denominator is a key component in fractions, located at the bottom of the fraction bar. It indicates into how many equal parts the whole is divided. For example, in the fraction \( \frac{4}{5} \), the denominator is 5. This number answers the question, "How many parts make a whole?"

• The denominator defines the total number of equal parts.
• It's always the bottom number of a fraction.
• When converting phrases to fractions, the word used for the whole (like "fifths," "thirds") signals what the denominator should be.

The denominator is crucial for determining the size of each piece in relation to the total amount. Without a denominator, we wouldn't know how large each part should be.

Simplifying Fractions

Simplifying fractions involves reducing the fraction to its simplest form, where the numerator and denominator have no common factors other than 1. For example, in the fraction \( \frac{4}{5} \), the numbers 4 and 5 are checked for common factors. Because they have none, the fraction is already simplified.

• Simplifying makes the fraction easier to understand and work with.
• It involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
• In some cases, fractions can be simplified to a whole number if the numerator is a multiple of the denominator.

Not all fractions can be simplified. But when they can, it’s an important step to ensure clarity and correctness in mathematical work.