Problem 6 - Fundamentals of Mathematics

Question

For problems 6-10, write each fraction using digits. Three fifths

Step-by-Step Solution

Answer

\( \frac{3}{5} \)

Step 1: Read the Words

Examine the fractional word 'three fifths'. This tells us that the numerator is 'three' and the denominator is 'fifths'.

Step 2: Identify the Numerator

The word 'three' indicates the numerator of the fraction. Numerator is the number above the line in a fraction.

Step 3: Identify the Denominator

The word 'fifths' indicates the denominator of the fraction. Denominator is the number below the line in a fraction.

Step 4: Write the Fraction

Convert the identified words into numbers. 'Three' becomes 3 and 'fifths' becomes 5. Therefore, the fraction is written as \( \frac{3}{5} \).

Key Concepts

Understanding the Numerator

The numerator plays a key role in understanding fractions. Often called the top number, the numerator represents how many parts of a whole are being considered. For example, in the fraction \( \frac{3}{5} \), the numerator is 3. This tells us that we are looking at three parts out of a total of five parts. It is important to remember that the numerator tells us *what part of the whole* we are dealing with.
To identify the numerator in word form, look for the number mentioned before the word that represents parts, like “three” in "three fifths". Learning to quickly pick out the numerator in any given word expression will become easier with practice. Keep in mind:

• Numerators determine part of the whole being considered.
• Often mentioned at the beginning in fraction word problems.

Exploring the Denominator

The denominator in a fraction is just as crucial as the numerator. You will find it at the bottom of the fraction. It tells us into how many equal parts the whole is divided. So, in the fraction \( \frac{3}{5} \), the number 5 is the denominator. This indicates that the whole is divided into five equal parts.
Understanding the denominator helps you know what each part represents. In our example of "three fifths," the term "fifths" signifies that the whole is divided into five parts. Key points to remember:

• Denominator shows total number of equal parts.
• Found after the word defining parts in word problems.

Breaking down the word form of the denominator, like converting "fifths" to 5, is essential to writing and understanding fractions correctly.

Basics of Fraction Conversion

Fraction conversion involves transforming a word expression of a fraction into a numerical form, which is often simple once you recognize the roles of the numerator and denominator. For example, the word fraction "three fifths" converts to a numerical fraction by identifying that "three" is the numerator and "fifths" is the denominator, giving us \( \frac{3}{5} \).
To effectively handle fraction conversion, follow these steps:

• Read the word expression carefully.
• Identify and convert the numerator words into numbers.
• Identify and convert the denominator words into numbers.
• Write the fraction with the numerator above the line and the denominator below.

Frequent practice will help in getting more familiar with these conversions, allowing for smoother mathematical problem solving.