Problem 31 - Fundamentals of Mathematics

Question

For the following 10 problems, write the fractions using whole numbers. forty-seven eighty-thirds

Step-by-Step Solution

Answer

The fraction is \( \frac{47}{83} \).

Step 1: Identify the Numerator

The problem gives us the fraction as "forty-seven eighty-thirds." In this phrase, "forty-seven" is the numerator. So, the numerator of our fraction is 47.

Step 2: Identify the Denominator

In the phrase "forty-seven eighty-thirds," "eighty-thirds" indicates the denominator. "Eighty-thirds" means each unit is divided into eighty-three equal parts, hence the denominator is 83.

Step 3: Write the Fraction

Now that we've determined our numerator is 47 and our denominator is 83, we can write the fraction using whole numbers. The fraction is written as \( \frac{47}{83} \).

Key Concepts

Understanding Numerators

In fractions, the numerator is a critical component. It is the top number in the fraction and indicates how many parts of a whole are being considered. When you hear or see a phrase like "forty-seven eighty-thirds," the number "forty-seven" is what we refer to as the numerator.
This number tells us specifically the count of portions we have out of the complete set described by the fraction.
For example:

• If you have a fraction \( \frac{3}{4} \), the numerator is 3, meaning you have 3 parts out of 4 total parts.
• In our example "forty-seven eighty-thirds," the numerator is 47, suggesting we have 47 parts out of a larger whole.

Understanding the role of the numerator helps in visualizing and working with fractions effectively.

Demystifying Denominators

The denominator is the bottom part of the fraction and it plays an equally crucial role. It tells you into how many equal parts the whole is divided. In the phrase "forty-seven eighty-thirds," the word "eighty-thirds" clues us in on the denominator.
This means our whole has been divided into 83 equal parts. It sets the size of each portion of the whole in context.

• In a fraction like \( \frac{1}{2} \), the denominator is 2, which suggests the whole is split into two equal pieces.
• For \( \frac{47}{83} \), the denominator 83 underscores that the entire entity is divided into 83 smaller sections.

Without a denominator, you wouldn't know the size of each part relative to the whole, which is vital for comparison and calculation.

Grasping Whole Numbers in Fractions

Whole numbers are essential building blocks in mathematics, and they are numbers without fractions or decimals. Fractions use whole numbers to express parts of a whole.
When fractions like \( \frac{47}{83} \) are described with whole numbers, both the numerator and the denominator are individual whole numbers. Each represents quantities and divisions that are complete and exact.

• A whole number example is 47 or 83, as seen in our fraction example. Both are complete numbers that describe portions of the whole.
• Another illustration could be \( \frac{3}{4} \), where 3 and 4 are whole numbers representing your parts and the total parts available.

Understanding whole numbers helps in seeing how fractions are constructed, providing clarity in how fractions are used for calculations and comparisons.