Problem 40 - Fundamentals of Mathematics

Question

For the following 10 problems, write the fractions using words. \(\frac{8}{15}\)

Step-by-Step Solution

Answer

Eight fifteenths.

Step 1: Introduction to Fraction Terminology

Fractions consist of two parts: the numerator (top number) and the denominator (bottom number). The numerator represents the number of parts considered, and the denominator represents the total number of equal parts.

Step 2: Represent the Numerator in Words

Identify the numerator in the fraction \(\frac{8}{15}\), which is 8. In words, the numerator is 'eight'.

Step 3: Represent the Denominator in Words

Identify the denominator in the fraction \(\frac{8}{15}\), which is 15. In words, the denominator is often expressed as an ordinal number, 'fifteenths'.

Step 4: Combine Numerator and Denominator in Word Form

To write the fraction \(\frac{8}{15}\) in words, combine both parts: 'eight fifteenths'.

Key Concepts

Numerator and Denominator

When we talk about fractions, it's vital to know that they are made up of two main components: the numerator and the denominator. The numerator is the number on the top of the fraction. It tells us how many parts of the whole we have. Think of it this way: if you have a pizza cut into 8 slices and you eat 3, the 3 would be your numerator because you have eaten 3 out of the total slices.

The denominator, found at the bottom of the fraction, shows the total number of equal parts that something is divided into. In our pizza example, if the pizza is cut into 8 slices, 8 becomes the denominator. This way, a fraction like \( \frac{3}{8} \) symbolizes that 3 out of the 8 parts are being considered. Understanding these two terms will help you grasp the concept of fractions better.

Writing Fractions in Words

Expressing fractions in words is another aspect of understanding fractions thoroughly. Let's say we have the fraction \( \frac{8}{15} \). To write it in words, you start by noting the numerator, which is 8. In words, this is 'eight'. This part is straightforward since numerators are typically written as regular numbers.

The denominator, however, should be written as an ordinal number. For instance, for 15, we use 'fifteenths.' When you combine the two, the complete expression in words would be 'eight fifteenths'.

• Step 1: Identify the numerator and write it down in words.
• Step 2: Express the denominator using ordinal terms.
• Step 3: Combine both to articulate the fraction in a word form.

This method ensures you are conveying the value accurately using words, making it easy to communicate fractions verbally.

Fraction Representation

Fractions provide a way to represent numbers that are less than a whole in many different formats. Visually, when you consider a fraction like \( \frac{8}{15} \), it can be represented in several ways, including pictorial illustrations or on a number line. For example, imagine a pie that's cut into 15 equal pieces and 8 of those pieces are shaded or marked to show \( \frac{8}{15} \).

Furthermore, fractions can be represented by using decimal or percentage equivalents. The fraction \( \frac{8}{15} \) approximates to 0.5333 as a decimal and 53.33% as a percentage. Each representation shows the same part-to-whole relationship, just in different formats.

• Visual Model: Showing shaded parts of a shape or diagram.
• Number Line: Placing a point on a line that represents the fraction.
• Decimal and Percentage: Converting the fraction into other numerical forms.

These varied formats facilitate better understanding and can provide deeper insight, especially when applying fractions in real-world scenarios.