Problem 17 - Fundamentals of Mathematics

Question

In the following 2 problems, state the numerator and denominator, and write each fraction in words. A dime is \(\frac{1}{10}\) of a dollar.

Step-by-Step Solution

Answer

Fraction is \( \frac{1}{10} \), read as "one tenth."

Step 1: Identify the Numerator

The given fraction is \( \frac{1}{10} \). The numerator is the top number of the fraction, which represents the number of parts being considered. In this fraction, the numerator is \( 1 \).

Step 2: Identify the Denominator

The fraction given is \( \frac{1}{10} \). The denominator is the bottom number of the fraction, representing the total number of equal parts into which the whole is divided. Here, the denominator is \( 10 \).

Step 3: Write the Fraction in Words

Now that we have identified the numerator and denominator, we can write the fraction in words. The fraction \( \frac{1}{10} \) is read as "one tenth."

Key Concepts

Numerator and Denominator

When dealing with fractions, two important components are the numerator and denominator. These terms help describe how a fraction is structured and what it represents.

• Numerator: This is the number on top of the fraction. In any given fraction, the numerator tells you how many parts of the whole are being considered. For example, if you have \( \frac{1}{10} \), the numerator is \( 1 \). This means one part out of the total parts is being looked at or used.
• Denominator: This number sits at the bottom of a fraction. It tells you into how many equal parts the whole is divided. In our example \( \frac{1}{10} \), the denominator is \( 10 \). Therefore, a dollar is divided into ten equal parts.

Understanding these two components helps you to analyze and solve fraction problems better. Always remember that the top number (numerator) and the bottom number (denominator) work together to show the relationship between the part and the whole.

Writing Fractions in Words

Once you identify the parts of a fraction, the next step is to write it out in words. This process helps in verbal communication and improves understanding by converting mathematical expressions into everyday language.

• To convert a fraction into words, firstly say the numerator followed by the denominator with a suffix that indicates parts of a whole.
• For example, the fraction \( \frac{1}{10} \) is read as "one tenth."
• This format uses the numerator "one" and the denominator "tenth," stressing the fact that the whole is divided into ten equal parts.

Writing fractions in words is a skill that is often applied in practical situations, like describing parts of a dollar or measuring ingredients in a recipe. Developing fluency in reading fractions as words supports better comprehension and reduces errors.

Fraction Interpretation

Interpreting fractions is all about understanding what they mean in a given context. It involves translating the numeric representation into something meaningful in everyday situations.

• A key to interpreting fractions is recognizing what whole the fraction relates to. For instance, in the phrase "A dime is \( \frac{1}{10} \) of a dollar," we know that a dollar is the whole.
• Recognize that "one tenth" signifies that the dollar is divided into ten equal parts and each dime represents one of these parts.
• Fractions often represent smaller pieces of a larger item or quantity, such as dividing a cake, sharing a pizza, or calculating an hour as 60 minutes.

By understanding the context in which a fraction is used, you will gain a deeper and more practical understanding of what the fraction actually represents, leading to more accurate problem-solving skills.