Problem 41 - Fundamentals of Mathematics

Question

For the following 10 problems, write the fractions using words. \(\frac{10}{13}\)

Step-by-Step Solution

Answer

The fraction is written as 'ten thirteenths'.

Step 1: Identify the Numerator and the Denominator

In the given fraction \( \frac{10}{13} \), the numerator is 10, and the denominator is 13.

Step 2: Convert Numerator to Words

The numerator in the fraction \( \frac{10}{13} \) is 10. In words, this is written as 'ten'.

Step 3: Convert Denominator to Words

The denominator in the fraction \( \frac{10}{13} \) is 13. In words, this is written as 'thirteen'.

Step 4: Write the Fraction Using Words

Combine the words for the numerator and the denominator to express the fraction in words. Therefore, \( \frac{10}{13} \) is written as 'ten thirteenths'.

Key Concepts

Understanding the Numerator

In a fraction, the term 'numerator' refers to the top number. This number tells us how many parts of a whole we are considering. Think of the numerator as a counter. It counts the pieces of the whole that we are interested in. For example, in the fraction \( \frac{10}{13} \), the numerator is \( 10 \), meaning we have 10 parts out of 13.

The numerator is crucial because it represents the quantity considered against the total expressed by the denominator. When translating this into words, the number of numeral in the numerator is written in letters. So for \( 10 \), it becomes "ten." This process of converting numbers into words is important for clear communication, especially in writing and verbally explaining fractions.

Exploring the Denominator

The denominator is the bottom number of a fraction. It signifies the total number of equal parts that make up a whole. In a way, it's a name tag for the size of each part. With the fraction \( \frac{10}{13} \), the denominator is \( 13 \), meaning the whole is divided into 13 equal parts.

Understanding the denominator is essential because it sets the scale for the fraction. It shows us how many equal parts the whole is divided into, allowing for proper comparison and contrast with other fractions. Converting the denominator into words follows the same process as with the numerator. For the number \( 13 \), it translates to "thirteen." When expressed in fractional form, this helps in understanding and communicating mathematical concepts better.

Converting Numbers to Words in Fractions

When dealing with fractions, converting numbers to words is a vital skill. It ensures clarity, especially when explaining math in written or spoken form. To convert numerators or denominators into words, you simply take the numerical value and translate it into its word equivalent.

Here's a step-by-step example using the fraction \( \frac{10}{13} \):

• First, identify the numerator \( 10 \). Convert this to "ten."
• Next, identify the denominator \( 13 \). Convert this to "thirteen."

Finally, when expressing the entire fraction, combine these words appropriately: "ten thirteenths."

This approach simplifies the fraction into an understandable format that aligns with everyday language use. Such skills enhance both comprehension and communication in math across different scenarios.