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Chapter 0: Problem 51

Write each mixed number as an improper fraction. $$ 10 \frac{1}{5} $$

Short Answer

Expert verified
The mixed number \(10 \frac{1}{5} \) is \( \frac{51}{5} \).

Step by step solution

01

Understand the Mixed Number

A mixed number consists of a whole number and a fraction. In this case, the mixed number is 10 \( \frac{1}{5} \).
02

Convert the Whole Number to a Fraction

Convert the whole number to a fraction by multiplying it by the denominator of the fraction part. Here, the whole number is 10 and the denominator is 5. So, \( 10 \times 5 = 50 \). This means 10 can be written as \( \frac{50}{5} \).
03

Add the Numerators

Now, add the numerator of the fraction part to the fraction obtained from the whole number. In this case, it is \( \frac{50}{5} + \frac{1}{5} \). Add the numerators: \( 50 + 1 = 51 \). So, \( \frac{50}{5} + \frac{1}{5} = \frac{51}{5} \).
04

Write the Improper Fraction

The mixed number \( 10 \frac{1}{5} \) can be written as the improper fraction \( \frac{51}{5} \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Mixed Numbers
A mixed number combines a whole number and a fraction. It's written as one number with another smaller number next to it, separated by a fraction bar. For example, in the mixed number 10 \(\frac{1}{5}\), 10 is the whole number and \(\frac{1}{5}\) is the fraction.
Mixed numbers are useful for representing quantities greater than one in a simplified form. They are often seen in real-life scenarios like recipes, measurements, and everyday calculations.
Understanding Improper Fractions
An improper fraction has a numerator larger than or equal to its denominator. This means the fraction represents a quantity equal to or greater than one. For instance, the fraction \(\frac{51}{5}\) is an improper fraction because the numerator (51) is greater than the denominator (5).
Improper fractions might seem harder to understand at first, but they are very useful in calculations and can easily be converted back to mixed numbers.
Converting Mixed Numbers to Improper Fractions
To convert a mixed number like 10 \(\frac{1}{5}\) to an improper fraction, follow these simple steps:
1. Multiply the whole number by the denominator of the fraction part. In this case, multiply 10 by 5 (\(10 \times 5 = 50\)).
2. Add the numerator of the fraction part to the result. Here, add 1 to 50 (\(50 + 1 = 51\)).
3. Write the result as the numerator over the original denominator. So, 10 \(\frac{1}{5}\) becomes \(\frac{51}{5}\).

This method simplifies calculations, making it easier to work with fractions in mathematical problems.
Addition of Fractions
When adding fractions, it's crucial to have a common denominator. Fractions with the same denominator can be added directly by adding their numerators. For example, in the conversion process, we added \(\frac{50}{5}\) and \(\frac{1}{5}\). Both fractions have the same denominator (5), so we simply add their numerators (50 + 1 = 51).
This basic understanding of adding fractions applies to many situations and is a foundational skill for more advanced math concepts. Always remember to simplify the result if possible.

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