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Chapter 3: Problem 31

Convert to fraction notation. $$ 101 \frac{5}{16} $$

Short Answer

Expert verified
The fraction notation is \(\frac{1621}{16}\).

Step by step solution

01

- Identify the whole number and the fraction

In the mixed number, identify the whole number and the fraction part. For the given number, the whole number is 101 and the fraction is \(\frac{5}{16}\).
02

- Convert the whole number to a fraction

Convert the whole number 101 to a fraction by writing it as \(\frac{101}{1}\).
03

- Combine the whole number and the fraction

Combine the whole number fraction \(\frac{101}{1}\) and the fraction \(\frac{5}{16}\) by getting a common denominator. The common denominator is 16, so multiply the numerator and denominator of \(\frac{101}{1}\) by 16 to get \(\frac{1616}{16}\).
04

- Add the fractions

Add the fractions: \(\frac{1616}{16} + \frac{5}{16} = \frac{1616 + 5}{16} = \frac{1621}{16}\).

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Key Concepts

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

Mixed Numbers
Mixed numbers are numbers that consist of a whole number and a fraction. For example, in the number 101\(\frac{5}{16}\), 101 is the whole number and \(\frac{5}{16}\) is the fraction. Mixed numbers are very common in everyday math because they represent numbers with both a complete part and an additional partial part. Understanding mixed numbers helps in many areas of math, such as measurement and division.
Fractions
Fractions represent a part of a whole. Fractions are written as \(\frac{a}{b}\) where \(a\) is the numerator and \(b\) is the denominator. The numerator shows how many parts you have, while the denominator shows how many equal parts the whole is divided into. For example, \(\frac{5}{16}\) means you have 5 parts out of 16.
Improper Fractions
Improper fractions are fractions where the numerator is larger than the denominator. This means the value is greater than 1. For example, in the mixed number 101\(\frac{5}{16}\), converting it results in the improper fraction \(\frac{1621}{16}\). Improper fractions are useful for various mathematical operations and can often make calculations easier.
Common Denominator
To combine or compare fractions, they must have a common denominator. This means both fractions need the same bottom number. In our example, the whole number 101 was converted to a fraction \(\frac{101}{1}\), then adjusted to have the same denominator as the fractional part \(\frac{5}{16}\). To do this, we multiplied the numerator and the denominator of \(\frac{101}{1}\) by 16, getting \(\frac{1616}{16}\). Now it can be easily added to \(\frac{5}{16}\).

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Most popular questions from this chapter

Add and simplify. $$ \frac{5}{7}+\frac{25}{52}+\frac{7}{4} $$

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