Question

Express the following notations in words: \(15 \frac{1}{2} \mathrm{lb}\)

Short answer

"Fifteen and one-half pounds."

Step-by-step solution

Understanding Mixed Numbers

The notation \(15 \frac{1}{2}\) consists of a whole number part, which is 15, and a fractional part, which is \(\frac{1}{2}\). This is read as "fifteen and one-half."

Understanding the Unit

The unit in the notation is \(\mathrm{lb}\), which stands for pounds. This is a unit of weight or mass commonly used in the United States and other parts of the world.

Combining Number and Unit

When expressing the notation in words, combine the interpreted number with the unit. Therefore, \(15 \frac{1}{2} \mathrm{lb}\) is read as "fifteen and one-half pounds."

Key concepts

Fractional Notation

Fractional notation is a way to show quantities that are not whole numbers. It consists of a numerator and a denominator. The numerator is the top number that tells how many parts we have. The denominator is the bottom number that tells how many parts the whole is divided into.
For instance, in the fraction \( \frac{1}{2} \), 1 is the numerator, and 2 is the denominator. This fraction indicates that we have one part of something that is divided into two equal parts.
Mixed numbers, like \(15 \frac{1}{2}\), are a combination of a whole number and a fraction. Here, 15 is the whole number part, and \(\frac{1}{2}\) is the fractional part. Expressing this in fractional notation means writing down both the whole number and the fraction.

Mathematical Expressions

Mathematical expressions are groups of numbers, symbols, and operators (like addition or subtraction) that represent a value. In our exercise, the expression \(15 \frac{1}{2}\) is a mathematical way to show a number that includes both a whole number and a part of a whole.
These expressions are useful for understanding and handling real-world quantities that aren't whole numbers, like slices of a pie or portions of a pound.
Understanding mathematical expressions helps in converting between different forms, such as between mixed numbers and improper fractions, or when performing calculations that involve these numbers.

Unit Conversion

Unit conversion is the process of converting a measurement from one unit to another. This is crucial when working with measurements like weight, length, or volume, especially when different systems of units are used.
In the context of the problem, the unit \(\mathrm{lb}\) stands for pounds, a unit of weight used mostly in countries like the United States. This can be converted into kilograms, another unit of mass, by using a conversion factor (1 pound is approximately 0.453592 kilograms).
Understanding how to perform unit conversions allows you to communicate measurements in different contexts effectively, which is particularly useful when dealing with scientific data or international trade.