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Chapter 7: Problem 21

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

Short Answer

Expert verified
The notation is expressed as "fifteen and one-half pounds."

Step by step solution

01

Understand the Fraction

The given notation is a mixed number, consisting of a whole number and a fractional part. The fraction is \(\frac{1}{2}\), which means "one-half".
02

Identify the Unit

The units indicated in the notation are \(\mathrm{lb}\), which stands for 'pounds,' a unit of mass or weight.
03

Combine the Components

Combine the whole number, the fractional part, and the unit to express the notation verbally: "fifteen and one-half pounds."

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Key Concepts

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

Mixed Numbers
A mixed number is a mathematical expression that combines a whole number and a fraction. For instance, in the expression \(15 \frac{1}{2}\), the part before the fraction, 15, is the whole number, and \(\frac{1}{2}\) is the fractional part. Mixed numbers are quite common in everyday measurements, such as when measuring weight, height, or distance.
  • The whole number represents a complete set or whole unit.
  • The fraction embodies a part of another unit, making the number not fully whole.
  • This combination aids in expressing quantities that aren't exactly an integer.
Mixed numbers are especially useful when exact values include portions smaller than a whole. For example, 15 and one-half pounds clearly communicates a precise measurement without the need for more complex decimals.
Fractions
Fractions represent parts of a whole. They consist of a numerator and a denominator, appearing in the form \(\frac{a}{b}\) where \(a\) is the numerator and \(b\) is the denominator.
  • The numerator indicates how many parts we have.
  • The denominator shows how many parts make up a whole.
In the mixed number \(15 \frac{1}{2}\), the fraction \(\frac{1}{2}\) indicates that you have one part of a whole that is divided into two equal parts.

Why Use Fractions?

Using fractions allows for precision, especially when measuring. They are more precise than whole numbers alone, and sometimes clearer than decimals, in showing the exact portion involved in various contexts like cooking, construction, or science.
Unit Conversion
Unit conversion is necessary when you need to understand or communicate measurements in different unit systems. In the example \(15 \frac{1}{2}\) lbs, "lbs" signifies pounds, which is commonly used in the United States for measuring weight.
  • The standard metric equivalent of pounds is kilograms (kg), where 1 lb is approximately equal to 0.453592 kg.
  • To convert pounds to kilograms, multiply the number of pounds by 0.453592.
  • Conversely, to convert kilograms to pounds, divide by 0.453592.
Understanding how to convert units ensures clear communication in scientific fields, international contexts, and in day-to-day activities when comparing measurements with the metric system.

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