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Chapter 6: Problem 50

Change 20 ounces to pounds. Express your answer as a fraction reduced to lowest terms.

Short Answer

Expert verified
20 ounces is equal to \( \frac{5}{4} \) pounds.

Step by step solution

01

Recall the Conversion Factor

To convert ounces to pounds, we need to know the relationship between these units. There are 16 ounces in one pound.
02

Set Up the Conversion Equation

Using the conversion factor, we can set up the conversion equation:\[ \text{pounds} = \frac{\text{ounces}}{16} \]Substituting 20 ounces into the equation gives:\[ \text{pounds} = \frac{20}{16} \]
03

Simplify the Fraction

Now, we simplify the fraction \( \frac{20}{16} \) by finding the greatest common divisor (GCD) of 20 and 16, which is 4. We divide both the numerator and the denominator by their GCD:\[ \frac{20}{16} = \frac{20 \div 4}{16 \div 4} = \frac{5}{4} \]
04

Final Conversion to Reduced Fraction

The simplified fraction \( \frac{5}{4} \) represents the pounds. Thus, 20 ounces is equal to \( \frac{5}{4} \) pounds after conversion.

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Key Concepts

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

Fractions
Fractions are a way to express a part of a whole or, more generally, any number of equal parts. When you see a fraction like \( \frac{5}{4} \), you are looking at two components: the numerator and the denominator.
  • The **numerator** is the top number, which shows how many parts we are discussing. In \( \frac{5}{4} \), this is 5.
  • The **denominator** is the bottom number, indicating how many equal parts the whole is divided into. Here, it's 4.
Fractions are more than just numbers; they are a way to present divisions and comparisons between numbers in a flexible manner.
This makes them incredibly useful in everyday life, such as in recipes, telling time, or in our case, unit conversions. Understanding fractions is crucial for solving problems that involve sharing, dividing, or converting measures.
Simplification
Simplification of fractions is important because it makes fractions easier to understand and work with. A fraction is simplified when the numerator and denominator have no common factors other than 1.
  • To simplify \( \frac{20}{16} \), we find the greatest common divisor (GCD).
  • The GCD of 20 and 16 is 4, so both numbers are divided by 4.
  • This turns the fraction into \( \frac{5}{4} \), which is the simplified form.
Simplification ensures that fractions are presented in their most reduced form.
This not only aids in clearer comprehension but also in further calculations. Simplified fractions are easier to compare, add, subtract, and convert than their more complex counterparts.
Conversion Factor
A conversion factor is a useful mathematical tool that helps us transform one unit of measurement into another. It's essentially a ratio that expresses how many of one unit are equivalent to another.
  • In our example, the conversion factor between ounces and pounds is \( \frac{1}{16} \).
  • It means that 1 pound is equal to 16 ounces, letting you convert ounces to pounds by dividing the number of ounces by 16.
Conversion factors enable seamless transitions between different measurement systems or units, aligning values so we can compare and compute across various contexts.
Understanding how to use conversion factors can simplify many real-life situations, such as cooking, shopping, or anytime you need to work with different measurement units.

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