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Chapter 9: Problem 20

Convert each measurement as indicated. $$ \frac{1}{2} \text { pint to quarts } $$

Short Answer

Expert verified
\( \frac{1}{2} \) pint is equal to \( \frac{1}{4} \) quart.

Step by step solution

01

Identify Conversion Factor

To convert between pints and quarts, we need the conversion factor. There are 2 pints in a quart.
02

Set Up the Conversion

We have \( \frac{1}{2} \) pint that we want to convert to quarts. Since there are 2 pints in a quart, we multiply by the conversion factor (\( \frac{1}{2} \)). This gives us: \[ \frac{1}{2} \text{ pint} \times \frac{1}{quart}{2 \text{ pints}} \]
03

Perform the Calculation

Calculate the value using the setup from the previous step: \[ \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \] The result is in quarts.

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Key Concepts

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

measurement conversion
Measurement conversion involves changing a quantity expressed in one unit into another unit, which helps us understand and compare different amounts in a consistent way. Measurements in daily life often need to be converted to perform recipes, science experiments, or construction projects.
For example, in cooking, you might need to convert ingredients from cups to tablespoons or from grams to ounces. To do this efficiently, a conversion factor is essential. It's a number that helps us switch easily between units.
  • Identify the unit you have (in this case, pint) and the unit you want (quart).
  • Find the conversion factor between these units. For instance, 2 pints equal 1 quart.
Once these steps are clear, you can convert any amount of pints to quarts using basic arithmetic, which we'll discuss next.
basic arithmetic
Basic arithmetic is the foundation of math that includes simple operations such as addition, subtraction, multiplication, and division. In measurement conversion, multiplication and division are commonly used.
When converting \( \frac{1}{2} \) pint to quarts, we need to multiply, using the conversion factor we identified: \( \frac{1}{2} \text{ pint} \times \frac{1 \text{ quart}}{2 \text{ pints}} \).
Here, we multiply fractions:
  • Multiply the numerators: \( \frac{1}{2} \times 1 = \frac{1}{2} \).
  • Multiply the denominators: \( 1 \times 2 = 2 \).
  • The resulting fraction is \( \frac{1}{4} \).
This indicates \( \frac{1}{4} \) quart, showing how arithmetic rules help provide precise conversions.
unit conversion
Unit conversion is a practical skill that allows us to use different measurement systems and achieve uniformity across various scales. It involves the use of specific conversion factors to translate one unit into another, maintaining accurate values.
For example, when converting pints to quarts, the conversion factor is \( \frac{1 \text{ quart}}{2 \text{ pints}} \), which means you divide by 2.
  • This step ensures that the pint units cancel out, leaving only quarts.
  • The relationship here is simple: divide any amount of pints by 2 to find the number of quarts.
Understanding unit conversion enhances problem-solving skills, as it requires recognizing relationships between units and using arithmetic to perform calculations, making it a key skill in science, cooking, and everyday life.

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