Problem 69 - Prealgebra

Question

An average adult's body contains about 5 quarts of blood. If a person donates 1 pint of blood, about how many pints are left?

Step-by-Step Solution

Answer

9 pints are left after the donation.

Step 1: Understand Units of Measurement

Remember that there are 2 pints in a quart. This is important because the total amount of blood is initially given in quarts, and we need to work with pints.

Step 2: Convert Quarts to Pints

First, convert the total amount of blood from quarts to pints. Multiply 5 quarts by 2 pints per quart: \(5 \text{ quarts} \times 2 \text{ pints/quart} = 10 \text{ pints}\).

Step 3: Subtract the Donated Blood

If a person donates 1 pint of blood, to find out how many pints are left, subtract 1 pint from the total amount calculated in the previous step: \(10 \text{ pints} - 1 \text{ pint} = 9 \text{ pints}\).

Key Concepts

Understanding Measurement Units

Measurement units help us quantify physical quantities like length, volume, and weight. In everyday situations, they enable clear communication about quantities. In this exercise, we deal with the volume measurement units: quarts and pints.

• Quart: This unit is commonly used in the United States for liquid volume. It is one of the larger units when comparing to pints.
• Pint: A smaller unit of liquid measurement, where 1 quart equals 2 pints.

Understanding how these units relate to each other is crucial for unit conversion tasks. For instance, knowing that 1 quart equals 2 pints allows us to switch between these units easily to achieve precise measurements in mathematical problems.

Prealgebra Basics for Solving Problems

Prealgebra is the foundation of all higher mathematics and helps us solve everyday problems. In this context, prealgebra involves understanding how to convert units and perform calculations to find solutions.
When tackling a problem like this, identifying the right operation is vital. Here’s a general strategy to approach such problems:

• Identify what is given: Start by noting the quantity and units you're provided, such as 5 quarts of blood.
• Determine what you need to find: In this case, the remaining volume in pints after donation.
• Convert units if necessary: If the units don't match, convert them so they do, facilitating smooth calculations.

Prealgebra thus forms a crucial bridge in school mathematics that makes higher-level concepts accessible through basic operations like unit conversions and understanding numerical relationships.

Basic Mathematical Operations in Unit Conversion

Mathematical operations such as multiplication and subtraction are key to solving unit conversion problems.
Here's how these operations apply:

• Multiplication for Conversion: When converting units, if you have a known conversion rate (like 1 quart = 2 pints), you multiply the given quantity by this rate. Thus, converting 5 quarts to pints involves multiplying 5 by 2, giving us 10 pints.
• Subtraction for Adjusting Quantity: Once you’ve converted to the necessary units, you can use subtraction to account for changes. For instance, after donating 1 pint from the total 10 pints, you subtract 1 to find the remaining amount, which is 9 pints.

Being proficient with these operations is essential as they form the bedrock for more complex mathematical challenges. By mastering unit conversions and basic operations, students build a strong foundation to tackle more intricate problems with ease.