Problem 11 - Prealgebra

Question

Use the following information. One pint of liquid is the same as 16 fluid ounces. Suppose the number of pints of liquid is represented by \(p\). Write an expression to find the number of fluid ounces.

Step-by-Step Solution

Answer

The expression is \( 16p \).

Step 1: Identify the Conversion Rate

We start by identifying the conversion rate between pints and fluid ounces. According to the information given: \( 1 \text{ pint} = 16 \text{ fluid ounces} \). This is the crucial conversion factor needed for the expression.

Step 2: Use the Conversion Rate

Knowing the conversion rate, we need to express the number of fluid ounces in terms of the number of pints \( p \). Since every pint contains 16 fluid ounces, multiplying the number of pints by 16 will give us the required number of fluid ounces.

Step 3: Write the Expression

Since each pint corresponds to 16 fluid ounces, the expression for the number of fluid ounces in terms of \( p \) is given by \( 16p \). This expression allows us to calculate the fluid ounces for any number of pints.

Key Concepts

Understanding Conversion Factors

In pre-algebra, conversion factors are vital tools. They help us change one unit of measurement into another. Imagine them as bridges that let you travel from one measurement system to another. In our exercise, we are bridging the gap between pints and fluid ounces.

• A conversion factor is a ratio or a fraction.
• In this case, the conversion factor is \( 1 \text{ pint} = 16 \text{ fluid ounces} \).
• This means for every 1 pint, there are 16 fluid ounces.

By understanding that this is a ratio, you can apply it to any number of pints. To find out how many fluid ounces are in multiple pints, keeping this conversion factor in mind is essential.

Building Mathematical Expressions

A mathematical expression represents a quantity or a relationship. It does this using numbers, variables, and operation symbols.

• In our exercise, the pint is represented by the variable \( p \).
• To find the fluid ounces, we write the relationship between pints and fluid ounces mathematically.
• We use multiplication because each pint equals 16 fluid ounces.

Thus, the expression is \( 16p \). This expression tells us: multiply the number of pints by 16, and you will get the total fluid ounces.

Mastering Unit Conversion

Unit conversions allow you to work interchangeably with different measurement systems. It is a key skill in mathematics and science.

• Here, we convert pints into fluid ounces.
• Think of pints as a larger unit and fluid ounces as a smaller one.
• To convert, multiply the number of pints by the conversion factor (16).

This means for any amount, simply inserting it into the expression \( 16p \) enables the conversion. Understanding this process ensures you can flexibly move between units with confidence in your calculations.