Problem 55 - Prealgebra

Question

Cups If a regular-size coffee cup holds about \(\frac{1}{2}\) pint, about how many cups can be filled from a 1-gallon coffee maker?

Step-by-Step Solution

Answer

A 1-gallon coffee maker can fill 16 cups.

Step 1: Understand the conversion

First, we need to know how many pints are in a gallon. By definition, 1 gallon equals 8 pints.

Step 2: Determine how many cups can fit in one pint

Since one regular-size cup holds \(\frac{1}{2}\) pint, this means that each pint can fill 2 cups (since \(\frac{1}{1/2} = 2\)).

Step 3: Calculate the total number of cups

If 1 gallon equals 8 pints, and each pint fills 2 cups, then the number of cups from 1 gallon is \(8 \, \text{pints} \times 2 \, \text{cups per pint} = 16 \, \text{cups}\).

Key Concepts

Pints to Gallons Conversion

When it comes to volume measurement, understanding conversions between different units is crucial. One common conversion is between pints and gallons. Knowing that there are exactly 8 pints in 1 gallon is fundamental.
This is a key piece of information because it allows you to work seamlessly between these two units of liquid volume.
For instance, if you have a recipe that requires 2 gallons of milk, you can quickly determine that this is equivalent to 16 pints.
Remember: this conversion is constant. No matter the substance, 1 gallon always equals 8 pints.

• 1 gallon = 8 pints
• 2 gallons = 16 pints
• 3 gallons = 24 pints

Being comfortable with this conversion enhances your fluid volume calculations, making tasks in the kitchen, science labs, or anywhere else that requires volume measurement much simpler.

Volume Measurement

Volume measurement refers to the determination or assessment of the amount of space that a substance (like a liquid) occupies.
Units like pints, gallons, cups, liters, and milliliters are used based on geographic location and context.
In the United States, units such as pints, gallons, and cups are common. Knowing how to convert between these units can make everyday tasks easier.

• A pint is half of a quart, and there are four quarts in a gallon.
• A cup is typically half a pint (especially for recipes in cooking).
• Converting these allows for flexibility in understanding and using various amounts as needed.

To convert between these units, using multiplication or division is necessary. For example, if you know how many gallons you have, multiplying by 8 gives you the number of pints.

Problem-Solving Steps

Approaching problems methodically can greatly improve understanding and accuracy. Let's explore a clear problem-solving approach:

**Step 1: Understand the Problem.**
Start by identifying what the problem is asking. Here, you want to determine how many cups you can fill from 1 gallon using the given conversion rate.

**Step 2: Identify Known Information.**
Recognize that 1 gallon is 8 pints, and each cup holds 1/2 pint. This helps understand how many cups you can fill from a single pint.

**Step 3: Implement the Solution.**
Use the information: since 1 pint can fill 2 cups, multiply the number of pints in a gallon by 2 to find the number of cups.
By multiplying 8 pints by 2 cups per pint, you find that 1 gallon can fill 16 cups.

**Conclusion:**
Solving step-by-step ensures nothing is overlooked and each part of the problem is addressed comprehensively.