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Chapter 9: Problem 35

Perform each indicated operation. $$ 8 \text { gal } 2 \mathrm{qt} \times 2 $$

Short Answer

Expert verified
17 gallons 0 quarts.

Step by step solution

01

Convert Gallons to Quarts

First, we need to convert gallons to quarts. Knowing that 1 gallon equals 4 quarts, multiply 8 gallons by 4 to convert to quarts.\[ 8 \text{ gal} = 8 \times 4 = 32 \text{ quarts} \]
02

Combine Quarts

Add the 2 quarts to the total quarts we have from converting gallons.\[ 32 \text{ quarts} + 2 \text{ quarts} = 34 \text{ quarts} \]
03

Multiply by 2

Now multiply the total quarts by 2, as the operation indicates.\[ 34 \text{ quarts} \times 2 = 68 \text{ quarts} \]
04

Convert Back to Gallons and Quarts

Finally, convert the total quarts back to gallons and quarts to present the final answer in the appropriate mixed unit format. Divide 68 quarts by 4 to find how many full gallons there are.\[ 68 \div 4 = 17 \text{ gal} \, 0 \text{ qt } \]

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Key Concepts

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

Gallons to Quarts
Understanding the relationship between gallons and quarts is essential in unit conversion. When converting gallons to quarts, it's important to know the conversion factor: 1 gallon is equal to 4 quarts.

This means that if you have multiple gallons, you can find the equivalent number of quarts by multiplying the number of gallons by 4.
  • For example, if you have 8 gallons, you multiply 8 by 4 to get 32 quarts.
Understanding this basic unit conversion will help you handle problems involving liquid volumes in a straightforward manner. Try to remember this conversion as it frequently appears in different scenarios.
Multiplying Measurements
When handling measurements, multiplying them often involves converting to a common unit first.

Once your units are congruent, you can perform operations such as multiplication with ease. In our exercise, after converting 8 gallons to quarts, we added the remaining quarts, resulting in 34 quarts. Then, we multiply by the factor stated in the problem.
  • In our example, we have 34 quarts and we need to multiply by 2, which gives us 68 quarts.
Multiplying measurements not only requires you to correctly calculate the arithmetic but also ensure that the units involved are consistent. After achieving these consistent units, you can proceed with multiplication confidently.
Converting Units in Calculations
Handling conversions in calculations is crucial for solving unit-related problems accurately. Not only do you need to convert units initially, but sometimes you must also revert them to their original form.

In many cases, like the problem we solved, you'll be required to present your answer in the starting unit.
  • After calculating 68 quarts, notice that we were asked to convert back into gallons.
This step ensures the problem reflects its original context, which could be helpful in day-to-day scenarios where mixed units are prevalent. To do this, divide the total quarts back by 4 to revert to gallons. This balancing act of converting back and forth emphasizes understanding the relationships between various measurement systems.

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