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Chapter 5: Problem 433

In the following exercises, write each rate as a fraction. 8.2 pounds per 3 square inches

Short Answer

Expert verified
The rate is \(\frac{8.2 \text{ pounds}}{3 \text{ square inches}}\).

Step by step solution

01

Identify the given rate

The given rate is '8.2 pounds per 3 square inches'.
02

Express the rate as a fraction

To express the rate as a fraction, note that the rate '8.2 pounds per 3 square inches' can be written as \(\frac{8.2 \text{ pounds}}{3 \text{ square inches}}\).
03

Simplify the fraction (if possible)

In this instance, \(\frac{8.2}{3}\) cannot be simplified further because 8.2 and 3 have no common factors other than 1.

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Key Concepts

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

Rates
A rate is a way to compare two different quantities with distinct units. For instance, 'miles per hour' is a rate comparing distance to time. In the given exercise, we compare weight and area: '8.2 pounds per 3 square inches'. This tells us how many pounds correspond to 3 square inches.
Recognizing rates helps in understanding relationships between different quantities. For example, knowing the rate of fuel consumption in 'miles per gallon' helps in understanding how efficient a car is with fuel.
Fractions
Fractions are essential in representing parts of a whole and relationships between quantities. In the context of rates, a fraction helps to visually and mathematically represent the rate. For the exercise '8.2 pounds per 3 square inches', the rate can be written as \(\frac{8.2 \text{ pounds}}{3 \text{ square inches}}\). This fractional representation tells us per unit area (in this case, square inches) how many pounds there are.
Remember, fractions consist of a numerator (the top number) and a denominator (the bottom number). Here, 8.2 is the numerator and 3 is the denominator.
Unit Conversion
Sometimes, it's necessary to convert units to make comparisons easier or understand the quantities better. For example, converting kilometers to miles or ounces to grams. In our exercise, there are no unit conversions needed since the units are specified directly.
However, understanding how to convert units is crucial. If we had '8.2 pounds per 3 square inches' and we needed to find the rate in 'kilograms per square meter', we would need to perform conversions for both weight and area. This ensures uniformity in comparing different rates.
Simplification
Simplification helps in making equations or fractions easier to understand and work with. It's the process of reducing a fraction to its simplest form. For instance, \(\frac{8.2}{3}\) cannot be simplified further since the numerator and denominator don鈥檛 have any common factors other than 1.
In cases where simplification is possible, identify the greatest common divisor (GCD) of the numerator and denominator and divide both by this number. This will give you the simplified form of the fraction. Simplification makes mathematical expressions cleaner and often easier to interpret and use.

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