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Simplifying fractions is a crucial mathematical skill. It helps to make complex ratios easier to understand and compare.
Let's break down how to simplify fractions using the fraction from the original exercise: \( \frac{140 \text{ calories}}{12 \text{ ounces}} \)
To simplify this fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator.
This will allow us to divide both the top and bottom of the fraction by the same number, reducing it to its simplest form. In our case, the GCD of 140 and 12 is 4.
So we divide both 140 and 12 by 4: \( \frac{140}{4} = 35 \)
\( \frac{12}{4} = 3 \)
This results in the simplified fraction: \( \frac{35 \text{ calories}}{3 \text{ ounces}} \)
This simplified form is easier to work with and understand.

Rates are a way to compare different quantities. By writing a rate as a fraction, you can easily see the relationship between the two quantities involved.
In the exercise, we had a rate of 140 calories per 12 ounces. When we write this as a fraction, it becomes: \( \frac{140 \text{ calories}}{12 \text{ ounces}} \)
This fraction tells us that for every 12 ounces, there are 140 calories.
Writing rates as fractions can help in solving problems related to proportions, making calculations straightforward.

The greatest common divisor (GCD) is the largest number that divides two or more numbers without leaving a remainder.
Finding the GCD is essential when simplifying fractions, as it allows you to reduce the fraction to its simplest form.
For the fraction \( \frac{140 \text{ calories}}{12 \text{ ounces}} \), we found that the GCD of 140 and 12 is 4.
Here's how you can find the GCD: \begin{enumerate} \item List the factors of both numbers. \(* Factors of 140: 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140 \) \(* Factors of 12: 1, 2, 3, 4, 6, 12 \) \item Identify the common factors. In this case, the common factors are 1, 2, and 4. \item The largest of these common factors is the GCD, which is 4. \end{enumerate}
By using the GCD to simplify fractions, you make them easier to understand and use in further calculations.