A Recipe Calls For $\frac{35}{6}$ Ounces Of Water And $\frac{21}{3}$ Ounces Of Milk. How Many More Ounces Of Water Than Milk Does The Recipe Call For?

Feb 27, 2025 by ADMIN 151 views

A Recipe for Math: Calculating the Difference Between Water and Milk

When it comes to cooking, recipes often require precise measurements of ingredients to achieve the desired outcome. In this article, we will explore a recipe that calls for a specific amount of water and milk. We will calculate the difference between the amount of water and milk required, providing a clear understanding of the mathematical concept involved.

The recipe calls for $\frac{35}{6}$ ounces of water and $\frac{21}{3}$ ounces of milk. To find the difference between the amount of water and milk, we need to subtract the amount of milk from the amount of water.

Simplifying the Fractions

Before we can perform the subtraction, we need to simplify the fractions. The fraction $\frac{35}{6}$ can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 1. Therefore, the fraction $\frac{35}{6}$ remains the same.

The fraction $\frac{21}{3}$ can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3. This results in the simplified fraction $\frac{7}{1}$ , which is equivalent to 7.

Subtracting the Fractions

Now that we have simplified the fractions, we can perform the subtraction. To subtract $\frac{7}{1}$ from $\frac{35}{6}$ , we need to find a common denominator. The least common multiple of 1 and 6 is 6. Therefore, we can rewrite $\frac{7}{1}$ as $\frac{42}{6}$ .

Now we can perform the subtraction:

\frac{35}{6} - \frac{42}{6} = \frac{35-42}{6} = \frac{-7}{6}

Interpreting the Result

The result of the subtraction is $\frac{-7}{6}$ . This means that the recipe calls for $\frac{7}{6}$ ounces less of milk than water.

Converting the Result to a Decimal

To make the result more understandable, we can convert it to a decimal. To do this, we divide the numerator by the denominator:

\frac{-7}{6} = -1.1667

In conclusion, the recipe calls for $\frac{35}{6}$ ounces of water and $\frac{21}{3}$ ounces of milk. By simplifying the fractions and performing the subtraction, we found that the recipe calls for $\frac{7}{6}$ ounces less of milk than water. This result can be converted to a decimal, providing a more understandable representation of the difference between the amount of water and milk required.

The concept of subtracting fractions is essential in various real-world applications, such as cooking, science, and engineering. In cooking, it is crucial to measure ingredients accurately to achieve the desired outcome. In science and engineering, subtracting fractions is used to calculate differences between quantities, such as the difference between the amount of a substance required and the amount available.

When working with fractions, it is essential to simplify them before performing operations. This can be done by dividing both the numerator and denominator by their greatest common divisor. Additionally, finding a common denominator is crucial when subtracting fractions.

When subtracting fractions, it is common to make mistakes by not finding a common denominator or not simplifying the fractions. To avoid these mistakes, it is essential to follow the steps outlined in this article.

In our previous article, we explored a recipe that calls for a specific amount of water and milk. We calculated the difference between the amount of water and milk required, providing a clear understanding of the mathematical concept involved. In this article, we will answer some frequently asked questions related to the recipe and the mathematical concept involved.

Q: What is the difference between the amount of water and milk required in the recipe?

A: The recipe calls for $\frac{35}{6}$ ounces of water and $\frac{21}{3}$ ounces of milk. By simplifying the fractions and performing the subtraction, we found that the recipe calls for $\frac{7}{6}$ ounces less of milk than water.

Q: How do I simplify fractions?

A: To simplify a fraction, you need to divide both the numerator and denominator by their greatest common divisor. For example, the fraction $\frac{35}{6}$ can be simplified by dividing both the numerator and denominator by 1, resulting in the same fraction. The fraction $\frac{21}{3}$ can be simplified by dividing both the numerator and denominator by 3, resulting in the simplified fraction $\frac{7}{1}$ .

Q: What is the least common multiple (LCM) of two numbers?

A: The LCM of two numbers is the smallest number that is a multiple of both numbers. For example, the LCM of 1 and 6 is 6, because 6 is the smallest number that is a multiple of both 1 and 6.

Q: How do I find the LCM of two numbers?

A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists. Alternatively, you can use the following formula:

LCM(a, b) = (a × b) / GCD(a, b)

where GCD(a, b) is the greatest common divisor of a and b.

Q: What is the greatest common divisor (GCD) of two numbers?

A: The GCD of two numbers is the largest number that divides both numbers without leaving a remainder. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that divides both 12 and 18 without leaving a remainder.

Q: How do I find the GCD of two numbers?

A: To find the GCD of two numbers, you can use the following methods:

List the factors of each number and find the largest factor that appears in both lists.
Use the Euclidean algorithm, which involves repeatedly dividing the larger number by the smaller number and taking the remainder.
Use the following formula:

GCD(a, b) = (a × b) / LCM(a, b)

where LCM(a, b) is the least common multiple of a and b.

Q: What is the difference between the amount of water and milk required in the recipe in decimal form?

A: To convert the fraction $\frac{-7}{6}$ to a decimal, we divide the numerator by the denominator:

\frac{-7}{6} = -1.1667

In conclusion, we have answered some frequently asked questions related to the recipe and the mathematical concept involved. We hope that this article has provided a clear understanding of the mathematical concept involved and has helped to clarify any doubts that you may have had.