A Sauce Recipe Calls For \[$\frac{3}{4}\$\] Cup Of Chicken Broth. To Make Enough Sauce For A Party, Marcy Needs To Triple The Recipe. $\[ \frac{3}{4} \times 3 = \left(\frac{3}{4}\right) \left(\frac{3}{1}\right) \\]She Estimates That

Introduction

When it comes to cooking for a party, having the right amount of ingredients is crucial. In this case, Marcy needs to triple a sauce recipe that calls for $\frac{3}{4}$ cup of chicken broth. To do this, she must multiply the fraction $\frac{3}{4}$ by 3. In this article, we will explore how to multiply fractions and apply this concept to Marcy's sauce recipe.

Multiplying Fractions

Multiplying fractions is a straightforward process that involves multiplying the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately. To multiply two fractions, we follow these steps:

1. Multiply the numerators: $a \times b$
2. Multiply the denominators: $c \times d$
3. Write the product as a fraction: $\frac{a \times b}{c \times d}$

Let's apply this process to Marcy's sauce recipe. We need to multiply $\frac{3}{4}$ by 3.

Multiplying $\frac{3}{4}$ by 3

To multiply $\frac{3}{4}$ by 3, we can use the distributive property of multiplication over addition. This means that we can multiply 3 by the numerator (3) and then multiply 3 by the denominator (4).

$\frac{3}{4} \times 3 = \left(\frac{3}{4}\right) \left(\frac{3}{1}\right)$

Using the distributive property, we can rewrite this as:

$\frac{3 \times 3}{4 \times 1}$

Now, we can simplify the numerator and denominator separately.

Simplifying the Numerator and Denominator

The numerator is $3 \times 3 = 9$. The denominator is $4 \times 1 = 4$.

So, the product of $\frac{3}{4}$ and 3 is:

$\frac{9}{4}$

Applying this Concept to Marcy's Sauce Recipe

Now that we have multiplied $\frac{3}{4}$ by 3, we can apply this concept to Marcy's sauce recipe. Marcy needs to triple the recipe, which means she needs to multiply the amount of chicken broth by 3.

Since the recipe calls for $\frac{3}{4}$ cup of chicken broth, Marcy needs to multiply this amount by 3.

$\frac{3}{4} \times 3 = \frac{9}{4}$

So, Marcy needs to use $\frac{9}{4}$ cup of chicken broth to make enough sauce for the party.

Conclusion

In this article, we explored how to multiply fractions and applied this concept to Marcy's sauce recipe. We saw that multiplying $\frac{3}{4}$ by 3 resulted in $\frac{9}{4}$. This means that Marcy needs to use $\frac{9}{4}$ cup of chicken broth to make enough sauce for the party. By understanding how to multiply fractions, we can apply this concept to a variety of real-world problems, including cooking and recipe scaling.

Real-World Applications of Multiplying Fractions

Multiplying fractions has many real-world applications, including:

• Cooking and recipe scaling: As we saw in Marcy's sauce recipe, multiplying fractions can help us scale up or down a recipe to make the right amount of food.
• Science and engineering: Multiplying fractions is used in many scientific and engineering applications, such as calculating the area of a rectangle or the volume of a cube.
• Finance and economics: Multiplying fractions is used in finance and economics to calculate interest rates, investment returns, and other financial metrics.

Tips and Tricks for Multiplying Fractions

Here are some tips and tricks for multiplying fractions:

• Use the distributive property: When multiplying fractions, use the distributive property to multiply the numerator and denominator separately.
• Simplify the numerator and denominator: Simplify the numerator and denominator separately to make the calculation easier.
• Use a calculator: If you're struggling with multiplying fractions, use a calculator to help you with the calculation.

Common Mistakes to Avoid When Multiplying Fractions

Here are some common mistakes to avoid when multiplying fractions:

• Not using the distributive property: Failing to use the distributive property can lead to incorrect calculations.
• Not simplifying the numerator and denominator: Failing to simplify the numerator and denominator can make the calculation more difficult than it needs to be.
• Not using a calculator: Failing to use a calculator can lead to errors in the calculation.

Conclusion

Q&A: Multiplying Fractions

Q: What is the formula for multiplying fractions?

A: The formula for multiplying fractions is:

$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$

Q: How do I multiply fractions with different denominators?

A: To multiply fractions with different denominators, you need to find the least common multiple (LCM) of the denominators. Then, multiply the numerators and denominators separately, and simplify the result.

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

A: The LCM of two numbers is the smallest number that both numbers can divide into evenly. For example, the LCM of 4 and 6 is 12.

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction, divide the numerator and denominator by their greatest common divisor (GCD). For example, if you have the fraction $\frac{12}{16}$, you can simplify it by dividing both numbers by 4, resulting in $\frac{3}{4}$.

Q: Can I multiply a fraction by a whole number?

A: Yes, you can multiply a fraction by a whole number. To do this, simply multiply the numerator by the whole number, and keep the denominator the same.

Q: How do I multiply a fraction by a decimal?

A: To multiply a fraction by a decimal, convert the decimal to a fraction by dividing it by 1. Then, multiply the fractions together.

Q: What is the difference between multiplying fractions and dividing fractions?

A: Multiplying fractions involves multiplying the numerators and denominators separately, while dividing fractions involves inverting the second fraction and multiplying.

Q: Can I multiply fractions with negative numbers?

A: Yes, you can multiply fractions with negative numbers. To do this, simply multiply the numerators and denominators separately, and remember that a negative times a negative is a positive.

Q: How do I multiply fractions with variables?

A: To multiply fractions with variables, simply multiply the numerators and denominators separately, and remember to distribute the variables to the terms in the numerator and denominator.

Q: Can I use a calculator to multiply fractions?

A: Yes, you can use a calculator to multiply fractions. Simply enter the fractions into the calculator, and it will give you the product.

Q: What are some common mistakes to avoid when multiplying fractions?

A: Some common mistakes to avoid when multiplying fractions include:

• Not using the distributive property
• Not simplifying the numerator and denominator
• Not using a calculator when needed
• Not inverting the second fraction when dividing

Conclusion

In conclusion, multiplying fractions is a crucial concept in mathematics that has many real-world applications. By understanding how to multiply fractions, you can apply this concept to a variety of problems, including cooking and recipe scaling. Remember to use the distributive property, simplify the numerator and denominator, and use a calculator if needed to avoid common mistakes. With practice and patience, you'll become a pro at multiplying fractions in no time!