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Introduction

Multiplying fractions is a fundamental concept in mathematics that helps us solve various problems, including those involving weights and measurements. In this article, we will explore how to multiply fractions to find the weight of rocks used in an aquarium. We will use the example of Venetta, who bought 15 pounds of rocks for her aquarium and used $\frac{3}{5}$ of them.

Understanding the Problem

Venetta bought 15 pounds of rocks for her aquarium. She wants to know how many pounds of rocks she used. To find the answer, we need to multiply the fraction $\frac{3}{5}$ by the total weight of rocks, which is 15 pounds.

Multiplying Fractions

To multiply fractions, we need to multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom). In this case, we have:

$\frac{3}{5} \times 15$

To multiply a fraction by a whole number, we can multiply the numerator by the whole number and keep the denominator the same. So, we can rewrite the problem as:

$\frac{3 \times 15}{5}$

Simplifying the Fraction

Now, we need to simplify the fraction by multiplying the numerator and the denominator. We can do this by multiplying 3 and 15:

$3 \times 15 = 45$

So, the fraction becomes:

$\frac{45}{5}$

Dividing the Numerator by the Denominator

To simplify the fraction further, we can divide the numerator by the denominator. We can do this by dividing 45 by 5:

$45 \div 5 = 9$

So, the final answer is:

$\frac{45}{5} = 9$

Conclusion

In this article, we learned how to multiply fractions to find the weight of rocks used in an aquarium. We used the example of Venetta, who bought 15 pounds of rocks and used $\frac{3}{5}$ of them. By multiplying the fraction by the total weight of rocks, we found that Venetta used 9 pounds of rocks in her aquarium.

Real-World Applications

Multiplying fractions has many real-world applications, including:

• Cooking: When a recipe calls for a certain amount of an ingredient, we need to multiply the fraction by the total amount of the ingredient to find the amount we need.
• Building: When building a structure, we need to multiply the fraction by the total amount of materials to find the amount we need.
• Science: When conducting experiments, we need to multiply the fraction by the total amount of materials to find the amount we need.

Tips and Tricks

Here are some tips and tricks for multiplying fractions:

• Use a calculator: If you have a calculator, you can use it to multiply fractions quickly and easily.
• Simplify the fraction: Before multiplying the fraction, simplify it by dividing the numerator by the denominator.
• Use a diagram: If you are having trouble multiplying fractions, try using a diagram to help you visualize the problem.

Practice Problems

Here are some practice problems to help you practice multiplying fractions:

• $\frac{2}{3} \times 12 = ?$
• $\frac{4}{5} \times 15 = ?$
• $\frac{3}{4} \times 20 = ?$

Answer Key

Here are the answers to the practice problems:

• $\frac{2}{3} \times 12 = 8$
• $\frac{4}{5} \times 15 = 12$
• $\frac{3}{4} \times 20 = 15$

Conclusion

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Frequently Asked Questions

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 a fraction by a whole number?

A: To multiply a fraction by a whole number, you can multiply the numerator by the whole number and keep the denominator the same. For example:

$\frac{3}{5} \times 12 = \frac{3 \times 12}{5} = \frac{36}{5}$

Q: Can I multiply a fraction by a decimal?

A: Yes, you can multiply a fraction by a decimal. To do this, you can convert the decimal to a fraction and then multiply the fractions. For example:

$\frac{3}{5} \times 0.8 = \frac{3}{5} \times \frac{8}{10} = \frac{24}{50}$

Q: How do I simplify a fraction after multiplying?

A: To simplify a fraction after multiplying, you can divide the numerator by the denominator. For example:

$\frac{36}{5} = 7.2$

Q: Can I multiply mixed numbers?

A: Yes, you can multiply mixed numbers. To do this, you can convert the mixed numbers to improper fractions and then multiply the fractions. For example:

$2\frac{1}{3} \times 3\frac{1}{4} = \frac{7}{3} \times \frac{13}{4} = \frac{91}{12}$

Q: How do I divide fractions?

A: To divide fractions, you can invert the second fraction and multiply. For example:

$\frac{3}{5} \div \frac{2}{3} = \frac{3}{5} \times \frac{3}{2} = \frac{9}{10}$

Q: Can I multiply fractions with different denominators?

A: Yes, you can multiply fractions with different denominators. To do this, you can find the least common multiple (LCM) of the denominators and then multiply the fractions. For example:

$\frac{3}{5} \times \frac{4}{7} = \frac{3 \times 4}{5 \times 7} = \frac{12}{35}$

Q: How do I use multiplying fractions in real-life situations?

A: Multiplying fractions has many real-life applications, including:

• Cooking: When a recipe calls for a certain amount of an ingredient, you need to multiply the fraction by the total amount of the ingredient to find the amount you need.
• Building: When building a structure, you need to multiply the fraction by the total amount of materials to find the amount you need.
• Science: When conducting experiments, you need to multiply the fraction by the total amount of materials to find the amount you need.

Conclusion

In this article, we answered some frequently asked questions about multiplying fractions. We covered topics such as multiplying fractions by whole numbers, decimals, and mixed numbers, as well as dividing fractions and multiplying fractions with different denominators. We also discussed the real-life applications of multiplying fractions and provided some examples to help illustrate the concepts.