Multiply The Following Fractions. Reduce Your Answer To Lowest Terms. 1 8 × 1 9 = \frac{1}{8} \times \frac{1}{9} = 8 1 ​ × 9 1 ​ = A. 2 17 \frac{2}{17} 17 2 ​ B. 2 72 \frac{2}{72} 72 2 ​ C. 1 72 \frac{1}{72} 72 1 ​ D. 17 72 \frac{17}{72} 72 17 ​

Introduction

Multiplying fractions is a fundamental concept in mathematics that helps us solve various problems in different fields, such as science, engineering, and finance. In this article, we will focus on multiplying two fractions, $\frac{1}{8}$ and $\frac{1}{9}$, and reducing the answer to its lowest terms.

What are Fractions?

A fraction is a way to represent a part of a whole. It consists of two parts: the numerator (the top number) and the denominator (the bottom number). The numerator tells us how many equal parts we have, while the denominator tells us how many parts the whole is divided into.

Multiplying Fractions

To multiply two fractions, we simply multiply the numerators together and multiply the denominators together. This is represented by the following formula:

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

Example: Multiplying $\frac{1}{8}$ and $\frac{1}{9}$

Using the formula above, we can multiply $\frac{1}{8}$ and $\frac{1}{9}$ as follows:

$\frac{1}{8} \times \frac{1}{9} = \frac{1 \times 1}{8 \times 9} = \frac{1}{72}$

Reducing the Answer to Lowest Terms

To reduce the answer to its lowest terms, we need to find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 1 and 72 is 1, so the answer is already in its lowest terms.

Answer Options

Now that we have multiplied the fractions and reduced the answer to its lowest terms, let's compare our answer with the options provided:

A. $\frac{2}{17}$ B. $\frac{2}{72}$ C. $\frac{1}{72}$ D. $\frac{17}{72}$

Our answer, $\frac{1}{72}$, matches option C.

Conclusion

Multiplying fractions is a straightforward process that involves multiplying the numerators together and multiplying the denominators together. By following this formula and reducing the answer to its lowest terms, we can solve various problems in mathematics and other fields. In this article, we multiplied $\frac{1}{8}$ and $\frac{1}{9}$ and reduced the answer to its lowest terms, resulting in $\frac{1}{72}$.

Common Mistakes to Avoid

When multiplying fractions, it's essential to remember the following common mistakes to avoid:

• Not multiplying the numerators together: Make sure to multiply the numerators together to get the correct numerator.
• Not multiplying the denominators together: Make sure to multiply the denominators together to get the correct denominator.
• Not reducing the answer to its lowest terms: Make sure to reduce the answer to its lowest terms by finding the greatest common divisor (GCD) of the numerator and the denominator.

Real-World Applications

Multiplying fractions has numerous real-world applications, such as:

• Cooking: When a recipe calls for a fraction of an ingredient, multiplying fractions can help you scale up or down the recipe.
• Science: In physics and chemistry, multiplying fractions is used to calculate quantities such as velocity, acceleration, and concentration.
• Finance: In finance, multiplying fractions is used to calculate interest rates, investment returns, and other financial metrics.

Practice Problems

To practice multiplying fractions, try the following problems:

• $\frac{2}{3} \times \frac{4}{5} = ?$
• $\frac{3}{4} \times \frac{2}{3} = ?$
• $\frac{5}{6} \times \frac{3}{4} = ?$

Conclusion

Introduction

Multiplying fractions is a fundamental concept in mathematics that helps us solve various problems in different fields, such as science, engineering, and finance. In this article, we will provide a Q&A guide to help you understand and master the concept of 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 the numerators together?

A: To multiply the numerators together, simply multiply the two numbers together. For example, if you are multiplying $\frac{2}{3}$ and $\frac{4}{5}$, you would multiply 2 and 4 together to get 8.

Q: How do I multiply the denominators together?

A: To multiply the denominators together, simply multiply the two numbers together. For example, if you are multiplying $\frac{2}{3}$ and $\frac{4}{5}$, you would multiply 3 and 5 together to get 15.

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

A: The greatest common divisor (GCD) is the largest number that divides two or more 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 reduce the answer to its lowest terms?

A: To reduce the answer to its lowest terms, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Then, divide both the numerator and the denominator by the GCD. For example, if you have the fraction $\frac{12}{18}$, the GCD of 12 and 18 is 6. So, you would divide both 12 and 18 by 6 to get $\frac{2}{3}$.

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

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

• Not multiplying the numerators together: Make sure to multiply the numerators together to get the correct numerator.
• Not multiplying the denominators together: Make sure to multiply the denominators together to get the correct denominator.
• Not reducing the answer to its lowest terms: Make sure to reduce the answer to its lowest terms by finding the greatest common divisor (GCD) of the numerator and the denominator.

Q: What are some real-world applications of multiplying fractions?

A: Multiplying fractions has numerous real-world applications, such as:

• Cooking: When a recipe calls for a fraction of an ingredient, multiplying fractions can help you scale up or down the recipe.
• Science: In physics and chemistry, multiplying fractions is used to calculate quantities such as velocity, acceleration, and concentration.
• Finance: In finance, multiplying fractions is used to calculate interest rates, investment returns, and other financial metrics.

Q: How can I practice multiplying fractions?

A: You can practice multiplying fractions by trying the following problems:

• $\frac{2}{3} \times \frac{4}{5} = ?$
• $\frac{3}{4} \times \frac{2}{3} = ?$
• $\frac{5}{6} \times \frac{3}{4} = ?$

Conclusion

Multiplying fractions is a fundamental concept in mathematics that has numerous real-world applications. By following the formula and reducing the answer to its lowest terms, we can solve various problems in mathematics and other fields. Remember to avoid common mistakes and practice multiplying fractions to become proficient in this skill.

Additional Resources

For more information on multiplying fractions, you can try the following resources:

• Khan Academy: Multiplying Fractions
• Mathway: Multiplying Fractions
• IXL: Multiplying Fractions

Practice Problems

Try the following practice problems to test your skills:

• $\frac{2}{3} \times \frac{4}{5} = ?$
• $\frac{3}{4} \times \frac{2}{3} = ?$
• $\frac{5}{6} \times \frac{3}{4} = ?$

Answer Key

• $\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$
• $\frac{3}{4} \times \frac{2}{3} = \frac{1}{2}$
• $\frac{5}{6} \times \frac{3}{4} = \frac{5}{8}$