Multiply. Write Your Answer As A Fraction, Whole Number, Or Mixed Number.\[$\frac{3}{5} \times 8 \frac{1}{2} =\$\]\[$\square\$\]

Understanding the Problem

When multiplying fractions and mixed numbers, it's essential to follow the correct order of operations. In this problem, we are asked to multiply $\frac{3}{5}$ by $8 \frac{1}{2}$. To solve this, we need to first convert the mixed number to an improper fraction.

Converting Mixed Numbers to Improper Fractions

A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. In this case, $8 \frac{1}{2}$ can be converted to an improper fraction as follows:

$$8 \frac{1}{2} = \frac{(8 \times 2) + 1}{2} = \frac{17}{2}$$

Multiplying Fractions

Now that we have both numbers in fraction form, we can multiply them together. When multiplying fractions, we multiply the numerators together and the denominators together.

$$\frac{3}{5} \times \frac{17}{2} = \frac{3 \times 17}{5 \times 2} = \frac{51}{10}$$

Simplifying the Result

The result of the multiplication is $\frac{51}{10}$. However, this fraction can be simplified further by dividing both the numerator and the denominator by their greatest common divisor, which is 1.

$$\frac{51}{10} = \frac{51}{10}$$

Writing the Answer as a Mixed Number

Since the problem asks for the answer as a fraction, whole number, or mixed number, we can convert the improper fraction to a mixed number. To do this, we divide the numerator by the denominator and write the remainder as the new numerator.

$$\frac{51}{10} = 5 \frac{1}{10}$$

Conclusion

In conclusion, when multiplying fractions and mixed numbers, it's essential to follow the correct order of operations and convert mixed numbers to improper fractions. By doing so, we can simplify the result and write the answer in the desired format.

Key Takeaways

• To multiply fractions and mixed numbers, convert the mixed number to an improper fraction.
• Multiply the numerators together and the denominators together.
• Simplify the result by dividing both the numerator and the denominator by their greatest common divisor.
• Convert the improper fraction to a mixed number by dividing the numerator by the denominator and writing the remainder as the new numerator.

Practice Problems

1. Multiply $\frac{2}{3}$ by $4 \frac{2}{3}$.
2. Multiply $\frac{5}{6}$ by $3 \frac{1}{6}$.
3. Multiply $\frac{3}{4}$ by $2 \frac{3}{4}$.

Answer Key

1. $\frac{20}{9}$
2. $\frac{25}{12}$
3. $\frac{15}{8}$
   Multiplication of Fractions and Mixed Numbers: Q&A =====================================================

Frequently Asked Questions

Q: What is the correct order of operations when multiplying fractions and mixed numbers?

A: The correct order of operations is to convert the mixed number to an improper fraction, then multiply the numerators together and the denominators together.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and then add the numerator. For example, $8 \frac{1}{2}$ can be converted to an improper fraction as follows:

$$8 \frac{1}{2} = \frac{(8 \times 2) + 1}{2} = \frac{17}{2}$$

Q: What is the difference between multiplying fractions and multiplying whole numbers?

A: When multiplying fractions, we multiply the numerators together and the denominators together. When multiplying whole numbers, we simply multiply the numbers together.

Q: Can I simplify the result of multiplying fractions and mixed numbers?

A: Yes, you can simplify the result by dividing both the numerator and the denominator by their greatest common divisor.

Q: How do I write the answer as a mixed number?

A: To write the answer as a mixed number, divide the numerator by the denominator and write the remainder as the new numerator.

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

A: Some common mistakes to avoid include:

• Not converting the mixed number to an improper fraction
• Not multiplying the numerators together and the denominators together
• Not simplifying the result
• Not writing the answer in the desired format

Q: Can I use a calculator to multiply fractions and mixed numbers?

A: Yes, you can use a calculator to multiply fractions and mixed numbers. However, it's always a good idea to double-check your work by converting the mixed number to an improper fraction and multiplying the numerators together and the denominators together.

Q: How do I multiply fractions and mixed numbers with different denominators?

A: To multiply fractions and mixed numbers with different denominators, find the least common multiple (LCM) of the denominators and convert both fractions to have the LCM as the denominator.

Q: Can I multiply fractions and mixed numbers with negative numbers?

A: Yes, you can multiply fractions and mixed numbers with negative numbers. When multiplying fractions and mixed numbers with negative numbers, the result will be negative.

Q: How do I multiply fractions and mixed numbers with decimals?

A: To multiply fractions and mixed numbers with decimals, convert the decimal to a fraction and then multiply the fractions together.

Q: Can I multiply fractions and mixed numbers with variables?

A: Yes, you can multiply fractions and mixed numbers with variables. When multiplying fractions and mixed numbers with variables, the result will be a fraction with variables in the numerator and denominator.

Practice Problems

1. Multiply $\frac{2}{3}$ by $4 \frac{2}{3}$.
2. Multiply $\frac{5}{6}$ by $3 \frac{1}{6}$.
3. Multiply $\frac{3}{4}$ by $2 \frac{3}{4}$.

Answer Key

1. $\frac{20}{9}$
2. $\frac{25}{12}$
3. $\frac{15}{8}$

Conclusion

Multiplying fractions and mixed numbers can be a challenging task, but with practice and patience, you can become proficient in this area of mathematics. Remember to follow the correct order of operations, convert mixed numbers to improper fractions, and simplify the result. By doing so, you can ensure that your answers are accurate and in the desired format.