Multiply. { -5 \frac{1}{2} \times -9 \frac{1}{10} = \square$}$

Introduction

Multiplication of mixed numbers is a fundamental concept in mathematics that involves multiplying two or more numbers, each of which is a combination of a whole number and a fraction. In this article, we will explore the concept of multiplying mixed numbers, with a focus on the specific problem of multiplying $-5 \frac{1}{2}$ and $-9 \frac{1}{10}$.

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction. For example, $3 \frac{1}{4}$ is a mixed number that represents the sum of 3 and the fraction $\frac{1}{4}$.

Multiplying Mixed Numbers

To multiply mixed numbers, we need to follow a specific procedure. The procedure involves converting the mixed numbers to improper fractions, multiplying the fractions, and then converting the result back to a mixed number.

Step 1: Convert Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we need to multiply the whole number part by the denominator and then add the numerator. The result is the new numerator, and the denominator remains the same.

For example, to convert $-5 \frac{1}{2}$ to an improper fraction, we multiply the whole number part (-5) by the denominator (2) and add the numerator (1). The result is $-11$ as the new numerator, and the denominator remains 2. Therefore, $-5 \frac{1}{2} = -\frac{11}{2}$.

Similarly, to convert $-9 \frac{1}{10}$ to an improper fraction, we multiply the whole number part (-9) by the denominator (10) and add the numerator (1). The result is $-91$ as the new numerator, and the denominator remains 10. Therefore, $-9 \frac{1}{10} = -\frac{91}{10}$.

Step 2: Multiply the Fractions

Now that we have converted the mixed numbers to improper fractions, we can multiply the fractions.

To multiply two fractions, we need to multiply the numerators and multiply the denominators. The result is a new fraction, which is the product of the two original fractions.

In this case, we need to multiply $-\frac{11}{2}$ and $-\frac{91}{10}$. To do this, we multiply the numerators (-11 and -91) and multiply the denominators (2 and 10). The result is $-\frac{11 \times -91}{2 \times 10}$.

Step 3: Simplify the Result

Now that we have multiplied the fractions, we need to simplify the result. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator and divide both numbers by the GCD.

In this case, the numerator is $11 \times -91 = -1001$ and the denominator is $2 \times 10 = 20$. The GCD of -1001 and 20 is 1, so we cannot simplify the fraction further.

Therefore, the result of multiplying $-5 \frac{1}{2}$ and $-9 \frac{1}{10}$ is $-\frac{1001}{20}$.

Conclusion

Multiplying mixed numbers involves converting the mixed numbers to improper fractions, multiplying the fractions, and then converting the result back to a mixed number. In this article, we have explored the concept of multiplying mixed numbers, with a focus on the specific problem of multiplying $-5 \frac{1}{2}$ and $-9 \frac{1}{10}$. We have shown that the result of multiplying these two mixed numbers is $-\frac{1001}{20}$.

Example Problems

Here are a few example problems that involve multiplying mixed numbers:

• $2 \frac{1}{3} \times 3 \frac{1}{4} = \square$
• $4 \frac{2}{5} \times 2 \frac{3}{10} = \square$
• $1 \frac{1}{2} \times 3 \frac{1}{5} = \square$

Practice Problems

Here are a few practice problems that involve multiplying mixed numbers:

• Multiply $-3 \frac{1}{4}$ and $-2 \frac{1}{5}$.
• Multiply $2 \frac{3}{10}$ and $3 \frac{1}{2}$.
• Multiply $1 \frac{1}{3}$ and $2 \frac{2}{5}$.

Answer Key

Here are the answers to the example problems and practice problems:

• $2 \frac{1}{3} \times 3 \frac{1}{4} = \frac{25}{12}$
• $4 \frac{2}{5} \times 2 \frac{3}{10} = \frac{83}{25}$
• $1 \frac{1}{2} \times 3 \frac{1}{5} = \frac{13}{5}$
• Multiply $-3 \frac{1}{4}$ and $-2 \frac{1}{5}$: $-\frac{77}{20}$
• Multiply $2 \frac{3}{10}$ and $3 \frac{1}{2}$: $\frac{33}{10}$
• Multiply $1 \frac{1}{3}$ and $2 \frac{2}{5}$: $\frac{17}{15}$
  Multiplication of Mixed Numbers: A Q&A Guide =====================================================

Introduction

Multiplication of mixed numbers is a fundamental concept in mathematics that involves multiplying two or more numbers, each of which is a combination of a whole number and a fraction. In this article, we will explore the concept of multiplying mixed numbers through a series of questions and answers.

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number part, $b$ is the numerator of the fraction, and $c$ is the denominator of the fraction.

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

A: To convert a mixed number to an improper fraction, you need to multiply the whole number part by the denominator and then add the numerator. The result is the new numerator, and the denominator remains the same.

For example, to convert $-5 \frac{1}{2}$ to an improper fraction, you multiply the whole number part (-5) by the denominator (2) and add the numerator (1). The result is $-11$ as the new numerator, and the denominator remains 2. Therefore, $-5 \frac{1}{2} = -\frac{11}{2}$.

Q: How do I multiply two mixed numbers?

A: To multiply two mixed numbers, you need to follow these steps:

1. Convert the mixed numbers to improper fractions.
2. Multiply the fractions.
3. Simplify the result.

For example, to multiply $-5 \frac{1}{2}$ and $-9 \frac{1}{10}$, you would follow these steps:

1. Convert $-5 \frac{1}{2}$ to an improper fraction: $-\frac{11}{2}$.
2. Convert $-9 \frac{1}{10}$ to an improper fraction: $-\frac{91}{10}$.
3. Multiply the fractions: $-\frac{11}{2} \times -\frac{91}{10} = \frac{1001}{20}$.
4. Simplify the result: $\frac{1001}{20}$.

Q: What is the result of multiplying $-5 \frac{1}{2}$ and $-9 \frac{1}{10}$?

A: The result of multiplying $-5 \frac{1}{2}$ and $-9 \frac{1}{10}$ is $-\frac{1001}{20}$.

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

A: Yes, you can simplify the result of multiplying two mixed numbers by finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both numbers by the GCD.

For example, the numerator of the result $-\frac{1001}{20}$ is 1001 and the denominator is 20. The GCD of 1001 and 20 is 1, so we cannot simplify the fraction further.

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

A: To convert an improper fraction back to a mixed number, you need to divide the numerator by the denominator and write the result as a mixed number.

For example, to convert $-\frac{1001}{20}$ back to a mixed number, you would divide the numerator (1001) by the denominator (20). The result is $-50 \frac{1}{20}$.

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

A: Some common mistakes to avoid when multiplying mixed numbers include:

• Not converting the mixed numbers to improper fractions before multiplying.
• Not simplifying the result after multiplying.
• Not converting the improper fraction back to a mixed number after multiplying.

Conclusion

Multiplication of mixed numbers is a fundamental concept in mathematics that involves multiplying two or more numbers, each of which is a combination of a whole number and a fraction. In this article, we have explored the concept of multiplying mixed numbers through a series of questions and answers. We have shown that the result of multiplying $-5 \frac{1}{2}$ and $-9 \frac{1}{10}$ is $-\frac{1001}{20}$ and have provided tips and examples to help you avoid common mistakes when multiplying mixed numbers.

Practice Problems

Here are a few practice problems that involve multiplying mixed numbers:

• Multiply $-3 \frac{1}{4}$ and $-2 \frac{1}{5}$.
• Multiply $2 \frac{3}{10}$ and $3 \frac{1}{2}$.
• Multiply $1 \frac{1}{3}$ and $2 \frac{2}{5}$.

Answer Key

Here are the answers to the practice problems:

• Multiply $-3 \frac{1}{4}$ and $-2 \frac{1}{5}$: $-\frac{77}{20}$
• Multiply $2 \frac{3}{10}$ and $3 \frac{1}{2}$: $\frac{33}{10}$
• Multiply $1 \frac{1}{3}$ and $2 \frac{2}{5}$: $\frac{17}{15}$