Multiply. Write Your Answer As A Fraction Or As A Whole Or Mixed Number.$\[ 4 \times 2 \frac{6}{11} = \\]$\[ \square \\]

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Understanding Mixed Numbers

Before we dive into the multiplication of mixed numbers, let's first understand what a mixed number is. A mixed number is a combination of a whole number and a fraction. It is written in the form of a b/c, where a is the whole number and b/c is the fraction. For example, 2 3/4 is a mixed number that represents 2 whole units and 3/4 of another unit.

Multiplication of Mixed Numbers

Now that we have a good understanding of mixed numbers, let's move on to the multiplication of mixed numbers. When multiplying mixed numbers, we need to follow a specific set of steps to ensure that we get the correct result.

Step 1: Multiply the Whole Numbers

The first step in multiplying mixed numbers is to multiply the whole numbers. In the given problem, we have 4 and 2 as the whole numbers. To multiply them, we simply multiply the two numbers together.

4 \times 2 = 8

Step 2: Multiply the Fractions

The next step is to multiply the fractions. In the given problem, we have 6/11 as the fraction. To multiply fractions, we need to multiply the numerators together and the denominators together.

\frac{6}{11} \times \frac{?}{?} = \frac{6 \times ?}{11 \times ?}

However, we need to multiply the fraction by the whole number 4. To do this, we can multiply the fraction by 4 as if it were a whole number.

4 \times \frac{6}{11} = \frac{4 \times 6}{11} = \frac{24}{11}

Step 3: Add the Whole Number and the Fraction

Now that we have multiplied the whole numbers and the fractions, we need to add the two results together. However, we need to make sure that the fraction is in its simplest form.

8 + \frac{24}{11} = 8 + 2\frac{2}{11} = 10\frac{2}{11}

Therefore, the final answer is:

10 2/11

Conclusion

Multiplying mixed numbers can be a bit tricky, but by following the steps outlined above, we can ensure that we get the correct result. Remember to multiply the whole numbers first, then multiply the fractions, and finally add the two results together. With practice, you will become more comfortable with multiplying mixed numbers and be able to solve problems like this one with ease.

Example Problems

Here are a few example problems to help you practice multiplying mixed numbers:

  • 3 1/2 \times 2 3/4 = ?
  • 5 1/3 \times 3 2/5 = ?
  • 2 3/4 \times 4 1/2 = ?

Try solving these problems on your own, and then check your answers with the solutions provided below.

Solutions

  • 3 1/2 \times 2 3/4 = 7 1/8
  • 5 1/3 \times 3 2/5 = 16 1/15
  • 2 3/4 \times 4 1/2 = 11 1/4

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about multiplying mixed numbers.

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 of a b/c, where a is the whole number and b/c is the fraction.

Q: How do I multiply mixed numbers?

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

  1. Multiply the whole numbers.
  2. Multiply the fractions.
  3. Add the whole number and the fraction.

Q: What if the fractions have different denominators?

A: If the fractions have different denominators, you need to find the least common multiple (LCM) of the denominators before multiplying the fractions.

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

A: Yes, you can multiply a mixed number by a whole number. To do this, you can multiply the whole number by the whole part of the mixed number, and then multiply the whole number by the fraction.

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

A: Yes, you can multiply a mixed number by a fraction. To do this, you can multiply the fraction by the whole part of the mixed number, and then multiply the fraction by the fraction.

Q: What if I get a fraction with a denominator that is not a multiple of 10?

A: If you get a fraction with a denominator that is not a multiple of 10, you need to simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD).

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

A: Yes, you can use a calculator to multiply mixed numbers. However, it's always a good idea to check your answer by multiplying the whole numbers and the fractions separately.

Common Mistakes to Avoid

When multiplying mixed numbers, there are several common mistakes to avoid:

  • Not multiplying the whole numbers first: Make sure to multiply the whole numbers before multiplying the fractions.
  • Not multiplying the fractions correctly: Make sure to multiply the numerators and the denominators correctly.
  • Not simplifying the fraction: Make sure to simplify the fraction by dividing both the numerator and the denominator by their GCD.
  • Not checking the answer: Make sure to check your answer by multiplying the whole numbers and the fractions separately.

Tips and Tricks

Here are some tips and tricks to help you multiply mixed numbers:

  • Use a diagram: Draw a diagram to help you visualize the problem.
  • Use a calculator: Use a calculator to check your answer.
  • Simplify the fraction: Simplify the fraction by dividing both the numerator and the denominator by their GCD.
  • Check your answer: Check your answer by multiplying the whole numbers and the fractions separately.

Conclusion

Multiplying mixed numbers can be a bit tricky, but by following the steps outlined above and avoiding common mistakes, you can ensure that you get the correct result. Remember to multiply the whole numbers first, then multiply the fractions, and finally add the two results together. With practice, you will become more comfortable with multiplying mixed numbers and be able to solve problems like this one with ease.