Perform The Following Division. Be Sure Answers Are Reduced To Lowest Terms.$\[ 1 \frac{1}{4} \div 7 = \\]A. \[$\frac{5}{28}\$\]B. \[$\frac{29}{28}\$\]C. \[$7 \frac{1}{4}\$\]D. \[$5 \frac{3}{5}\$\]

Feb 28, 2025 by ADMIN 198 views

**Performing Division with Mixed Numbers**

In mathematics, division is a fundamental operation that involves finding the quotient of two numbers. When dealing with mixed numbers, which consist of a whole number and a fraction, division can be a bit more complex. In this article, we will explore how to perform division with mixed numbers and reduce the answers to their lowest terms.

Understanding Mixed Numbers

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

Performing Division with Mixed Numbers

To perform division with mixed numbers, we need to follow a step-by-step process. Here's how to do it:

Convert the mixed number to an improper fraction: The first step is to convert the mixed number to an improper fraction. To do this, we multiply the whole number by the denominator and add the numerator. For example, to convert $1 \frac{1}{4}$ to an improper fraction, we multiply $1$ by $4$ and add $1$ , which gives us $\frac{5}{4}$ .
Invert the divisor and multiply: Once we have the improper fraction, we can proceed with the division. To do this, we invert the divisor (i.e., flip the numerator and denominator) and multiply. For example, to divide $\frac{5}{4}$ by $7$ , we invert $7$ to get $\frac{1}{7}$ and multiply $\frac{5}{4}$ by $\frac{1}{7}$ .
Multiply the numerators and denominators: When multiplying fractions, we multiply the numerators together and the denominators together. In this case, we multiply $5$ by $1$ to get $5$ and $4$ by $7$ to get $28$ .
Simplify the result: The final step is to simplify the result by dividing both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of $5$ and $28$ is $1$ , so the result is already simplified.

Applying the Steps to the Given Problem

Now that we have the steps, let's apply them to the given problem: $1 \frac{1}{4} \div 7$ . Here's how we do it:

Convert the mixed number to an improper fraction: We multiply $1$ by $4$ and add $1$ to get $\frac{5}{4}$ .
Invert the divisor and multiply: We invert $7$ to get $\frac{1}{7}$ and multiply $\frac{5}{4}$ by $\frac{1}{7}$ .
Multiply the numerators and denominators: We multiply $5$ by $1$ to get $5$ and $4$ by $7$ to get $28$ .
Simplify the result: The result is $\frac{5}{28}$ , which is already simplified.

Conclusion

In conclusion, performing division with mixed numbers involves converting the mixed number to an improper fraction, inverting the divisor, multiplying, and simplifying the result. By following these steps, we can perform division with mixed numbers and reduce the answers to their lowest terms.

Answer

The correct answer is:

A. $\frac{5}{28}$

Why the Other Options are Incorrect

Let's take a look at the other options and see why they are incorrect:

Option B: $\frac{29}{28}$ : This option is incorrect because it does not result from the division of $1 \frac{1}{4}$ by $7$ .
Option C: $7 \frac{1}{4}$ : This option is incorrect because it is the result of multiplying $1 \frac{1}{4}$ by $7$ , not dividing it.
Option D: $5 \frac{3}{5}$ : This option is incorrect because it does not result from the division of $1 \frac{1}{4}$ by $7$ .

Final Thoughts

In the previous article, we explored how to perform division with mixed numbers and reduce the answers to their lowest terms. However, we know that there are many more questions that you may have about this topic. In this article, we will answer some of the most frequently asked questions about performing division with mixed numbers.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, written in the form of $a \frac{b}{c}$ . An improper fraction, on the other hand, is a fraction where the numerator is greater than or equal to the denominator, written in the form of $\frac{a}{b}$ .

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 by the denominator and add the numerator. For example, to convert $1 \frac{1}{4}$ to an improper fraction, you would multiply $1$ by $4$ and add $1$ , which gives you $\frac{5}{4}$ .

Q: What is the rule for inverting the divisor when dividing fractions?

A: When dividing fractions, you need to invert the divisor (i.e., flip the numerator and denominator) and multiply. For example, to divide $\frac{5}{4}$ by $7$ , you would invert $7$ to get $\frac{1}{7}$ and multiply $\frac{5}{4}$ by $\frac{1}{7}$ .

Q: How do I simplify the result of a division problem involving fractions?

A: To simplify the result of a division problem involving fractions, you need to divide both the numerator and denominator by their greatest common divisor (GCD). For example, if the result of a division problem is $\frac{10}{20}$ , you would divide both $10$ and $20$ by their GCD, which is $10$ , to get $\frac{1}{2}$ .

Q: What is the difference between dividing fractions and multiplying fractions?

A: Dividing fractions is the opposite of multiplying fractions. When you divide fractions, you invert the divisor and multiply. When you multiply fractions, you multiply the numerators together and the denominators together.

Q: Can I use a calculator to perform division with mixed numbers?

A: Yes, you can use a calculator to perform division with mixed numbers. However, it's always a good idea to check your work by hand to make sure that the calculator is giving you the correct answer.

Q: What are some common mistakes to avoid when performing division with mixed numbers?

A: Some common mistakes to avoid when performing division with mixed numbers include:

Not converting the mixed number to an improper fraction
Not inverting the divisor
Not multiplying the numerators and denominators
Not simplifying the result
Not checking your work by hand

Q: How can I practice performing division with mixed numbers?

A: You can practice performing division with mixed numbers by working through problems in a textbook or online resource. You can also try creating your own problems and solving them on your own.

Conclusion

In conclusion, performing division with mixed numbers requires a step-by-step approach. By converting the mixed number to an improper fraction, inverting the divisor, multiplying, and simplifying the result, you can perform division with mixed numbers and reduce the answers to their lowest terms. We hope that this article has helped to answer some of the most frequently asked questions about performing division with mixed numbers.