Why This Expression is the Best Estimate

Oct 13, 2025 by magicalceylontours.com 24 views

Which Expression Best Estimates ${-18 \frac{1}{4} \div 2 \frac{2}{3}}$ ?

Understanding the Problem

When dealing with division of mixed numbers, it's essential to convert them into improper fractions first. This process involves multiplying the whole number part by the denominator and then adding the numerator. The result is then written as a fraction with the original denominator.

Step 1: Convert Mixed Numbers to Improper Fractions

To convert ${-18 \frac{1}{4}}$ and ${2 \frac{2}{3}}$ into improper fractions, we follow these steps:

For ${-18 \frac{1}{4}}$ $- 18 \frac{1}{4}$ :
- Multiply the whole number part (-18) by the denominator (4): -18 × 4 = -72
- Add the numerator (1) to the result: -72 + 1 = -71
- Write the result as a fraction with the original denominator (4): ${-\frac{71}{4}}$
For ${2 \frac{2}{3}}$ $2 \frac{2}{3}$ :
- Multiply the whole number part (2) by the denominator (3): 2 × 3 = 6
- Add the numerator (2) to the result: 6 + 2 = 8
- Write the result as a fraction with the original denominator (3): ${\frac{8}{3}}$

Step 2: Perform Division

Now that we have the improper fractions, we can perform the division:

${-\frac{71}{4} \div \frac{8}{3}}$

To divide fractions, we multiply by the reciprocal of the divisor:

${-\frac{71}{4} \times \frac{3}{8}}$

Step 3: Multiply the Numerators and Denominators

Multiply the numerators (-71 and 3) and the denominators (4 and 8):

${-71 \times 3 = -213}$ ${4 \times 8 = 32}$

Step 4: Write the Result as a Fraction

Write the result as a fraction with the product of the denominators (32) as the new denominator:

${-\frac{213}{32}}$

Step 5: Convert the Result to a Mixed Number

To convert the improper fraction to a mixed number, divide the numerator (-213) by the denominator (32):

${-213 ÷ 32 = -6.65625}$

Since the result is negative, we can write it as a mixed number with a negative whole number part:

${-6 \frac{21}{32}}$

Step 6: Compare the Result to the Answer Choices

Now that we have the result, we can compare it to the answer choices:

A. ${18 \div 3}$ B. ${-18 \div 3}$ C. ${-18 \div (-3)}$ D. ${18 \div (-3)}$

The result ${-6 \frac{21}{32}}$ is closest to answer choice B, ${-18 \div 3}$ .

Conclusion

The expression that best estimates ${-18 \frac{1}{4} \div 2 \frac{2}{3}}$ is ${-18 \div 3}$ .

Why This Expression is the Best Estimate

This expression is the best estimate because it is the closest to the actual result ${-6 \frac{21}{32}}$ . The other answer choices are not as close to the actual result, and therefore, are not the best estimates.

What to Remember

When dealing with division of mixed numbers, it's essential to convert them into improper fractions first. Then, perform the division by multiplying by the reciprocal of the divisor. Finally, compare the result to the answer choices to determine the best estimate.

Common Mistakes to Avoid

When dealing with division of mixed numbers, some common mistakes to avoid include:

Not converting the mixed numbers to improper fractions
Not performing the division by multiplying by the reciprocal of the divisor
Not comparing the result to the answer choices to determine the best estimate

Real-World Applications

Division of mixed numbers has many real-world applications, such as:

Calculating the cost of items on a shopping list
Determining the amount of time it takes to complete a task
Finding the area of a room or a piece of land

Practice Problems

To practice dividing mixed numbers, try the following problems:

${12 \frac{3}{4} \div 3 \frac{1}{2}}$
${-9 \frac{2}{3} \div 2 \frac{1}{4}}$
${15 \frac{1}{6} \div 4 \frac{3}{4}}$

Conclusion

Division of mixed numbers is an essential math concept that has many real-world applications. By following the steps outlined in this article, you can perform division of mixed numbers and determine the best estimate. Remember to convert the mixed numbers to improper fractions, perform the division by multiplying by the reciprocal of the divisor, and compare the result to the answer choices to determine the best estimate.
Q&A: Division of Mixed Numbers

Frequently Asked Questions

Q: What is the first step in dividing mixed numbers?

A: The first step in dividing mixed numbers is to convert them into improper fractions. This involves multiplying the whole number part by the denominator and then adding the numerator.

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

A: To convert a mixed number to an improper fraction, follow these steps:

Multiply the whole number part by the denominator
Add the numerator to the result
Write the result as a fraction with the original denominator

Q: What is the next step after converting the mixed numbers to improper fractions?

A: After converting the mixed numbers to improper fractions, the next step is to perform the division by multiplying by the reciprocal of the divisor.

Q: How do I perform the division by multiplying by the reciprocal of the divisor?

A: To perform the division by multiplying by the reciprocal of the divisor, follow these steps:

Multiply the numerators
Multiply the denominators
Write the result as a fraction with the product of the denominators as the new denominator

Q: What is the final step in dividing mixed numbers?

A: The final step in dividing mixed numbers is to compare the result to the answer choices to determine the best estimate.

Q: Why is it essential to compare the result to the answer choices?

A: It's essential to compare the result to the answer choices to determine the best estimate. This ensures that you choose the answer that is closest to the actual result.

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

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

Not converting the mixed numbers to improper fractions
Not performing the division by multiplying by the reciprocal of the divisor
Not comparing the result to the answer choices to determine the best estimate

Q: What are some real-world applications of division of mixed numbers?

A: Division of mixed numbers has many real-world applications, such as:

Calculating the cost of items on a shopping list
Determining the amount of time it takes to complete a task
Finding the area of a room or a piece of land

Q: How can I practice dividing mixed numbers?

A: To practice dividing mixed numbers, try the following problems:

${12 \frac{3}{4} \div 3 \frac{1}{2}}$
${-9 \frac{2}{3} \div 2 \frac{1}{4}}$
${15 \frac{1}{6} \div 4 \frac{3}{4}}$

Q: What is the best way to learn division of mixed numbers?

A: The best way to learn division of mixed numbers is to practice, practice, practice. Try different problems and scenarios to become more comfortable with the concept.

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

A: Yes, you can use a calculator to divide mixed numbers. However, it's essential to understand the concept and be able to perform the division by hand.

Q: How can I apply division of mixed numbers to my everyday life?

A: Division of mixed numbers can be applied to your everyday life in many ways, such as:

Calculating the cost of items on a shopping list
Determining the amount of time it takes to complete a task
Finding the area of a room or a piece of land

Conclusion

Division of mixed numbers is an essential math concept that has many real-world applications. By following the steps outlined in this article and practicing with different problems, you can become more comfortable with the concept and apply it to your everyday life.