Derek Mows \[$\frac{3}{8}\$\] Of A Lawn In \[$\frac{3}{4}\$\] Of An Hour. Calculate:$\[ \frac{3}{8} \div \left(\frac{3}{4}\right) = \frac{3}{8} \times \frac{4}{3} = \\]

Feb 28, 2025 by ADMIN 170 views

Understanding the Problem

When Derek mows a lawn, he covers a fraction of the lawn in a fraction of an hour. To calculate how much of the lawn he mows in one hour, we need to divide the fraction of the lawn he mows by the fraction of the hour it takes him to mow it. In this case, Derek mows $\frac{3}{8}$ of a lawn in $\frac{3}{4}$ of an hour.

The Math Behind the Problem

To solve this problem, we need to use the concept of division and multiplication of fractions. When we divide one fraction by another, we can multiply the first fraction by the reciprocal of the second fraction. In this case, we need to divide $\frac{3}{8}$ by $\frac{3}{4}$ .

Calculating the Result

To calculate the result, we need to multiply $\frac{3}{8}$ by the reciprocal of $\frac{3}{4}$ , which is $\frac{4}{3}$ . This can be written as:

\frac{3}{8} \div \left(\frac{3}{4}\right) = \frac{3}{8} \times \frac{4}{3}

Simplifying the Expression

To simplify the expression, we need to multiply the numerators and denominators separately. The numerator is $3 \times 4 = 12$ , and the denominator is $8 \times 3 = 24$ . Therefore, the simplified expression is:

\frac{3}{8} \times \frac{4}{3} = \frac{12}{24}

Reducing the Fraction

To reduce the fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 12 and 24 is 12. Therefore, we can divide both the numerator and denominator by 12 to get:

\frac{12}{24} = \frac{1}{2}

Conclusion

In conclusion, Derek mows $\frac{1}{2}$ of a lawn in one hour. This means that if he mows at the same rate, he will be able to mow the entire lawn in two hours.

Real-World Applications

This problem has real-world applications in various fields, such as:

Landscaping: If you are a landscaper, you need to calculate how much of a lawn you can mow in a given time to determine how many lawns you can complete in a day.
Construction: If you are a construction worker, you need to calculate how much of a building you can complete in a given time to determine how many buildings you can complete in a day.
Business: If you are a business owner, you need to calculate how much of a product you can produce in a given time to determine how many products you can sell in a day.

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

Use a calculator: If you are having trouble multiplying fractions, you can use a calculator to get the answer.
Simplify the expression: Before multiplying the fractions, simplify the expression by finding the GCD of the numerator and denominator.
Check your work: After multiplying the fractions, check your work by dividing the numerator and denominator by the GCD.

Common Mistakes

Here are some common mistakes to avoid when solving this problem:

Not simplifying the expression: Failing to simplify the expression before multiplying the fractions can lead to incorrect answers.
Not checking your work: Failing to check your work after multiplying the fractions can lead to incorrect answers.
Not using a calculator: Failing to use a calculator when multiplying fractions can lead to incorrect answers.

Conclusion

In conclusion, Derek mows $\frac{1}{2}$ of a lawn in one hour. This means that if he mows at the same rate, he will be able to mow the entire lawn in two hours. This problem has real-world applications in various fields, such as landscaping, construction, and business. By following the tips and tricks and avoiding common mistakes, you can solve this problem with ease.

Understanding the Problem

Q&A

Q: What is the problem asking us to find?

A: The problem is asking us to find how much of the lawn Derek mows in one hour.

Q: How do we calculate the result?

A: We need to divide $\frac{3}{8}$ by $\frac{3}{4}$ , which is equivalent to multiplying $\frac{3}{8}$ by the reciprocal of $\frac{3}{4}$ , which is $\frac{4}{3}$ .

Q: How do we simplify the expression?

A: We need to multiply the numerators and denominators separately. The numerator is $3 \times 4 = 12$ , and the denominator is $8 \times 3 = 24$ . Therefore, the simplified expression is $\frac{12}{24}$ .

Q: How do we reduce the fraction?

A: We need to find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 12 and 24 is 12. Therefore, we can divide both the numerator and denominator by 12 to get $\frac{1}{2}$ .

Q: What is the final answer?

A: The final answer is $\frac{1}{2}$ .

Q: What does the final answer mean?

A: The final answer means that Derek mows $\frac{1}{2}$ of a lawn in one hour. This means that if he mows at the same rate, he will be able to mow the entire lawn in two hours.