Brian Irons 2 9 \frac{2}{9} 9 2 Of His Shirt In 3 3 5 3 \frac{3}{5} 3 5 3 Minutes. Brian Irons At A Constant Rate. At This Rate, How Much Of His Shirt Does He Iron Each Minute?

Mar 12, 2025 by ADMIN 181 views

**Brian's Ironing Rate: A Mathematical Analysis**

Introduction

Brian's ironing rate is a classic problem in mathematics that involves finding the rate at which Brian irons his shirt per minute. The problem states that Brian irons $\frac{2}{9}$ of his shirt in $3 \frac{3}{5}$ minutes. To find the rate at which Brian irons his shirt per minute, we need to divide the fraction of the shirt ironed by the time taken.

Understanding the Problem

The problem involves two key components: the fraction of the shirt ironed and the time taken to iron that fraction. The fraction of the shirt ironed is given as $\frac{2}{9}$ , and the time taken is given as $3 \frac{3}{5}$ minutes. To find the rate at which Brian irons his shirt per minute, we need to convert the mixed number $3 \frac{3}{5}$ to an improper fraction.

Converting Mixed Numbers to Improper Fractions

A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we need to multiply the whole number by the denominator and add the numerator. In this case, the mixed number is $3 \frac{3}{5}$ . To convert it to an improper fraction, we multiply the whole number $3$ by the denominator $5$ and add the numerator $3$ .

$3 \frac{3}{5} = \frac{(3 \times 5) + 3}{5} = \frac{15 + 3}{5} = \frac{18}{5}$

Finding the Rate at Which Brian Irons His Shirt Per Minute

Now that we have the fraction of the shirt ironed and the time taken in improper fractions, we can find the rate at which Brian irons his shirt per minute. To do this, we divide the fraction of the shirt ironed by the time taken.

$\frac{\text{Fraction of shirt ironed}}{\text{Time taken}} = \frac{\frac{2}{9}}{\frac{18}{5}}$

Dividing Fractions

To divide fractions, we need to invert the second fraction and multiply. In this case, we invert the second fraction $\frac{18}{5}$ to $\frac{5}{18}$ and multiply.

$\frac{\frac{2}{9}}{\frac{18}{5}} = \frac{2}{9} \times \frac{5}{18} = \frac{2 \times 5}{9 \times 18} = \frac{10}{162}$

Simplifying the Fraction

The fraction $\frac{10}{162}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ .

$\frac{10}{162} = \frac{10 \div 2}{162 \div 2} = \frac{5}{81}$

Conclusion

In conclusion, Brian irons $\frac{5}{81}$ of his shirt per minute. This means that Brian irons a fraction of his shirt that is equivalent to $\frac{1}{81}$ of the shirt per minute.

Real-World Applications

The concept of finding the rate at which Brian irons his shirt per minute has real-world applications in various fields, such as:

Manufacturing: Finding the rate at which a machine produces a product per minute can help manufacturers optimize production and reduce costs.
Logistics: Finding the rate at which a delivery truck can deliver packages per minute can help logistics companies optimize their routes and reduce delivery times.
Finance: Finding the rate at which an investment grows per minute can help investors make informed decisions about their investments.

Tips and Tricks

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

Read the problem carefully: Make sure you understand what the problem is asking for.
Convert mixed numbers to improper fractions: This can make it easier to solve the problem.
Divide fractions by inverting the second fraction and multiplying: This is a key step in solving problems like this.
Simplify fractions: This can make it easier to understand the solution.

Practice Problems

Here are some practice problems to help you practice solving problems like this:

Problem 1: Tom irons $\frac{3}{4}$ of his shirt in $2 \frac{1}{2}$ minutes. Find the rate at which Tom irons his shirt per minute.
Problem 2: Sarah irons $\frac{2}{3}$ of her shirt in $4 \frac{2}{3}$ minutes. Find the rate at which Sarah irons her shirt per minute.
Problem 3: John irons $\frac{1}{2}$ of his shirt in $3 \frac{1}{4}$ minutes. Find the rate at which John irons his shirt per minute.

Conclusion

In conclusion, finding the rate at which Brian irons his shirt per minute is a classic problem in mathematics that involves dividing fractions. By following the steps outlined in this article, you can solve problems like this and apply the concept to real-world situations.

Introduction

In our previous article, we explored the concept of Brian's ironing rate and how to find the rate at which Brian irons his shirt per minute. In this article, we will answer some frequently asked questions about Brian's ironing rate and provide additional insights and examples.

Q&A

Q: What is Brian's ironing rate?

A: Brian's ironing rate is the rate at which he irons his shirt per minute. In our previous article, we found that Brian irons $\frac{5}{81}$ of his shirt per minute.

Q: How do I find Brian's ironing rate?

A: To find Brian's ironing rate, you need to divide the fraction of the shirt ironed by the time taken. This involves converting mixed numbers to improper fractions, dividing fractions by inverting the second fraction and multiplying, and simplifying the resulting fraction.

Q: What if the time taken is not a mixed number?

A: If the time taken is not a mixed number, you can simply divide the fraction of the shirt ironed by the time taken. For example, if the time taken is $2$ minutes and the fraction of the shirt ironed is $\frac{3}{4}$ , you can simply divide $\frac{3}{4}$ by $2$ .

Q: Can I use a calculator to find Brian's ironing rate?

A: Yes, you can use a calculator to find Brian's ironing rate. However, it's always a good idea to understand the underlying math and be able to solve the problem manually.

Q: How does Brian's ironing rate relate to real-world applications?

A: Brian's ironing rate has real-world applications in various fields, such as manufacturing, logistics, and finance. For example, finding the rate at which a machine produces a product per minute can help manufacturers optimize production and reduce costs.

Q: Can I use Brian's ironing rate to solve other problems?

A: Yes, you can use Brian's ironing rate to solve other problems. For example, if you know the rate at which Brian irons his shirt per minute, you can use that information to find the time it takes him to iron a certain fraction of his shirt.

Q: What if I get stuck on a problem?

A: If you get stuck on a problem, don't worry! You can try breaking down the problem into smaller steps, using visual aids, or seeking help from a teacher or tutor.

Additional Insights and Examples

Example 1: Tom's Ironing Rate

Tom irons $\frac{3}{4}$ of his shirt in $2 \frac{1}{2}$ minutes. Find the rate at which Tom irons his shirt per minute.

To solve this problem, we need to convert the mixed number $2 \frac{1}{2}$ to an improper fraction. We can do this by multiplying the whole number $2$ by the denominator $2$ and adding the numerator $1$ .

$2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{4 + 1}{2} = \frac{5}{2}$

Now that we have the time taken in improper fractions, we can find the rate at which Tom irons his shirt per minute by dividing the fraction of the shirt ironed by the time taken.

$\frac{\text{Fraction of shirt ironed}}{\text{Time taken}} = \frac{\frac{3}{4}}{\frac{5}{2}}$

To divide fractions, we need to invert the second fraction and multiply.

$\frac{\frac{3}{4}}{\frac{5}{2}} = \frac{3}{4} \times \frac{2}{5} = \frac{3 \times 2}{4 \times 5} = \frac{6}{20}$

We can simplify the fraction $\frac{6}{20}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ .

$\frac{6}{20} = \frac{6 \div 2}{20 \div 2} = \frac{3}{10}$

Therefore, Tom irons $\frac{3}{10}$ of his shirt per minute.

Example 2: Sarah's Ironing Rate

Sarah irons $\frac{2}{3}$ of her shirt in $4 \frac{2}{3}$ minutes. Find the rate at which Sarah irons her shirt per minute.

To solve this problem, we need to convert the mixed number $4 \frac{2}{3}$ to an improper fraction. We can do this by multiplying the whole number $4$ by the denominator $3$ and adding the numerator $2$ .

$4 \frac{2}{3} = \frac{(4 \times 3) + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}$

Now that we have the time taken in improper fractions, we can find the rate at which Sarah irons her shirt per minute by dividing the fraction of the shirt ironed by the time taken.

$\frac{\text{Fraction of shirt ironed}}{\text{Time taken}} = \frac{\frac{2}{3}}{\frac{14}{3}}$

To divide fractions, we need to invert the second fraction and multiply.

$\frac{\frac{2}{3}}{\frac{14}{3}} = \frac{2}{3} \times \frac{3}{14} = \frac{2 \times 3}{3 \times 14} = \frac{6}{42}$

We can simplify the fraction $\frac{6}{42}$ by dividing both the numerator and the denominator by their greatest common divisor, which is $6$ .

$\frac{6}{42} = \frac{6 \div 6}{42 \div 6} = \frac{1}{7}$

Therefore, Sarah irons $\frac{1}{7}$ of her shirt per minute.

Conclusion

In conclusion, Brian's ironing rate is a classic problem in mathematics that involves finding the rate at which Brian irons his shirt per minute. By following the steps outlined in this article, you can solve problems like this and apply the concept to real-world situations. Remember to always convert mixed numbers to improper fractions, divide fractions by inverting the second fraction and multiplying, and simplify the resulting fraction.