Solving Notebook Purchase How Many Can Rani Buy With 130 Rupees?

by BRAINLY IN FTUNILA 65 views
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Hey guys! Ever wondered how many notebooks you can snag with a certain amount of cash? Let's dive into a real-world problem where we figure out just that. We'll break down the cost of notebooks and see how many Rani can buy with her money. Get ready for some math fun!

Understanding the Problem

In this scenario, notebook costs play a crucial role. Rani's situation is a classic example of how we use math in everyday life. To start, we know the cost of one notebook is 4 1/3 (which is a mixed fraction, by the way), and Rani has ₹130. Our mission? To find out the maximum number of notebooks Rani can purchase. This involves converting the mixed fraction to an improper fraction, understanding the division concept, and a bit of arithmetic. So, let's roll up our sleeves and get started!

Converting Mixed Fraction to Improper Fraction

First things first, we need to convert the mixed fraction 4 1/3 into an improper fraction. Remember, a mixed fraction has a whole number part and a fractional part. To convert it, we multiply the whole number (4) by the denominator (3) and add the numerator (1). This gives us the new numerator, while the denominator stays the same. So, (4 * 3) + 1 = 13. Therefore, 4 1/3 becomes 13/3. This means each notebook costs ₹13/3. Now, we're one step closer to solving the problem. Converting to an improper fraction makes it easier to perform division later on. Keep this trick in your math toolkit; it's super handy!

Calculating the Number of Notebooks

Next up, we need to figure out how many notebooks Rani can buy with her ₹130. This is where division comes into play. We'll divide the total amount Rani has (₹130) by the cost of one notebook (₹13/3). Dividing by a fraction can seem tricky, but here's a neat trick: dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of 13/3 is 3/13. So, our problem now looks like this: 130 ÷ (13/3) = 130 * (3/13). Isn't that much simpler? Now, we can multiply 130 by 3, which gives us 390, and then divide by 13. The result is 30. So, Rani can buy 30 notebooks. High five for solving the problem!

Step-by-Step Solution

Let's break down the solution into clear, easy-to-follow steps. This way, you can tackle similar problems like a pro!

  1. Identify the Cost of One Notebook: The cost is given as 4 1/3.
  2. Convert the Mixed Fraction to an Improper Fraction: As we discussed, 4 1/3 becomes 13/3.
  3. Identify the Total Amount Rani Has: Rani has ₹130.
  4. Divide the Total Amount by the Cost of One Notebook: This is 130 ÷ (13/3).
  5. Multiply by the Reciprocal: Remember, dividing by a fraction is the same as multiplying by its reciprocal. So, 130 ÷ (13/3) becomes 130 * (3/13).
  6. Calculate the Result: 130 * (3/13) = 390/13 = 30.
  7. State the Answer: Rani can buy 30 notebooks.

See? When we break it down step by step, it's not so daunting after all. Each step makes the process more manageable and easier to understand.

Importance of Understanding Fractions and Division

Understanding fractions and division is super important in real life. Fractions help us deal with parts of a whole, and division helps us split things up equally or figure out how many times one thing fits into another. Think about it: when you're sharing a pizza with friends, you're using fractions. When you're figuring out how many slices each person gets, you're using division. In our notebook problem, fractions helped us represent the cost of one notebook, and division helped us figure out how many notebooks Rani could buy. These skills aren't just for math class; they're for life! So, keep practicing those fractions and divisions, guys!

Real-World Applications of Fractions

Fractions are everywhere, not just in math textbooks. Think about cooking: recipes often call for fractions of ingredients, like 1/2 cup of flour or 1/4 teaspoon of salt. Without understanding fractions, it would be tough to bake a cake or cook a delicious meal. In construction, fractions are used to measure materials and ensure things fit together perfectly. A builder might need to cut a piece of wood to be 3/4 of an inch thick. In finance, fractions come up when dealing with interest rates or stock prices. A stock price might increase by 1/8 of a dollar. So, whether you're in the kitchen, on a construction site, or managing your finances, fractions are your friends.

Real-World Applications of Division

Division is just as crucial as fractions. It helps us share things fairly, figure out how many groups we can make, and solve all sorts of practical problems. Imagine you're planning a road trip with your friends. You need to figure out how to split the cost of gas. That's division in action! Or suppose you're organizing a sports team and need to divide the players into equal groups. Again, division comes to the rescue. In business, division is used to calculate profits, divide resources, and determine pricing. A store owner might need to divide the total revenue by the number of items sold to find the average price. So, from everyday tasks to complex business decisions, division is a skill you'll use again and again.

Practice Problems

Want to sharpen your skills? Here are a couple of practice problems similar to the one we just solved. Give them a try, and you'll become a math whiz in no time!

  1. The cost of a pen is 5 1/2. Rohan has ₹165. How many pens can he buy?
  2. The cost of a book is 7 1/4. Priya has ₹200. How many books can she buy?

Remember, the key is to break down the problem into smaller steps, just like we did earlier. Convert those mixed fractions, use division wisely, and you'll nail it. And hey, if you get stuck, don't worry! Go back and review the steps we discussed. Practice makes perfect, guys!

Solutions to Practice Problems

Okay, let's check our answers. For the first problem, Rohan can buy 30 pens. For the second problem, Priya can buy 27 books. Did you get them right? Awesome! If not, no biggie. Let's quickly walk through the solutions to make sure we're all on the same page.

For the first problem, we convert 5 1/2 to an improper fraction, which is 11/2. Then we divide 165 by 11/2, which is the same as multiplying 165 by 2/11. This gives us 330/11, which simplifies to 30. So, Rohan can buy 30 pens.

For the second problem, we convert 7 1/4 to an improper fraction, which is 29/4. Then we divide 200 by 29/4, which is the same as multiplying 200 by 4/29. This gives us 800/29, which is approximately 27.58. Since Priya can't buy a fraction of a book, she can buy 27 books. Remember, in real-world problems, we often need to round down to the nearest whole number. Keep up the great work, everyone!

Conclusion

So, there you have it! We've cracked the code on figuring out how many notebooks Rani can buy. We've seen how fractions and division are essential tools in solving everyday problems. By converting mixed fractions, understanding the concept of reciprocals, and breaking down the problem into manageable steps, we made math look easy. Remember, math isn't just about numbers and equations; it's about understanding the world around us. Keep practicing, keep exploring, and you'll be amazed at how math can help you in your daily life. You've got this!