Tell A Story That Shows $35 \div 7 = 5$. Illustrate It With A Diagram.
Introduction
Mathematics is not just about numbers and formulas; it's about understanding the world around us. In this story, we'll explore the concept of division and how it can be applied to real-life situations. We'll follow the adventures of a group of friends who stumble upon a treasure chest filled with gold coins. As they try to divide the treasure among themselves, they'll learn the value of division and how it can help them share their wealth fairly.
The Treasure Chest
Imagine a group of five friends - Alex, Ben, Charlie, David, and Emily - who have been searching for a treasure chest for years. Finally, after many days of searching, they stumble upon a chest filled with gold coins. The chest is locked, but they manage to open it, and to their surprise, they find 35 gold coins inside.
The Problem
The friends are excited to share the treasure among themselves, but they quickly realize that they need to divide the coins fairly. They decide to divide the coins equally among themselves, but they're not sure how many coins each person should get. That's when they remember the concept of division.
Division: A Key to Fair Sharing
Division is a mathematical operation that helps us share a certain number of items into equal groups. In this case, the friends want to divide 35 gold coins into 5 equal groups. To do this, they need to find out how many coins each group should get. This is where the concept of $35 \div 7 = 5$ comes in.
Illustrating the Concept with a Diagram
Let's create a diagram to illustrate the concept of division. Imagine a big rectangle with 35 small squares inside it, representing the 35 gold coins. The friends want to divide these coins into 5 equal groups, so they draw 5 smaller rectangles inside the big rectangle, each with 7 small squares.
+---------------+
| 7 | 7 | 7 | 7 | 7 |
+---------------+
| 7 | 7 | 7 | 7 | 7 |
+---------------+
| 7 | 7 | 7 | 7 | 7 |
+---------------+
| 7 | 7 | 7 | 7 | 7 |
+---------------+
| 7 | 7 | 7 | 7 | 7 |
+---------------+
The Answer
As we can see from the diagram, each group of 7 small squares represents 7 gold coins. Since there are 5 groups, each group will get 7 gold coins. Therefore, the answer to the division problem $35 \div 7 = 5$ is indeed 5.
Conclusion
In this story, we've seen how the concept of division can be applied to real-life situations. By dividing the treasure chest into 5 equal groups, the friends were able to share the gold coins fairly. The diagram helped us visualize the concept of division and see how it can be used to solve problems. Whether you're dividing a treasure chest or sharing a pizza with friends, division is an essential mathematical concept that can help you share your resources fairly.
Real-World Applications
Division is not just limited to sharing treasure or pizzas. It has many real-world applications, such as:
- Cooking: When you're cooking for a group of people, you need to divide ingredients into equal portions. For example, if you're making a cake for 8 people, you'll need to divide the ingredients into 8 equal parts.
- Shopping: When you're shopping for groceries, you need to divide the cost of the items among yourself or with others. For example, if you're buying a pack of 12 cookies for $3, you'll need to divide the cost by 12 to find out how much each cookie costs.
- Science: In science, division is used to measure the concentration of a solution. For example, if you're making a solution with 35 grams of sugar in 7 liters of water, you'll need to divide the sugar by 7 to find out the concentration of the solution.
Tips and Tricks
Here are some tips and tricks to help you understand division better:
- Use real-life examples: Try to relate division to real-life situations, such as sharing treasure or cooking for a group of people.
- Use diagrams: Draw diagrams to visualize the concept of division and see how it can be used to solve problems.
- Practice, practice, practice: Practice division problems to become more comfortable with the concept and to develop your problem-solving skills.
Conclusion
In conclusion, division is a fundamental mathematical concept that can be applied to real-life situations. By understanding division, you can share your resources fairly, measure concentrations, and solve problems. Remember to use real-life examples, diagrams, and practice to become more comfortable with the concept of division. Whether you're a student or a professional, division is an essential skill that can help you succeed in many areas of life.
Introduction
In our previous article, we explored the concept of division and how it can be applied to real-life situations. We also saw how division can be used to solve problems and share resources fairly. In this article, we'll answer some frequently asked questions about division and provide additional tips and tricks to help you understand the concept better.
Q: What is division?
A: Division is a mathematical operation that helps us share a certain number of items into equal groups. It's the opposite of multiplication, where we're finding the number of groups instead of the total number of items.
Q: How do I divide numbers?
A: To divide numbers, you need to follow the order of operations (PEMDAS):
- Parentheses: Evaluate any expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: What is the difference between division and multiplication?
A: Division and multiplication are inverse operations, meaning that they "undo" each other. For example, if you multiply 6 and 7, you get 42. If you divide 42 by 7, you get 6. This is because division is the opposite of multiplication.
Q: Can I divide decimals?
A: Yes, you can divide decimals. To divide decimals, you need to follow the same steps as dividing whole numbers. For example, if you want to divide 0.5 by 0.2, you would follow these steps:
0.5 รท 0.2 = ?
To solve this problem, you can multiply both the dividend (0.5) and the divisor (0.2) by 10 to get rid of the decimals:
5 รท 2 = 2.5
Q: What is the remainder in division?
A: The remainder in division is the amount left over after dividing a number by another number. For example, if you divide 17 by 5, you get 3 with a remainder of 2. This means that 17 can be divided into 3 groups of 5, with 2 left over.
Q: Can I divide fractions?
A: Yes, you can divide fractions. To divide fractions, you need to follow these steps:
- Invert the second fraction (i.e., flip the numerator and denominator).
- Multiply the two fractions together.
For example, if you want to divide 1/2 by 3/4, you would follow these steps:
1/2 รท 3/4 = ?
To solve this problem, you would invert the second fraction and multiply the two fractions together:
1/2 ร 4/3 = 4/6 = 2/3
Q: What is the difference between division and ratio?
A: Division and ratio are related but distinct concepts. Division is a mathematical operation that helps us share a certain number of items into equal groups. A ratio, on the other hand, is a comparison of two or more numbers. For example, if you have 3 apples and 4 oranges, the ratio of apples to oranges is 3:4.
Conclusion
In conclusion, division is a fundamental mathematical concept that can be applied to real-life situations. By understanding division, you can share your resources fairly, measure concentrations, and solve problems. We hope this article has answered some of your frequently asked questions about division and provided additional tips and tricks to help you understand the concept better.
Additional Resources
If you're looking for more information on division and other mathematical concepts, here are some additional resources:
- Math textbooks: Check out your local library or online resources for math textbooks that cover division and other mathematical concepts.
- Online tutorials: Websites like Khan Academy, Mathway, and IXL offer interactive tutorials and practice problems to help you understand division and other mathematical concepts.
- Math apps: Download math apps like Photomath, Math Tricks, and Math Games to practice division and other mathematical concepts on the go.
Practice Problems
Here are some practice problems to help you reinforce your understanding of division:
- Problem 1: Divide 24 by 4.
- Problem 2: Divide 0.5 by 0.2.
- Problem 3: Divide 17 by 5.
- Problem 4: Divide 1/2 by 3/4.
- Problem 5: Find the remainder when 17 is divided by 5.
We hope these practice problems help you reinforce your understanding of division and other mathematical concepts.