Divide Fractions: Whole-Number Quotients - Instruction - Level FJack Is Making Banaha. Each Banaha Uses $\frac{3}{2}$ Oz Of Dough, And Jack Has 6 Oz Of Dough In Total.Complete The Model To Show How Many Banaha Jack Can Make With 6 Oz Of Dough.

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Understanding the Problem

Jack is making banaha, a delicious pastry that requires a specific amount of dough. Each banaha uses 32\frac{3}{2} oz of dough, and Jack has a total of 6 oz of dough available. To determine how many banaha Jack can make with the given amount of dough, we need to divide the total amount of dough by the amount of dough required for each banaha.

Dividing Fractions by Whole Numbers

When dividing a fraction by a whole number, we can multiply the fraction by the reciprocal of the whole number. In this case, we need to divide 32\frac{3}{2} oz by 6. To do this, we will multiply 32\frac{3}{2} oz by the reciprocal of 6, which is 16\frac{1}{6}.

Modeling the Problem

Let's create a model to represent the problem. We can use a diagram to show the relationship between the amount of dough available and the number of banaha Jack can make.

+---------------+
|  6 oz (total)  |
+---------------+
|  3/2 oz (per  |
|  banaha)     |
+---------------+
|  ? (number of  |
|  banaha)     |
+---------------+

Solving the Problem

To solve the problem, we need to multiply 32\frac{3}{2} oz by 16\frac{1}{6}. This will give us the number of banaha Jack can make with the given amount of dough.

$\frac{3}{2}$ oz $\times$ $\frac{1}{6}$ = $\frac{3}{2}$ $\times$ $\frac{1}{6}$ = $\frac{3}{12}$ = $\frac{1}{4}$

Interpreting the Result

The result of the division is 14\frac{1}{4}. This means that Jack can make 14\frac{1}{4} of a banaha with the given amount of dough. However, since we cannot make a fraction of a banaha, we need to round down to the nearest whole number.

Conclusion

In conclusion, Jack can make 14\frac{1}{4} of a banaha with the given amount of dough. However, since we cannot make a fraction of a banaha, we need to round down to the nearest whole number. Therefore, Jack can make 0 banaha with the given amount of dough.

Real-World Applications

Dividing fractions by whole numbers has many real-world applications. For example, in cooking, we often need to divide ingredients by a certain number to make a specific recipe. In this case, we can use the concept of dividing fractions by whole numbers to determine the amount of ingredients needed.

Practice Problems

Here are some practice problems to help you understand the concept of dividing fractions by whole numbers.

  1. A recipe requires 23\frac{2}{3} cup of flour. If you have 9 cups of flour available, how many recipes can you make?
  2. A bookshelf has 34\frac{3}{4} meter of space available. If you have 12 meters of bookshelf space, how many books can you fit on the shelf?
  3. A recipe requires 12\frac{1}{2} cup of sugar. If you have 8 cups of sugar available, how many recipes can you make?

Answer Key

  1. 4
  2. 9
  3. 4

Conclusion

Q&A: Dividing Fractions by Whole Numbers

Q: What is dividing fractions by whole numbers?

A: Dividing fractions by whole numbers is a mathematical operation that involves dividing a fraction by a whole number. This can be done by multiplying the fraction by the reciprocal of the whole number.

Q: How do I divide a fraction by a whole number?

A: To divide a fraction by a whole number, you can multiply the fraction by the reciprocal of the whole number. For example, to divide 32\frac{3}{2} by 6, you would multiply 32\frac{3}{2} by 16\frac{1}{6}.

Q: What is the reciprocal of a whole number?

A: The reciprocal of a whole number is a fraction that has the same value as the whole number. For example, the reciprocal of 6 is 16\frac{1}{6}.

Q: Can I divide a fraction by a fraction?

A: Yes, you can divide a fraction by a fraction. To do this, you can multiply the first fraction by the reciprocal of the second fraction. For example, to divide 32\frac{3}{2} by 16\frac{1}{6}, you would multiply 32\frac{3}{2} by 61\frac{6}{1}.

Q: What is the difference between dividing fractions by whole numbers and dividing fractions by fractions?

A: The main difference between dividing fractions by whole numbers and dividing fractions by fractions is the type of number you are dividing by. When you divide a fraction by a whole number, you are multiplying the fraction by the reciprocal of the whole number. When you divide a fraction by a fraction, you are multiplying the first fraction by the reciprocal of the second fraction.

Q: Can I use a calculator to divide fractions by whole numbers?

A: Yes, you can use a calculator to divide fractions by whole numbers. However, it's always a good idea to understand the concept behind the operation and to check your work to make sure you are getting the correct answer.

Q: What are some real-world applications of dividing fractions by whole numbers?

A: Dividing fractions by whole numbers has many real-world applications, including cooking, architecture, and science. For example, in cooking, you may need to divide ingredients by a certain number to make a specific recipe. In architecture, you may need to divide a fraction of a building by a whole number to determine the size of a room.

Q: How can I practice dividing fractions by whole numbers?

A: You can practice dividing fractions by whole numbers by working through problems and exercises. You can also use online resources, such as math websites and apps, to practice dividing fractions by whole numbers.

Q: What are some common mistakes to avoid when dividing fractions by whole numbers?

A: Some common mistakes to avoid when dividing fractions by whole numbers include:

  • Not using the reciprocal of the whole number
  • Not multiplying the fraction by the reciprocal of the whole number
  • Not simplifying the fraction
  • Not checking your work

Conclusion

In conclusion, dividing fractions by whole numbers is an essential concept in mathematics. It has many real-world applications and can be used to solve problems in cooking, architecture, and other fields. By understanding the concept of dividing fractions by whole numbers, you can become a more confident and proficient problem-solver.