Mr. Thompson Had 10 1 2 10 \frac{1}{2} 10 2 1 ​ Pounds Of Plant Food. He Will Put Equal Amounts Of The Food Into 6 Containers. How Much Plant Food Will Be In Each Container?A. 2 3 4 2 \frac{3}{4} 2 4 3 ​ Lb B. 1 3 4 1 \frac{3}{4} 1 4 3 ​ Lb C. $1

Introduction

In mathematics, dividing mixed numbers can be a challenging task, especially when dealing with real-world problems. In this article, we will explore how to divide mixed numbers and apply this concept to a real-world scenario. We will use the example of Mr. Thompson, who has $10 \frac{1}{2}$ pounds of plant food and wants to put equal amounts into 6 containers.

Understanding Mixed Numbers

Before we dive into the problem, let's review what mixed numbers are. A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. For example, $3 \frac{1}{2}$ is a mixed number that represents $3$ whole units and $\frac{1}{2}$ of a unit.

The Problem

Mr. Thompson has $10 \frac{1}{2}$ pounds of plant food and wants to put equal amounts into 6 containers. To find out how much plant food will be in each container, we need to divide the total amount of plant food by the number of containers.

Dividing Mixed Numbers

To divide mixed numbers, we need to follow these steps:

1. Convert the mixed number to an improper fraction.
2. Divide the numerator of the improper fraction by the denominator.
3. Simplify the result, if possible.

Let's apply these steps to Mr. Thompson's problem.

Step 1: Convert the Mixed Number to an Improper Fraction

To convert the mixed number $10 \frac{1}{2}$ to an improper fraction, we need to multiply the whole number by the denominator and add the numerator.

$10 \frac{1}{2} = \frac{(10 \times 2) + 1}{2} = \frac{20 + 1}{2} = \frac{21}{2}$

Step 2: Divide the Numerator by the Denominator

Now that we have the improper fraction $\frac{21}{2}$, we can divide the numerator by the denominator to find the result.

$\frac{21}{2} \div 6 = \frac{21}{2} \times \frac{1}{6} = \frac{21}{12}$

Step 3: Simplify the Result

To simplify the result, we can divide both the numerator and the denominator by their greatest common divisor (GCD).

The GCD of 21 and 12 is 3.

$\frac{21}{12} = \frac{21 \div 3}{12 \div 3} = \frac{7}{4}$

The Final Answer

So, how much plant food will be in each container? The answer is $\frac{7}{4}$ pounds, which is equivalent to $1 \frac{3}{4}$ pounds.

Conclusion

In this article, we explored how to divide mixed numbers and applied this concept to a real-world problem. We used the example of Mr. Thompson, who has $10 \frac{1}{2}$ pounds of plant food and wants to put equal amounts into 6 containers. By following the steps to divide mixed numbers, we found that each container will have $1 \frac{3}{4}$ pounds of plant food.

Discussion

What do you think about dividing mixed numbers? Do you have any questions or concerns about this topic? Share your thoughts in the comments below!

Related Topics

• Adding and subtracting mixed numbers
• Multiplying and dividing fractions
• Converting mixed numbers to improper fractions
• Converting improper fractions to mixed numbers

Practice Problems

1. A recipe calls for $2 \frac{1}{4}$ cups of flour. If you want to make half the recipe, how much flour will you need?
2. A bookshelf has $5 \frac{1}{2}$ feet of space on each shelf. If you want to put 3 shelves in a row, how much space will you have in total?
3. A recipe calls for $\frac{3}{4}$ cup of sugar. If you want to make 2 batches of the recipe, how much sugar will you need?

Answer Key

1. $\frac{3}{8}$ cup
2. $16 \frac{1}{2}$ feet
3. $\frac{3}{2}$ cups
   Dividing Mixed Numbers: A Real-World Problem =====================================================

Q&A: Dividing Mixed Numbers

Q: What is a mixed number?

A: A mixed number is a combination of a whole number and a fraction. It is written in the form $a \frac{b}{c}$, where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and add the numerator. Then, write the result as a fraction with the denominator.

For example, to convert $10 \frac{1}{2}$ to an improper fraction, you would multiply 10 by 2 and add 1:

$10 \frac{1}{2} = \frac{(10 \times 2) + 1}{2} = \frac{20 + 1}{2} = \frac{21}{2}$

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

A: To divide a mixed number by a whole number, you need to follow these steps:

1. Convert the mixed number to an improper fraction.
2. Divide the numerator of the improper fraction by the denominator.
3. Simplify the result, if possible.

For example, to divide $10 \frac{1}{2}$ by 6, you would follow these steps:

1. Convert $10 \frac{1}{2}$ to an improper fraction: $\frac{21}{2}$
2. Divide the numerator by the denominator: $\frac{21}{2} \div 6 = \frac{21}{2} \times \frac{1}{6} = \frac{21}{12}$
3. Simplify the result: $\frac{21}{12} = \frac{7}{4}$

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD).

For example, to simplify $\frac{21}{12}$, you would find the GCD of 21 and 12, which is 3. Then, you would divide both the numerator and the denominator by 3:

$\frac{21}{12} = \frac{21 \div 3}{12 \div 3} = \frac{7}{4}$

Q: What is the final answer to Mr. Thompson's problem?

A: The final answer to Mr. Thompson's problem is $\frac{7}{4}$ pounds, which is equivalent to $1 \frac{3}{4}$ pounds.

Q: Can I use a calculator to divide mixed numbers?

A: Yes, you can use a calculator to divide mixed numbers. However, you need to make sure that the calculator is set to the correct mode (e.g., fraction mode) and that you enter the mixed number correctly.

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

A: To divide a mixed number by a fraction, you need to follow these steps:

1. Convert the mixed number to an improper fraction.
2. Multiply the improper fraction by the reciprocal of the fraction.
3. Simplify the result, if possible.

For example, to divide $10 \frac{1}{2}$ by $\frac{2}{3}$, you would follow these steps:

1. Convert $10 \frac{1}{2}$ to an improper fraction: $\frac{21}{2}$
2. Multiply the improper fraction by the reciprocal of the fraction: $\frac{21}{2} \times \frac{3}{2} = \frac{63}{4}$
3. Simplify the result: $\frac{63}{4} = 15 \frac{3}{4}$

Conclusion

In this article, we explored how to divide mixed numbers and answered some common questions about this topic. We used the example of Mr. Thompson, who has $10 \frac{1}{2}$ pounds of plant food and wants to put equal amounts into 6 containers. By following the steps to divide mixed numbers, we found that each container will have $1 \frac{3}{4}$ pounds of plant food.

Discussion

What do you think about dividing mixed numbers? Do you have any questions or concerns about this topic? Share your thoughts in the comments below!

Related Topics

• Adding and subtracting mixed numbers
• Multiplying and dividing fractions
• Converting mixed numbers to improper fractions
• Converting improper fractions to mixed numbers

Practice Problems

1. A recipe calls for $2 \frac{1}{4}$ cups of flour. If you want to make half the recipe, how much flour will you need?
2. A bookshelf has $5 \frac{1}{2}$ feet of space on each shelf. If you want to put 3 shelves in a row, how much space will you have in total?
3. A recipe calls for $\frac{3}{4}$ cup of sugar. If you want to make 2 batches of the recipe, how much sugar will you need?

Answer Key

1. $\frac{3}{8}$ cup
2. $16 \frac{1}{2}$ feet
3. $\frac{3}{2}$ cups