A Restaurant Has 6 1 2 6 \frac{1}{2} 6 2 1 ​ Pounds Of Jalapeño Peppers, 4 3 4 4 \frac{3}{4} 4 4 3 ​ Pounds Of Red Bell Peppers, And 5 1 4 5 \frac{1}{4} 5 4 1 ​ Pounds Of Poblano Peppers. How Many Pounds Of Peppers Does The Restaurant Have In All?

Introduction

In this article, we will explore the concept of adding mixed numbers to find the total weight of peppers in a restaurant's collection. Mixed numbers are a combination of a whole number and a fraction, and they can be added together to find the total value. We will use the given information about the restaurant's pepper collection to calculate the total weight of peppers.

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 b/c

where a is the whole number, b is the numerator, and c is the denominator. For example, 2 3/4 is a mixed number that represents 2 whole units and 3/4 of a unit.

The Restaurant's Pepper Collection

The restaurant has the following amounts of peppers:

• Jalapeño peppers: $6 \frac{1}{2}$ pounds
• Red bell peppers: $4 \frac{3}{4}$ pounds
• Poblano peppers: $5 \frac{1}{4}$ pounds

We need to find the total weight of peppers in the restaurant's collection.

Converting Mixed Numbers to Improper Fractions

To add mixed numbers, we need to convert them to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. Then, we write the result as a fraction with the denominator.

Let's convert the mixed numbers to improper fractions:

• $6 \frac{1}{2}$ pounds = $\frac{(6 \times 2) + 1}{2}$ = $\frac{12 + 1}{2}$ = $\frac{13}{2}$ pounds
• $4 \frac{3}{4}$ pounds = $\frac{(4 \times 4) + 3}{4}$ = $\frac{16 + 3}{4}$ = $\frac{19}{4}$ pounds
• $5 \frac{1}{4}$ pounds = $\frac{(5 \times 4) + 1}{4}$ = $\frac{20 + 1}{4}$ = $\frac{21}{4}$ pounds

Adding the Improper Fractions

Now that we have converted the mixed numbers to improper fractions, we can add them together. To add improper fractions, we need to find a common denominator. The least common multiple (LCM) of the denominators is the smallest number that is a multiple of all the denominators. In this case, the LCM of 2, 4, and 4 is 4.

We can rewrite each fraction with a denominator of 4:

• $\frac{13}{2}$ = $\frac{13 \times 2}{2 \times 2}$ = $\frac{26}{4}$
• $\frac{19}{4}$ = $\frac{19 \times 1}{4 \times 1}$ = $\frac{19}{4}$
• $\frac{21}{4}$ = $\frac{21 \times 1}{4 \times 1}$ = $\frac{21}{4}$

Now we can add the fractions:

$\frac{26}{4} + \frac{19}{4} + \frac{21}{4}$ = $\frac{26 + 19 + 21}{4}$ = $\frac{66}{4}$

Simplifying the Result

The result is an improper fraction, but we can simplify it by dividing the numerator by the denominator:

$\frac{66}{4}$ = $16 \frac{2}{4}$

We can simplify the fraction further by dividing the numerator and denominator by their greatest common divisor, which is 2:

$16 \frac{2}{4}$ = $16 \frac{1}{2}$

Conclusion

In this article, we calculated the total weight of peppers in a restaurant's collection by adding mixed numbers. We converted the mixed numbers to improper fractions, found a common denominator, and added the fractions together. The result was an improper fraction, which we simplified to a mixed number. The total weight of peppers in the restaurant's collection is $16 \frac{1}{2}$ pounds.

Final Answer

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Introduction

In our previous article, we explored the concept of adding mixed numbers to find the total weight of peppers in a restaurant's collection. We calculated the total weight of peppers by converting mixed numbers to improper fractions, finding a common denominator, and adding the fractions together. In this article, we will answer some frequently asked questions about the problem.

Q&A

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 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 multiply the whole number by the denominator and add the numerator. Then, you write the result as a fraction with the denominator.

For example, to convert 2 3/4 to an improper fraction, you would multiply 2 by 4 and add 3:

2 x 4 = 8 8 + 3 = 11

So, 2 3/4 = 11/4

Q: What is an improper fraction?

A: An improper fraction is a fraction where the numerator is greater than or equal to the denominator. It is written in the form:

a/b

where a is the numerator and b is the denominator.

Q: How do I add improper fractions?

A: To add improper fractions, you need to find a common denominator. The least common multiple (LCM) of the denominators is the smallest number that is a multiple of all the denominators.

For example, to add 3/4 and 5/6, you would find the LCM of 4 and 6, which is 12. Then, you would rewrite each fraction with a denominator of 12:

3/4 = 9/12 5/6 = 10/12

Now, you can add the fractions:

9/12 + 10/12 = 19/12

Q: How do I simplify an improper fraction?

A: To simplify an improper fraction, you divide the numerator by the denominator. If the result is a whole number, you can write it as a mixed number.

For example, to simplify 11/4, you would divide 11 by 4:

11 ÷ 4 = 2 with a remainder of 3

So, 11/4 = 2 3/4

Q: What is the total weight of peppers in the restaurant's collection?

A: The total weight of peppers in the restaurant's collection is $16 \frac{1}{2}$ pounds.

Conclusion

In this article, we answered some frequently asked questions about the problem of calculating the total weight of peppers in a restaurant's collection. We covered topics such as mixed numbers, improper fractions, and simplifying fractions. We hope that this article has been helpful in understanding the problem and its solution.

Final Answer

The final answer is: $\boxed{16 \frac{1}{2}}$