Calculate The Product:$\[ 1 \frac{4}{5} \times 1 \frac{1}{3} \times 1 \frac{3}{4} \\]

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Understanding Mixed Numbers

Before we dive into the calculation, let's understand what mixed numbers are. A mixed number is a combination of a whole number and a fraction. It is written in the form of a whole number followed by a fraction, separated by a space. For example, 1 3/4 is a mixed number that represents 1 whole and 3/4 of another whole.

The Problem

We are given the product of three mixed numbers: 1 4/5, 1 1/3, and 1 3/4. Our goal is to calculate the product of these three numbers.

Step 1: Convert Mixed Numbers to Improper Fractions

To calculate the product, we need to convert the mixed numbers to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

  • 1 4/5 = (5 × 1 + 4) / 5 = 9/5
  • 1 1/3 = (3 × 1 + 1) / 3 = 4/3
  • 1 3/4 = (4 × 1 + 3) / 4 = 7/4

Step 2: Multiply the Numerators and Denominators

Now that we have the improper fractions, we can multiply the numerators and denominators separately.

  • Numerator: 9 × 4 × 7 = 252
  • Denominator: 5 × 3 × 4 = 60

Step 3: Simplify the Result

The product of the three mixed numbers is 252/60. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD).

  • GCD(252, 60) = 12
  • 252 ÷ 12 = 21
  • 60 ÷ 12 = 5

Therefore, the simplified product is 21/5.

Converting the Result to a Mixed Number

To convert the improper fraction 21/5 to a mixed number, we divide the numerator by the denominator and write the remainder as the new numerator.

  • 21 ÷ 5 = 4 with a remainder of 1
  • Therefore, 21/5 = 4 1/5

Conclusion

In this article, we calculated the product of three mixed numbers: 1 4/5, 1 1/3, and 1 3/4. We converted the mixed numbers to improper fractions, multiplied the numerators and denominators, simplified the result, and finally converted the improper fraction to a mixed number.

Key Takeaways

  • Mixed numbers can be converted to improper fractions by multiplying the whole number by the denominator and adding the numerator.
  • To multiply mixed numbers, convert them to improper fractions, multiply the numerators and denominators, and simplify the result.
  • To convert an improper fraction to a mixed number, divide the numerator by the denominator and write the remainder as the new numerator.

Real-World Applications

Calculating the product of mixed numbers has many real-world applications, such as:

  • Cooking: When a recipe calls for a mixed number of ingredients, you need to calculate the product to ensure you have the correct amount.
  • Building: When building a structure, you may need to calculate the product of mixed numbers to determine the total amount of materials required.
  • Finance: When calculating interest rates or investments, you may need to calculate the product of mixed numbers to determine the total amount.

Common Mistakes

When calculating the product of mixed numbers, some common mistakes to avoid include:

  • Forgetting to convert mixed numbers to improper fractions: Failing to convert mixed numbers to improper fractions can lead to incorrect calculations.
  • Not simplifying the result: Failing to simplify the result can lead to incorrect answers.
  • Not converting the result to a mixed number: Failing to convert the result to a mixed number can make it difficult to interpret the answer.

Conclusion

Frequently Asked Questions

In this article, we will address some of the most frequently asked questions about calculating the product of mixed numbers.

Q: What is the product of 1 3/4 and 2 1/2?

A: To calculate the product, we need to convert the mixed numbers to improper fractions.

  • 1 3/4 = (4 × 1 + 3) / 4 = 7/4
  • 2 1/2 = (2 × 2 + 1) / 2 = 5/2

Now, we can multiply the numerators and denominators:

  • Numerator: 7 × 5 = 35
  • Denominator: 4 × 2 = 8

Therefore, the product is 35/8.

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

A: To convert a mixed number to an improper fraction, follow these steps:

  1. Multiply the whole number by the denominator.
  2. Add the numerator to the result.
  3. Write the result as the new numerator over the denominator.

For example, to convert 2 1/4 to an improper fraction:

  1. Multiply 2 by 4: 2 × 4 = 8
  2. Add 1 to the result: 8 + 1 = 9
  3. Write the result as the new numerator over the denominator: 9/4

Q: What is the product of 3 1/3 and 2 2/3?

A: To calculate the product, we need to convert the mixed numbers to improper fractions.

  • 3 1/3 = (3 × 3 + 1) / 3 = 10/3
  • 2 2/3 = (3 × 2 + 2) / 3 = 8/3

Now, we can multiply the numerators and denominators:

  • Numerator: 10 × 8 = 80
  • Denominator: 3 × 3 = 9

Therefore, the product is 80/9.

Q: How do I simplify a fraction?

A: To simplify a fraction, follow these steps:

  1. Find the greatest common divisor (GCD) of the numerator and denominator.
  2. Divide both the numerator and denominator by the GCD.

For example, to simplify 12/16:

  1. Find the GCD of 12 and 16: 4
  2. Divide both the numerator and denominator by 4: 12 ÷ 4 = 3, 16 ÷ 4 = 4
  3. Write the result as the simplified fraction: 3/4

Q: What is the product of 1 1/2 and 3 3/4?

A: To calculate the product, we need to convert the mixed numbers to improper fractions.

  • 1 1/2 = (2 × 1 + 1) / 2 = 3/2
  • 3 3/4 = (4 × 3 + 3) / 4 = 15/4

Now, we can multiply the numerators and denominators:

  • Numerator: 3 × 15 = 45
  • Denominator: 2 × 4 = 8

Therefore, the product is 45/8.

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

A: To convert an improper fraction to a mixed number, follow these steps:

  1. Divide the numerator by the denominator.
  2. Write the result as the whole number.
  3. Write the remainder as the new numerator over the denominator.

For example, to convert 9/4 to a mixed number:

  1. Divide 9 by 4: 9 ÷ 4 = 2 with a remainder of 1
  2. Write the result as the whole number: 2
  3. Write the remainder as the new numerator over the denominator: 1/4

Therefore, 9/4 = 2 1/4.

Conclusion

In this article, we addressed some of the most frequently asked questions about calculating the product of mixed numbers. We provided step-by-step solutions to each question and explained the concepts in detail. By following these examples and explanations, you can confidently calculate the product of mixed numbers and apply it to real-world scenarios.