Calculate The Product Of The Following Mixed Numbers:$\[3 \frac{5}{8} \times 4 \frac{2}{3}\\]

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**Calculate the Product of Mixed Numbers: A Step-by-Step Guide** ===========================================================

What are Mixed Numbers?

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, such as 3 5/8. In this article, we will learn how to calculate the product of mixed numbers.

Why is it Important to Learn How to Calculate the Product of Mixed Numbers?

Calculating the product of mixed numbers is an essential skill in mathematics, particularly in algebra and geometry. It is used to solve problems involving area, volume, and other mathematical concepts. By learning how to calculate the product of mixed numbers, you will be able to solve complex mathematical problems with ease.

How to Calculate the Product of Mixed Numbers

To calculate the product of mixed numbers, you need to follow these steps:

Step 1: Convert the Mixed Numbers to Improper Fractions

To calculate the product of mixed numbers, you 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, 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 3 5/8 to an improper fraction, multiply 3 by 8 and add 5:

3 × 8 = 24 24 + 5 = 29

So, 3 5/8 is equal to 29/8.

Step 2: Multiply the Numerators and Denominators

Once you have converted the mixed numbers to improper fractions, multiply the numerators and denominators separately.

  • Multiply the numerators: 29 × 8 = 232
  • Multiply the denominators: 8 × 8 = 64

Step 3: Simplify the Result

To simplify the result, divide the numerator by the denominator:

232 ÷ 64 = 3.625

So, the product of 3 5/8 and 4 2/3 is 3.625.

Example 2: Calculate the Product of 2 3/4 and 5 1/2

To calculate the product of 2 3/4 and 5 1/2, follow the same steps:

Step 1: Convert the Mixed Numbers to Improper Fractions

  • To convert 2 3/4 to an improper fraction, multiply 2 by 4 and add 3: 2 × 4 = 8 8 + 3 = 11

    So, 2 3/4 is equal to 11/4.

  • To convert 5 1/2 to an improper fraction, multiply 5 by 2 and add 1: 5 × 2 = 10 10 + 1 = 11

    So, 5 1/2 is equal to 11/2.

Step 2: Multiply the Numerators and Denominators

  • Multiply the numerators: 11 × 11 = 121
  • Multiply the denominators: 4 × 2 = 8

Step 3: Simplify the Result

To simplify the result, divide the numerator by the denominator:

121 ÷ 8 = 15.125

So, the product of 2 3/4 and 5 1/2 is 15.125.

Frequently Asked Questions

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

A: To calculate the product of 1 2/3 and 2 1/4, follow the same steps:

  • Convert the mixed numbers to improper fractions: 1 2/3 = 5/3 2 1/4 = 9/4

  • Multiply the numerators and denominators: 5 × 9 = 45 3 × 4 = 12

  • Simplify the result: 45 ÷ 12 = 3.75

So, the product of 1 2/3 and 2 1/4 is 3.75.

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

A: To calculate the product of 3 1/2 and 4 3/4, follow the same steps:

  • Convert the mixed numbers to improper fractions: 3 1/2 = 7/2 4 3/4 = 19/4

  • Multiply the numerators and denominators: 7 × 19 = 133 2 × 4 = 8

  • Simplify the result: 133 ÷ 8 = 16.625

So, the product of 3 1/2 and 4 3/4 is 16.625.

Conclusion

Calculating the product of mixed numbers is an essential skill in mathematics. By following the steps outlined in this article, you can easily calculate the product of mixed numbers. Remember to convert the mixed numbers to improper fractions, multiply the numerators and denominators, and simplify the result. With practice, you will become proficient in calculating the product of mixed numbers and be able to solve complex mathematical problems with ease.