Multiply. Write Your Answer As A Mixed Number In Simplest Form.$2 \frac{5}{6} \times 10$

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Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form of a b/c, where a is the whole number and b/c is the fraction. In the given problem, we have the mixed number 2 5/6. To multiply mixed numbers, we need to follow a specific procedure.

Multiplying Mixed Numbers: A Step-by-Step Approach

To multiply mixed numbers, we can follow these steps:

  1. Multiply the Whole Numbers: Multiply the whole numbers in the two mixed numbers. In this case, we have 2 and 10. Multiply them together: 2 × 10 = 20.
  2. Multiply the Fractions: Multiply the fractions in the two mixed numbers. In this case, we have 5/6 and 1 (since 10 can be written as 10/1). Multiply them together: (5/6) × (10/1) = 50/6.
  3. Add the Whole Number and the Fraction: Add the whole number obtained in step 1 to the fraction obtained in step 2. To add a whole number and a fraction, we need to convert the whole number to a fraction with the same denominator as the fraction. In this case, we can write 20 as 120/6. Now, add the two fractions: 120/6 + 50/6 = 170/6.

Simplifying the Result

The result obtained in the previous step is 170/6. To simplify this fraction, we need to find the greatest common divisor (GCD) of 170 and 6. The GCD of 170 and 6 is 2. Divide both the numerator and the denominator by the GCD: 170 ÷ 2 = 85 and 6 ÷ 2 = 3. The simplified fraction is 85/3.

Writing the Result as a Mixed Number

To write the result as a mixed number, we need to divide the numerator by the denominator. Divide 85 by 3: 85 ÷ 3 = 28 with a remainder of 1. The mixed number is 28 1/3.

Conclusion

In this article, we learned how to multiply mixed numbers. We followed a step-by-step approach to multiply the whole numbers and the fractions, and then added the whole number and the fraction. We also simplified the result and wrote it as a mixed number. The final answer is 28 1/3.

Key Takeaways

  • To multiply mixed numbers, multiply the whole numbers and the fractions separately.
  • Add the whole number and the fraction by converting the whole number to a fraction with the same denominator.
  • Simplify the result by finding the greatest common divisor of the numerator and the denominator.
  • Write the result as a mixed number by dividing the numerator by the denominator.

Practice Problems

  1. Multiply the mixed numbers 3 2/5 and 4 3/4.
  2. Multiply the mixed numbers 2 1/2 and 3 1/3.
  3. Multiply the mixed numbers 5 3/4 and 2 2/3.

Answer Key

  1. 12 13/20
  2. 7 5/6
  3. 14 1/3
    Multiplication of Mixed Numbers: Q&A =====================================

Frequently Asked Questions

In this article, we will answer some frequently asked questions about multiplying mixed numbers.

Q: What is the rule for multiplying mixed numbers?

A: To multiply mixed numbers, you need to multiply the whole numbers and the fractions separately. Then, add the whole number and the fraction by converting the whole number to a fraction with the same denominator.

Q: How do I multiply fractions?

A: To multiply fractions, you need to multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately. For example, to multiply 5/6 and 10/1, you would multiply the numerators 5 and 10 to get 50, and multiply the denominators 6 and 1 to get 6. The result is 50/6.

Q: How do I add a whole number and a fraction?

A: To add a whole number and a fraction, you need to convert the whole number to a fraction with the same denominator as the fraction. For example, to add 20 and 50/6, you would convert 20 to 120/6 and then add 120/6 and 50/6 to get 170/6.

Q: How do I simplify a fraction?

A: To simplify a fraction, you need to find the greatest common divisor (GCD) of the numerator and the denominator. Then, divide both the numerator and the denominator by the GCD. For example, to simplify 170/6, you would find the GCD of 170 and 6 to be 2, and then divide both 170 and 6 by 2 to get 85/3.

Q: How do I write a fraction as a mixed number?

A: To write a fraction as a mixed number, you need to divide the numerator by the denominator. For example, to write 85/3 as a mixed number, you would divide 85 by 3 to get 28 with a remainder of 1. The mixed number is 28 1/3.

Q: What are some common mistakes to avoid when multiplying mixed numbers?

A: Some common mistakes to avoid when multiplying mixed numbers include:

  • Not multiplying the whole numbers and the fractions separately
  • Not converting the whole number to a fraction with the same denominator when adding
  • Not simplifying the result
  • Not writing the result as a mixed number

Q: How can I practice multiplying mixed numbers?

A: You can practice multiplying mixed numbers by working through examples and exercises. You can also use online resources, such as worksheets and practice tests, to help you practice.

Q: What are some real-world applications of multiplying mixed numbers?

A: Multiplying mixed numbers has many real-world applications, including:

  • Cooking: When a recipe calls for a certain amount of ingredients, you may need to multiply mixed numbers to get the correct amount.
  • Building: When building a structure, you may need to multiply mixed numbers to get the correct amount of materials.
  • Finance: When calculating interest rates or investments, you may need to multiply mixed numbers.

Conclusion

In this article, we answered some frequently asked questions about multiplying mixed numbers. We covered topics such as multiplying fractions, adding whole numbers and fractions, simplifying fractions, and writing fractions as mixed numbers. We also discussed common mistakes to avoid and real-world applications of multiplying mixed numbers.