How to Simplify Mixed Numbers

Oct 13, 2025 by miodeya.com 77 views

**Simplifying Mixed Numbers: A Step-by-Step Guide** =====================================================

What is a Mixed Number?

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 2 1/2 or 3 3/4. Mixed numbers can be added, subtracted, multiplied, and divided just like whole numbers and fractions.

How to Simplify Mixed Numbers

Step 1: Convert the Mixed Number to an Improper Fraction

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 an improper fraction.

Example: Convert 2 1/2 to an improper fraction.

Multiply the whole number by the denominator: 2 × 2 = 4
Add the numerator: 4 + 1 = 5
Write the result as an improper fraction: 5/2

Step 2: Perform the Desired Operation

Once you have converted the mixed number to an improper fraction, you can perform the desired operation, such as addition, subtraction, multiplication, or division.

Example: Simplify 2 1/2 × 3 3/4.

Convert the mixed numbers to improper fractions: 2 1/2 = 5/2 and 3 3/4 = 15/4
Multiply the improper fractions: (5/2) × (15/4) = 75/8
Simplify the result: 75/8 = 9 3/8

Step 3: Convert the Result Back to a Mixed Number

If the result is an improper fraction, you can convert it back to a mixed number by dividing the numerator by the denominator and writing the result as a whole number and a fraction.

Example: Convert 75/8 to a mixed number.

Divide the numerator by the denominator: 75 ÷ 8 = 9 with a remainder of 3
Write the result as a mixed number: 9 3/8

Frequently Asked Questions

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction with a numerator that is greater than or equal to the denominator.

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

A: 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 an improper fraction.

Q: Can I add, subtract, multiply, and divide mixed numbers?

A: Yes, you can add, subtract, multiply, and divide mixed numbers just like whole numbers and fractions.

Q: How do I simplify a mixed number?

A: To simplify a mixed number, convert it to an improper fraction, perform the desired operation, and then convert the result back to a mixed number.

Q: What is the result of multiplying two mixed numbers?

A: The result of multiplying two mixed numbers is an improper fraction, which can be simplified to a mixed number.

Conclusion

Simplifying mixed numbers involves converting the mixed number to an improper fraction, performing the desired operation, and then converting the result back to a mixed number. By following these steps, you can simplify mixed numbers and perform various operations with them. Remember to convert mixed numbers to improper fractions and vice versa to make calculations easier and more efficient.

Additional Resources

Mathway: A math problem solver that can help you simplify mixed numbers and perform various operations with them.
Khan Academy: A free online learning platform that offers video lessons and practice exercises on simplifying mixed numbers and other math topics.
Math Open Reference: An online math reference book that provides detailed explanations and examples on simplifying mixed numbers and other math topics.