solving problems W/ mixed numbers

Solving Problems with Mixed Numbers

Definition of Mixed Numbers

  • A mixed number consists of a whole number and a proper fraction. For example, 2 1/3 is a mixed number, where 2 is the whole number and 1/3 is the proper fraction.

Step to Convert Mixed Numbers into Improper Fractions

  1. Identify Components

    • Whole Number: The part of the mixed number that is not a fraction.

    • Proper Fraction: The fractional component of the mixed number.

  2. Conversion Process

    • Multiply the Denominator by the Whole Number: This step involves taking the denominator of the proper fraction and multiplying it by the whole number in the mixed number.

      • Example: For the mixed number 2 1/3, the denominator is 3, and the whole number is 2.

      • Calculation: 2 (whole number) * 3 (denominator) = 6.

    • Add the Numerator: After calculating the product from the previous step, add the numerator of the proper fraction to this product.

      • Example: Continuing with 2 1/3:

      • Original product from the last step = 6.

      • Add the numerator (1): 6 + 1 = 7.

    • Keep the Original Denominator: The denominator of the resulting improper fraction will be the same as that of the mixed number.

      • Final Result: Combine the results into the improper fraction format. Therefore, the improper fraction for 2 1/3 is ( \frac{7}{3} ).

Summary of Conversion Formula

  • The final formula to convert a mixed number ( ( a \frac{b}{c} ) where a is the whole number, b is the numerator, and c is the denominator) into an improper fraction is given by:
    (a×c)+bc\frac{(a \times c) + b}{c}