How to Add Mixed Numbers

To add mixed numbers, you need to follow these steps:

Step 1: Convert the mixed numbers to improper fractions. - To do this, multiply the whole number by the denominator of the fraction and add the numerator. The result becomes the new numerator of the improper fraction, while the denominator remains the same. - For example, to convert the mixed number 2 1/4 to an improper fraction, you would multiply 2 by 4 and add 1, which gives you 9. The denominator stays the same, so the improper fraction is 9/4.

Step 2: Find a common denominator for the fractions. - To add fractions, you need to have a common denominator. To find a common denominator, multiply the denominators of the fractions together. - For example, if you are adding 1/3 and 1/4, you would multiply 3 by 4 to get a common denominator of 12.

Step 3: Convert the improper fractions to equivalent fractions with the common denominator. - To do this, multiply the numerator and denominator of each fraction by the same number that will make the denominator equal to the common denominator found in Step 2.

Step 4: Add the equivalent fractions. - Add the numerators of the equivalent fractions and write the sum over the common denominator.

Step 5: Simplify the result, if necessary. - If the result can be simplified, divide both the numerator and denominator by their greatest common factor.

Step 6: Convert the result back to a mixed number, if desired. - If the result is an improper fraction and you want to express it as a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder becomes the numerator of the fraction part.

Example: Add 2 1/4 and 3 2/3.

Step 1: Convert the mixed numbers to improper fractions. - 2 1/4 = 9/4 - 3 2/3 = 11/3

Step 2: Find a common denominator for the fractions. - The common denominator is 4 x 3 = 12.

Step 3: Convert the improper fractions to equivalent fractions with the common denominator. - 9/4 = 27/12 - 11/3 = 44/12

Step 4: Add the equivalent fractions. - 27/12 + 44/12 = 71/12

Step 5: Simplify the result, if necessary. - 71/12 is already simplified.

Step 6: Convert the result back to a mixed number, if desired. - To convert 71/12 to a mixed number, divide the numerator by the denominator: 71 ÷ 12 = 5 with a remainder of 11. - The mixed number is 5 11/12.