How to Calculate Total Weight by Adding Unlike Fractions

Question

Three letters weigh 1/2 ounces, 1/6 ounces, and 7/12 ounces. What is the total weight of the letters? Simplify your answer.

Accepted Answer

1 7/12 ounces or 19/12 ounces

Answer

Step 1: Identify the common denominator for the fractions. The denominators are 2, 6, and 12; the least common denominator is 12. Step 2: Convert each fraction to have the denominator of 12: 1/2 = 6/12, 1/6 = 2/12, 7/12 remains 7/12. Step 3: Add the converted fractions together: 6/12 + 2/12 + 7/12 = (6+2+7)/12 = 15/12. Step 4: Simplify the improper fraction: 15/12 = 5/4 = 1 1/4? Correction: 6+2+7=15? No, 6+2=8, 8+7=15? Wait, 1/2 is 6/12, 1/6 is 2/12, 6+2+7=15, 15/12=5/4=1 1/4. Wait, no, 1/2 +1/6= (3+1)/6=4/6=2/3, 2/3 +7/12= (8+7)/12=15/12=5/4=1 1/4. Yes, correct. So total weight is 1 1/4 ounces or 5/4 ounces. Step 4 correction: Recalculate the sum: 6/12 + 2/12 + 7/12 = 15/12. Simplify 15/12 by dividing numerator and denominator by 3: 5/4, which converts to the mixed number 1 1/4.