Solve: 7⅔ + 6⅙ + 4⅑ Mixed Number Addition Problem

Question

723+616+419=? 7\frac{2}{3}+6\frac{1}{6}+4\frac{1}{9}=\text{?}

Video Solution

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Convert mixed numbers to improper fractions.
  • Step 2: Find a common denominator.
  • Step 3: Add the fractions.
  • Step 4: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step:

Step 1: Convert each mixed number to an improper fraction.

  • 723=7×3+23=233 7\frac{2}{3} = \frac{7 \times 3 + 2}{3} = \frac{23}{3}
  • 616=6×6+16=376 6\frac{1}{6} = \frac{6 \times 6 + 1}{6} = \frac{37}{6}
  • 419=4×9+19=379 4\frac{1}{9} = \frac{4 \times 9 + 1}{9} = \frac{37}{9}

Step 2: Find a common denominator for the fractions.

The denominators are 3, 6, and 9. The least common multiple (LCM) is 18.

Step 3: Convert all fractions to have this common denominator.

  • 233=23×63×6=13818 \frac{23}{3} = \frac{23 \times 6}{3 \times 6} = \frac{138}{18}
  • 376=37×36×3=11118 \frac{37}{6} = \frac{37 \times 3}{6 \times 3} = \frac{111}{18}
  • 379=37×29×2=7418 \frac{37}{9} = \frac{37 \times 2}{9 \times 2} = \frac{74}{18}

Step 4: Add the fractions.

13818+11118+7418=32318 \frac{138}{18} + \frac{111}{18} + \frac{74}{18} = \frac{323}{18}

Step 5: Convert this improper fraction back to a mixed number.

Divide 323 by 18.

323÷18=17 323 \div 18 = 17 with a remainder of 17, so

32318=171718 \frac{323}{18} = 17\frac{17}{18}

Therefore, the solution to the problem is 171718 17\frac{17}{18} .

Answer

171718 17\frac{17}{18}