Calculate the Sum: 6⅔ + 1⅔ + 1⅝ Mixed Number Addition

Question

629+123+159= 6\frac{2}{9}+1\frac{2}{3}+1\frac{5}{9}=

Video Solution

Step-by-Step Solution

To solve this problem, we will follow these steps:

  • Step 1: Convert each mixed number into an improper fraction.
  • Step 2: Identify the least common denominator (LCD) for the fractions.
  • Step 3: Add the fractions together.
  • Step 4: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step in detail:

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

  • 629=(6×9)+29=54+29=5696\frac{2}{9} = \frac{(6 \times 9) + 2}{9} = \frac{54 + 2}{9} = \frac{56}{9}
  • 123=(1×3)+23=3+23=531\frac{2}{3} = \frac{(1 \times 3) + 2}{3} = \frac{3 + 2}{3} = \frac{5}{3}
  • 159=(1×9)+59=9+59=1491\frac{5}{9} = \frac{(1 \times 9) + 5}{9} = \frac{9 + 5}{9} = \frac{14}{9}

Step 2: Identify the least common denominator (LCD) for the fractions.

The denominators are 9 and 3. The least common multiple of these is 9.

Step 3: Add the fractions.

  • First, convert all fractions to have the same denominator.
  • 53\frac{5}{3} should be converted: 5×33×3=159\frac{5 \times 3}{3 \times 3} = \frac{15}{9}.
  • Add: 569+159+149=859\frac{56}{9} + \frac{15}{9} + \frac{14}{9} = \frac{85}{9}.

Step 4: Convert 859\frac{85}{9} back to a mixed number.

  • Perform the division: 85÷9=985 ÷ 9 = 9 remainder 44.
  • Therefore, 859=949\frac{85}{9} = 9\frac{4}{9}.

Therefore, the solution to the problem is 9499\frac{4}{9}.

Answer

949 9\frac{4}{9}