Solve Mixed Number Division: 6⅔ ÷ 2½ Step-by-Step

Question

623:212= 6\frac{2}{3}:2\frac{1}{2}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Convert each mixed number to an improper fraction.
  • Step 2: Divide the fractions by multiplying by the reciprocal of the divisor.
  • Step 3: Simplify the resulting improper fraction and convert it back to a mixed number.

Let's work through these steps:

Step 1: Convert the mixed numbers:
623=6×3+23=203 6\frac{2}{3} = \frac{6 \times 3 + 2}{3} = \frac{20}{3}
212=2×2+12=52 2\frac{1}{2} = \frac{2 \times 2 + 1}{2} = \frac{5}{2}

Step 2: Divide the fractions:
To divide 203\frac{20}{3} by 52\frac{5}{2}, we multiply by the reciprocal of 52\frac{5}{2}:
203×25=20×23×5=4015\frac{20}{3} \times \frac{2}{5} = \frac{20 \times 2}{3 \times 5} = \frac{40}{15}

Step 3: Simplify and convert back:
Simplify 4015\frac{40}{15}:
The greatest common divisor of 40 and 15 is 5:
4015=83\frac{40}{15} = \frac{8}{3}
Convert 83\frac{8}{3} to a mixed number:
8÷3=28\div3 = 2 remainder 22, so 83=223\frac{8}{3} = 2\frac{2}{3}.

Therefore, the solution to the problem is 223 2\frac{2}{3} .

Answer

223 2\frac{2}{3}