Solve: 3/10 Divided by 2½ - Mixed Number Division

Question

310:212= \frac{3}{10}:2\frac{1}{2}=

Video Solution

Step-by-Step Solution

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

  • Step 1: Convert the mixed number to an improper fraction.
  • Step 2: Find the reciprocal of the improper fraction.
  • Step 3: Multiply the first fraction by this reciprocal.
  • Step 4: Simplify the result to get the final answer.

Let's go through each step in detail:

Step 1: Convert 212 2\frac{1}{2} to an improper fraction:

212 2\frac{1}{2} is equal to 2+12=42+12=52 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} .

Step 2: Find the reciprocal of 52 \frac{5}{2} :

The reciprocal of 52 \frac{5}{2} is 25 \frac{2}{5} .

Step 3: Multiply 310 \frac{3}{10} by 25 \frac{2}{5} :

310×25=3×210×5=650 \frac{3}{10} \times \frac{2}{5} = \frac{3 \times 2}{10 \times 5} = \frac{6}{50} .

Step 4: Simplify 650 \frac{6}{50} :

To simplify, we find the greatest common divisor of 6 and 50, which is 2:

650=325 \frac{6}{50} = \frac{3}{25} after dividing the numerator and denominator by 2.

Therefore, the solution to the problem is 325 \frac{3}{25} . This matches choice 2.

Answer

325 \frac{3}{25}