Solve Mixed Number Addition: 2⅗ + 4⅙ Step-by-Step

Question

235+416= 2\frac{3}{5}+4\frac{1}{6}=

Video Solution

Step-by-Step Solution

To solve the addition of these mixed numbers, we'll follow these steps:

  • Step 1: Convert each mixed number to an improper fraction.
  • Step 2: Find a common denominator and add the fractions.
  • Step 3: Convert the resulting improper fraction back to a mixed number.

Now, let's work through each step:

Step 1: Convert the mixed numbers:
For 235 2\frac{3}{5} , convert to an improper fraction: 2×5+3=10+3=13 2 \times 5 + 3 = 10 + 3 = 13 , so 235=135 2\frac{3}{5} = \frac{13}{5} .
For 416 4\frac{1}{6} , convert to an improper fraction: 4×6+1=24+1=25 4 \times 6 + 1 = 24 + 1 = 25 , so 416=256 4\frac{1}{6} = \frac{25}{6} .

Step 2: Addition of the fractions:
The denominators are 5 and 6. The least common denominator (LCD) is 30 30 .
Convert 135 \frac{13}{5} to 13×65×6=7830 \frac{13 \times 6}{5 \times 6} = \frac{78}{30} .
Convert 256 \frac{25}{6} to 25×56×5=12530 \frac{25 \times 5}{6 \times 5} = \frac{125}{30} .
Now add: 7830+12530=78+12530=20330 \frac{78}{30} + \frac{125}{30} = \frac{78 + 125}{30} = \frac{203}{30} .

Step 3: Convert 20330 \frac{203}{30} back to a mixed number:
Divide 203 by 30: The quotient is 6 and the remainder is 23.
Thus, 20330=62330 \frac{203}{30} = 6\frac{23}{30} .

Therefore, the solution to the problem is 62330 6\frac{23}{30} , which matches choice 3.

Answer

62330 6\frac{23}{30}