Solve Mixed Number Expression: 5½ - 2¾ + 4⅓

Question

512234+426= 5\frac{1}{2}-2\frac{3}{4}+4\frac{2}{6}=

Video Solution

Step-by-Step Solution

To solve this problem, we will perform the following steps:

  • Convert each mixed fraction into an improper fraction.
  • Find a common denominator for these fractions.
  • Perform the subtraction and addition operations.
  • Convert the result back into a mixed number.
  • Simplify the final answer if necessary.

Let’s proceed with these steps.

Step 1: Convert to improper fractions
For 512 5\frac{1}{2} :
512=5×2+12=112 5\frac{1}{2} = \frac{5 \times 2 + 1}{2} = \frac{11}{2}

For 234 2\frac{3}{4} :
234=2×4+34=114 2\frac{3}{4} = \frac{2 \times 4 + 3}{4} = \frac{11}{4}

For 426 4\frac{2}{6} (simplified as 413 4\frac{1}{3} ):
426=413=4×3+13=133 4\frac{2}{6} = 4\frac{1}{3} = \frac{4 \times 3 + 1}{3} = \frac{13}{3}

Step 2: Find a common denominator
The denominators are 22, 44, and 33. The least common multiple of these is 1212.
Convert each fraction:
112=11×62×6=6612 \frac{11}{2} = \frac{11 \times 6}{2 \times 6} = \frac{66}{12}
114=11×34×3=3312 \frac{11}{4} = \frac{11 \times 3}{4 \times 3} = \frac{33}{12}
133=13×43×4=5212 \frac{13}{3} = \frac{13 \times 4}{3 \times 4} = \frac{52}{12}

Step 3: Perform the operations
First, perform the subtraction:
66123312=3312 \frac{66}{12} - \frac{33}{12} = \frac{33}{12}

Now, add 3312 \frac{33}{12} and 5212 \frac{52}{12} :
3312+5212=8512 \frac{33}{12} + \frac{52}{12} = \frac{85}{12}

Step 4: Convert back to a mixed number
8512 \frac{85}{12} as a mixed number is 7112 7\frac{1}{12} because:
8512=7 \frac{85}{12} = 7 remainder 11, thus 71127\frac{1}{12}.

Step 5: Simplify
The fraction 112 \frac{1}{12} is already in its simplest form.

Therefore, the correct answer is 7112 7\frac{1}{12} .

Answer

7112 7\frac{1}{12}