Solve: Adding Mixed Numbers 4⅖ + 1³/₁₀ + 2¹/₂₀ + 2³/₅

Question

425+1310+2120+235= 4\frac{2}{5}+1\frac{3}{10}+2\frac{1}{20}+2\frac{3}{5}=

Video Solution

Step-by-Step Solution

To solve this problem of adding mixed numbers, follow these well-defined steps:

  • Step 1: Convert the mixed numbers to improper fractions.
  • Step 2: Find the least common denominator (LCD).
  • Step 3: Convert each fraction to have the LCD as the denominator.
  • Step 4: Sum the fractions, and finally, convert back to a mixed number if necessary.

Let us apply these steps to the given numbers:

Step 1: Convert to improper fractions:
- 425=225 4\frac{2}{5} = \frac{22}{5}
- 1310=1310 1\frac{3}{10} = \frac{13}{10}
- 2120=4120 2\frac{1}{20} = \frac{41}{20}
- 235=135 2\frac{3}{5} = \frac{13}{5}

Step 2: Find the least common denominator: The denominators are 5, 10, and 20. The LCD of these is 20.

Step 3: Convert fractions to have this LCD:
- 225=8820 \frac{22}{5} = \frac{88}{20}
- 1310=2620 \frac{13}{10} = \frac{26}{20}
- 4120 remains 4120 \frac{41}{20} \text{ remains } \frac{41}{20}
- 135=5220 \frac{13}{5} = \frac{52}{20}

Step 4: Add the fractions:
8820+2620+4120+5220=20720\frac{88}{20} + \frac{26}{20} + \frac{41}{20} + \frac{52}{20} = \frac{207}{20}

Convert 20720\frac{207}{20} into a mixed number:
207÷20=10 207 \div 20 = 10 remainder 7 7 , so we have 10720 10\frac{7}{20} .

Therefore, the sum of the mixed numbers 425+1310+2120+235 4\frac{2}{5} + 1\frac{3}{10} + 2\frac{1}{20} + 2\frac{3}{5} is 10720 10\frac{7}{20} .

Answer

10720 10\frac{7}{20}