$41 \frac{1}{2}+4 \frac{1}{6}$
Answer (1)
Convert the mixed numbers to improper fractions: 41 2 1 = 2 83 and 4 6 1 = 6 25 .
Find a common denominator and add the fractions: 2 83 + 6 25 = 6 249 + 6 25 = 6 274 .
Convert the improper fraction back to a mixed number: 6 274 = 45 6 4 .
Simplify the mixed number: 45 6 4 = 45 3 2 . The final answer is 45 3 2 .
Explanation
Problem Analysis We are asked to add two mixed numbers: 41 2 1 and 4 6 1 . To do this, we will first convert the mixed numbers to improper fractions, then add the fractions, and finally convert the result back to a mixed number.
Converting to Improper Fractions First, convert the mixed numbers to improper fractions:
41 2 1 = 2 41 × 2 + 1 = 2 82 + 1 = 2 83
4 6 1 = 6 4 × 6 + 1 = 6 24 + 1 = 6 25
Adding the Improper Fractions Now, add the two improper fractions. To do this, we need a common denominator, which is the least common multiple (LCM) of 2 and 6. The LCM of 2 and 6 is 6. So, we rewrite 2 83 with a denominator of 6:
2 83 = 2 × 3 83 × 3 = 6 249
Now we can add the fractions:
6 249 + 6 25 = 6 249 + 25 = 6 274
Converting back to Mixed Number Finally, convert the resulting improper fraction back to a mixed number:
6 274 . We divide 274 by 6 to get the whole number part and the remainder:
274 ÷ 6 = 45 with a remainder of 4.
So, 6 274 = 45 6 4 . We can simplify the fraction 6 4 by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
6 4 = 6 ÷ 2 4 ÷ 2 = 3 2
Therefore, the mixed number is 45 3 2
Final Answer The sum of 41 2 1 and 4 6 1 is 45 3 2 .
Examples
In carpentry, if you need to add the lengths of two pieces of wood, one measuring 41 2 1 inches and another measuring 4 6 1 inches, you would perform this calculation to determine the total length needed. This ensures accurate measurements and proper fitting of materials in your project. Knowing how to add mixed numbers is essential for precise work in various practical applications.
