$2 \frac{1}{2}+4 \frac{3}{4}
Answer (1)
Convert the mixed numbers to improper fractions: 2 2 1 = 2 5 and 4 4 3 = 4 19 .
Find a common denominator and add the fractions: 2 5 + 4 19 = 4 10 + 4 19 = 4 29 .
Convert the improper fraction back to a mixed number: 4 29 = 7 4 1 .
The sum of the mixed numbers is 7 4 1 .
Explanation
Problem Analysis We are asked to add two mixed numbers: 2 2 1 and 4 4 3 . To do this, we will first convert them into improper fractions, then add the fractions, and finally convert the result back into a mixed number.
Converting to Improper Fractions First, convert the mixed numbers to improper fractions: 2 2 1 = 2 2 × 2 + 1 = 2 4 + 1 = 2 5 4 4 3 = 4 4 × 4 + 3 = 4 16 + 3 = 4 19
Finding Common Denominator Now, add the improper fractions. To add them, we need a common denominator. The least common multiple of 2 and 4 is 4. So, we convert 2 5 to a fraction with a denominator of 4: 2 5 = 2 × 2 5 × 2 = 4 10
Adding the Fractions Now we can add the fractions: 4 10 + 4 19 = 4 10 + 19 = 4 29
Converting Back to Mixed Number Finally, convert the improper fraction 4 29 back to a mixed number. To do this, we divide 29 by 4: 29 ÷ 4 = 7 with a remainder of 1. So, 4 29 = 7 4 1
Final Answer Therefore, 2 2 1 + 4 4 3 = 7 4 1 .
Examples
Understanding how to add mixed numbers is useful in everyday situations, such as when you're cooking and need to combine different amounts of ingredients. For example, if a recipe calls for 2 2 1 cups of flour and 4 4 3 cups of sugar, you need to add these amounts to know the total quantity of dry ingredients. The calculation 2 2 1 + 4 4 3 = 7 4 1 tells you that you'll have a total of 7 4 1 cups of dry ingredients.
