$8 \frac{1}{4}+2 \frac{1}{2}=$
Answer (1)
Convert the mixed numbers to improper fractions: 8 4 1 = 4 33 and 2 2 1 = 2 5 .
Find a common denominator and rewrite the fractions: 2 5 = 4 10 .
Add the fractions: 4 33 + 4 10 = 4 43 .
Convert the improper fraction back to a mixed number: 4 43 = 10 4 3 . The final answer is 10 4 3 .
Explanation
Understanding the Problem We are asked to calculate the sum of two mixed numbers: 8 4 1 and 2 2 1 . A mixed number is a whole number and a proper fraction combined. To add them, we can convert them to improper fractions, add the fractions, and then convert back to a mixed number or a simplified fraction.
Converting to Improper Fractions First, let's convert the mixed numbers to improper fractions. 8 4 1 = 4 8 × 4 + 1 = 4 32 + 1 = 4 33 2 2 1 = 2 2 × 2 + 1 = 2 4 + 1 = 2 5
Finding a Common Denominator Now, we need to add the two improper fractions: 4 33 + 2 5 . To do this, we need a common denominator. The least common denominator of 4 and 2 is 4. So, we rewrite 2 5 with a denominator of 4: 2 5 = 2 × 2 5 × 2 = 4 10
Adding the Fractions Now we can add the fractions: 4 33 + 4 10 = 4 33 + 10 = 4 43
Converting Back to a Mixed Number Finally, we convert the improper fraction 4 43 back to a mixed number. We divide 43 by 4: 43 ÷ 4 = 10 with a remainder of 3. So, 4 43 = 10 4 3
Final Answer Therefore, 8 4 1 + 2 2 1 = 10 4 3 .
Examples
Imagine you are baking a cake and the recipe calls for 8 4 1 cups of flour and 2 2 1 cups of sugar. To find the total amount of dry ingredients, you need to add these two mixed numbers together. The result, 10 4 3 cups, tells you the total volume of dry ingredients required for the cake. This kind of calculation is useful in many everyday situations involving measurements and quantities.
