$4 \frac{1}{2}+2 \frac{1}{3}$
Answer (2)
Convert the mixed numbers to improper fractions: 4 2 1 = 2 9 and 2 3 1 = 3 7 .
Find a common denominator and add the fractions: 2 9 + 3 7 = 6 27 + 6 14 = 6 41 .
Convert the improper fraction back to a mixed number: 6 41 = 6 6 5 .
The final answer is: 6 6 5 .
Explanation
Understanding the problem We are asked to evaluate the sum of two mixed numbers: 4 r a c 1 2 + 2 r a c 1 3 . A mixed number is a whole number and a proper fraction combined. To add them, we will first convert them into improper fractions, then find a common denominator to 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. To do this, we multiply the whole number by the denominator of the fraction and add the numerator. This result becomes the new numerator, and we keep the same denominator.
For 4 r a c 1 2 , we have 4 t im es 2 + 1 = 9 , so 4 r a c 1 2 = r a c 9 2 .
For 2 r a c 1 3 , we have 2 t im es 3 + 1 = 7 , so 2 r a c 1 3 = r a c 7 3 .
Finding a common denominator Now we need to add the two improper fractions: 2 9 + 3 7 . To add fractions, we need a common denominator. The least common multiple of 2 and 3 is 6. So, we will convert both fractions to have a denominator of 6.
To convert 2 9 to a fraction with a denominator of 6, we multiply both the numerator and denominator by 3: 2 × 3 9 × 3 = 6 27 .
To convert 3 7 to a fraction with a denominator of 6, we multiply both the numerator and denominator by 2: 3 × 2 7 × 2 = 6 14 .
Adding the fractions Now we can add the fractions: 6 27 + 6 14 = 6 27 + 14 = 6 41 .
Converting back to a mixed number Finally, we convert the improper fraction 6 41 back to a mixed number. We divide 41 by 6. The quotient is 6, and the remainder is 5. So, 6 41 = 6 6 5 .
Therefore, 4 2 1 + 2 3 1 = 6 6 5 .
Final Answer The sum of 4 2 1 and 2 3 1 is 6 6 5 .
Examples
Understanding how to add mixed numbers is useful in everyday situations, such as when you're combining measurements in a recipe or calculating the total time spent on multiple tasks. For example, if you need 4 2 1 cups of flour for one cake and 2 3 1 cups of flour for another cake, you can use this skill to determine that you need a total of 6 6 5 cups of flour. This ensures you have enough ingredients and helps in planning your baking efficiently.
The sum of the mixed numbers 4 2 1 and 2 3 1 calculates to 6 6 5 . First, the mixed numbers are converted to improper fractions, then added together using a common denominator, and finally converted back to a mixed number. Thus, the final answer is 6 6 5 .
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