Add. $6 \frac{1}{3}+4 \frac{3}{4}+3 \frac{7}{12}=$
A. $14 \frac{7}{8}$
B. $13 \frac{11}{12}$
C. $13 \frac{2}{3}$
D. $14 \frac{2}{3}$
Answer (2)
Convert the mixed numbers to improper fractions: 6 3 1 = 3 19 , 4 4 3 = 4 19 , 3 12 7 = 12 43 .
Find a common denominator (12) and convert the fractions: 3 19 = 12 76 , 4 19 = 12 57 .
Add the fractions: 12 76 + 12 57 + 12 43 = 12 176 .
Convert the improper fraction back to a mixed number and simplify: 12 176 = 14 12 8 = 14 3 2 .
The final answer is 14 3 2
Explanation
Problem Analysis We need to add three mixed numbers: 6 3 1 , 4 4 3 , and 3 12 7 . To do this, we will first convert each mixed number to an improper fraction.
Converting to Improper Fractions Let's convert the mixed numbers to improper fractions:
6 3 1 = 3 6 × 3 + 1 = 3 18 + 1 = 3 19
4 4 3 = 4 4 × 4 + 3 = 4 16 + 3 = 4 19
3 12 7 = 12 3 × 12 + 7 = 12 36 + 7 = 12 43
Finding a Common Denominator Now we need to add these improper fractions: 3 19 + 4 19 + 12 43 . To add them, we need to find a common denominator. The least common multiple of 3, 4, and 12 is 12. So, we will convert each fraction to have a denominator of 12.
Converting to Equivalent Fractions Converting each fraction to have a denominator of 12:
3 19 = 3 × 4 19 × 4 = 12 76
4 19 = 4 × 3 19 × 3 = 12 57
12 43 (already has a denominator of 12)
Adding the Fractions Now we can add the fractions:
12 76 + 12 57 + 12 43 = 12 76 + 57 + 43 = 12 176
Converting Back to a Mixed Number Now we convert the improper fraction 12 176 back to a mixed number. To do this, we divide 176 by 12:
176 ÷ 12 = 14 with a remainder of 8. So, 12 176 = 14 12 8 .
Simplifying the Fraction We can simplify the fraction 12 8 by dividing both the numerator and denominator by their greatest common divisor, which is 4:
12 8 = 12 ÷ 4 8 ÷ 4 = 3 2
So, 14 12 8 = 14 3 2
Final Answer Therefore, 6 3 1 + 4 4 3 + 3 12 7 = 14 3 2 .
Examples
Understanding how to add mixed numbers is very useful in everyday life. For example, if you are baking and need to combine different amounts of flour from multiple bags, you'll need to add mixed numbers. Suppose you have 6 3 1 cups of flour in one bag, 4 4 3 cups in another, and 3 12 7 cups in a third bag. Adding these quantities together, as we did in the problem, allows you to determine the total amount of flour you have, which is 14 3 2 cups. This ensures you have the correct amount for your recipe!
The sum of the mixed numbers 6 3 1 , 4 4 3 , and 3 12 7 is 14 3 2 . Thus, the correct answer is option D: 14 3 2 .
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