Divide the sum of 3/11 and 2/5 by their product
The Correct Answer and Explanation is:
To solve the problem, follow these steps:
Step 1: Add the fractions 311\frac{3}{11}113 and 25\frac{2}{5}52
To add fractions, find a common denominator. The least common denominator (LCD) of 11 and 5 is 55.311=3×511×5=1555\frac{3}{11} = \frac{3 \times 5}{11 \times 5} = \frac{15}{55}113=11×53×5=551525=2×115×11=2255\frac{2}{5} = \frac{2 \times 11}{5 \times 11} = \frac{22}{55}52=5×112×11=5522
Now add them:1555+2255=3755\frac{15}{55} + \frac{22}{55} = \frac{37}{55}5515+5522=5537
Step 2: Multiply the fractions 311×25\frac{3}{11} \times \frac{2}{5}113×52
Multiply the numerators and then the denominators:311×25=3×211×5=655\frac{3}{11} \times \frac{2}{5} = \frac{3 \times 2}{11 \times 5} = \frac{6}{55}113×52=11×53×2=556
Step 3: Divide the sum by the product
We now divide:3755655\frac{\frac{37}{55}}{\frac{6}{55}}5565537
When dividing fractions, multiply by the reciprocal of the divisor:3755÷655=3755×556\frac{37}{55} \div \frac{6}{55} = \frac{37}{55} \times \frac{55}{6}5537÷556=5537×655
Now cancel the 55 from numerator and denominator:=3755556=376= \frac{37 \cancel{55}}{\cancel{55} 6} = \frac{37}{6}=5563755=637
Final Answer:
376\boxed{\frac{37}{6}}637
Explanation
To solve this problem, we are asked to divide the sum of two fractions by their product. We begin by adding 311\frac{3}{11}113 and 25\frac{2}{5}52. Since the denominators are different, we must find a common denominator. The smallest number that both 11 and 5 divide into is 55. We convert each fraction so they have this common denominator, turning 311\frac{3}{11}113 into 1555\frac{15}{55}5515 and 25\frac{2}{5}52 into 2255\frac{22}{55}5522. Adding these gives 3755\frac{37}{55}5537.
Next, we compute the product of the same two fractions. To multiply, we multiply the numerators together (3 times 2 equals 6) and the denominators together (11 times 5 equals 55), resulting in 655\frac{6}{55}556.
Now, we divide the sum 3755\frac{37}{55}5537 by the product 655\frac{6}{55}556. When dividing fractions, we multiply the first fraction by the reciprocal of the second. The reciprocal of 655\frac{6}{55}556 is 556\frac{55}{6}655. Multiplying 3755\frac{37}{55}5537 by 556\frac{55}{6}655 allows the 55 to cancel out, simplifying the expression to 376\frac{37}{6}637.
The final answer, expressed as an improper fraction, is 376\frac{37}{6}637. This value represents how many times the product of the two original fractions fits into their sum.
