Final answer:
To calculate the total number of boxes recycled, we add 5(4/6) boxes and 3(4/10) boxes by converting them to improper fractions, simplifying, finding a common denominator, and adding. The total comes to 9(1/15) recycled boxes.
Step-by-step explanation:
The question asks us to find the total number of recycled boxes by Mrs. Brick's class over two months. To calculate this, we need to add the two mixed numbers: 5(4/6) boxes recycled in January and 3(4/10) boxes recycled in February.
Let's first convert the mixed numbers to improper fractions:
5(4/6) = (5 × 6 + 4) / 6 = (30 + 4) / 6 = 34/6, and
3(4/10) = (3 × 10 + 4) / 10 = (30 + 4) / 10 = 34/10.
Next, we should simplify these fractions:
34/6 = 17/3 (after dividing both numerator and denominator by 2), and
34/10 = 17/5 (after dividing both numerator and denominator by 2).
Now we can add these simplified fractions:
17/3 + 17/5.
To add these, we first find a common denominator, which is 15. We then convert each fraction:
17/3 = (17 × 5) / (3 × 5) = 85/15, and
17/5 = (17 × 3) / (5 × 3) = 51/15.
Finally, add the numerators:
85/15 + 51/15 = (85 + 51) / 15 = 136/15.
To convert this back into a mixed number, divide the numerator by the denominator:
136 ÷ 15 = 9 with a remainder of 1, so we get 9(1/15) boxes.
Therefore, the total number of boxes recycled by Mrs. Brick's class over the two months is 9(1/15) boxes.