Answer :
Final answer:
To distribute 122 5/8 pounds of mulch across six homes, convert to an improper fraction, divide by six, and simplify to find that each home will receive 20 7/16 pounds.
Explanation:
To divide 122 5/8 pounds of mulch evenly among six homes, we first need to convert the mixed number to an improper fraction. We do this by multiplying the whole number 122 by the denominator 8 and then adding the numerator 5. The conversion is as follows: 122 × 8 + 5 = 976 + 5 = 981. So, 122 5/8 pounds is the same as 981/8 pounds.
Next, we divide 981/8 by 6 to find out how much each home will receive. Dividing a fraction by a whole number is the same as multiplying the fraction by the reciprocal of the whole number. The reciprocal of 6 is 1/6, so we get the following equation:
981/8 × 1/6 = 981/48
To simplify 981/48, we divide both the numerator and the denominator by their greatest common divisor, which is 3. Thus, 981/48 simplifies to 327/16, which is 20 7/16. Therefore, each home will receive 20 7/16 pounds of mulch if it's distributed equally.
