Trish is sorting bolts for her home repair business. She has an 8-pound bag of bolts. If each kitchen her team repairs requires 1/5
pound of bolts, how many kitchen can she repair? Joshua solves the problem by finding 8 ÷ 1/5 = 40
. Melanie solves the problem by finding 8 × 5= 40
. Use the drop-down menus to explain why Joshua and Melanie are both correct.
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a whole number by a unit fraction is the same as multiplying a whole number by the
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of the unit fraction.
First, Joshua is correct because division by a fraction is the same as multiplication by its reciprocal. So, 8 ÷ 1/5 is the same as 8 × 5, which equals 40.
Melanie is also correct because multiplying a whole number by a unit fraction is the same as finding a fraction of that whole number. So, 8 × 5 represents dividing the 8-pound bag of bolts into 1/5 pound portions, which equals 40 portions or kitchens that she can repair.
Therefore, both Joshua and Melanie are correct in their methods of solving the problem.
can you be more specific and among the question pls
Joshua is correct because dividing 8 pounds by 1/5 pound is the same as multiplying by the reciprocal of 1/5, which is 5. So, 8 ÷ 1/5 = 8 × 5, which equals 40.
Melanie is correct because multiplying 8 pounds by the unit fraction 5/1 (representing 1/5 pound) gives the total amount of bolts available, which is 8 × 5 = 40. This represents the number of 1/5 pound portions in the 8-pound bag of bolts.
In conclusion, both Joshua and Melanie are correct in their methods of solving the problem because dividing by a fraction is the same as multiplying by its reciprocal, and multiplying a whole number by a unit fraction is the same as finding a fraction of that whole number.