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.
________ a whole number by a unit fraction is the same as multiplying a whole number by the _______ of the unit fraction.
_________ options:
First ___: Multiplying or Dividing
Second ___: Numerator or Denominator
First blank: Dividing
Second blank: Reciprocal
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.
________ a whole number by a unit fraction is the same as multiplying a whole number by the _______ of the unit fraction.
_________ options:
First ___: Multiplying or Dividing
Second ___: Numerator or. Denominator
First blank: Dividing
Second blank: Reciprocal
Explanation: When dividing a whole number by a unit fraction, it is equivalent to multiplying the whole number by the reciprocal of the unit fraction. In this case, 8 ÷ 1/5 is the same as 8 multiplied by the reciprocal of 1/5, which is 5. Both Joshua's and Melanie's methods are correct because they essentially used this concept to determine the number of kitchens Trish can repair with the 8-pound bag of bolts.
________ a whole number by a unit fraction is the same as multiplying a whole number by the _______ of the unit fraction.
Dividing a whole number by a unit fraction is the same as multiplying a whole number by the reciprocal of the unit fraction.
What does reciprocal mean
In mathematics, the reciprocal of a number is essentially the multiplicative inverse of that number. For any non-zero number "a", its reciprocal is 1/a. This means that when you multiply a number by its reciprocal, the result is always 1.
Does it mean numerator or denominator
The reciprocal of a fraction refers to flipping the numerator and denominator of the fraction. For example, the reciprocal of the fraction 2/3 is 3/2. So, when we talk about multiplying a whole number by the reciprocal of a unit fraction, we are essentially multiplying the whole number by the flipped fraction in which the numerator and denominator have been interchanged.
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.
________ a whole number by a unit fraction is the same as multiplying a whole number by the _______ of the unit fraction.
_________ options:
First ___: Multiplying or Dividing
Second ___: Denominator or Numerator