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.

Question

________ 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

Answer 1

First blank: Dividing

Second blank: Reciprocal

Answer 2

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

Answer 3

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.

Answer 4

________ a whole number by a unit fraction is the same as multiplying a whole number by the _______ of the unit fraction.

Answer 5

Dividing a whole number by a unit fraction is the same as multiplying a whole number by the reciprocal of the unit fraction.

Answer 6

What does reciprocal mean

Answer 7

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.

Answer 8

Does it mean numerator or denominator

Answer 9

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.

Answer 10

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

Answer 11

First blank: Dividing

Second blank: Reciprocal

Explanation: Dividing a whole number by a unit fraction is equivalent to multiplying the whole number by the reciprocal of the unit fraction. The reciprocal of 1/5 is 5/1 (which is just 5), so both Joshua's (8 ÷ 1/5) and Melanie's (8 × 5) methods are correct for determining the number of kitchens Trish can repair with the 8-pound bag of bolts.