Question
Trish is sorting bolts for her home repair business she has an 8 lb bag of bolts if each kitchen her team repairs requires one over five Pound of bolts How many kitchens can she repair Joshua solves the problem by finding 8 / 1/5 equal 40 Melanie solves a problem by finding 8 * 5 = 40 use a drop down menus to explain why Joshua and Melanie are both correct blank A multiplying B dividing a whole number by a unit fraction is the same as multiplying a whole number by the blank A numerator B denominator of the unit fraction
Answers
Answered by
GPT-4o mini
Both Joshua and Melanie are correct in their calculations, but they approached the problem from different perspectives using different operations.
1. **Joshua's approach:**
- He divides the total weight of bolts (8 pounds) by the weight needed for one kitchen (1/5 pound). The calculation he performed is \( 8 \div (1/5) \). When you divide by a fraction, it is equivalent to multiplying by its reciprocal, so this is the same as \( 8 \times 5 = 40 \). Thus, he correctly finds that she can repair 40 kitchens.
2. **Melanie's approach:**
- She multiplies the total weight of bolts by the whole number in the denominator (5). Her calculation \( 8 \times 5 = 40 \) essentially arrived at the same result but from a different viewpoint: she is figuring out how many units of 1/5 pound are in 8 pounds.
Based on this, we can fill in the blank from the dropdown menus:
1. **For Joshua's method:**
- A: **dividing**
2. **For Melanie's method:**
- B: **denominator**
So, the complete sentence would be: "Dividing a whole number by a unit fraction is the same as multiplying a whole number by the denominator of the unit fraction."
1. **Joshua's approach:**
- He divides the total weight of bolts (8 pounds) by the weight needed for one kitchen (1/5 pound). The calculation he performed is \( 8 \div (1/5) \). When you divide by a fraction, it is equivalent to multiplying by its reciprocal, so this is the same as \( 8 \times 5 = 40 \). Thus, he correctly finds that she can repair 40 kitchens.
2. **Melanie's approach:**
- She multiplies the total weight of bolts by the whole number in the denominator (5). Her calculation \( 8 \times 5 = 40 \) essentially arrived at the same result but from a different viewpoint: she is figuring out how many units of 1/5 pound are in 8 pounds.
Based on this, we can fill in the blank from the dropdown menus:
1. **For Joshua's method:**
- A: **dividing**
2. **For Melanie's method:**
- B: **denominator**
So, the complete sentence would be: "Dividing a whole number by a unit fraction is the same as multiplying a whole number by the denominator of the unit fraction."