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How to Solve Dan's Milk Carton Serving Fraction Word Problem
Mathematics
Grade 6
Question Content
Apply Math Models: Dan has 4 cartons of milk. He uses 1/8 of a carton for each person at a camp site. How many people can he serve? Draw a picture to help you answer the question.
Correct Answer
32 people
Detailed Solution Steps
1
Step 1: Understand the problem: We have 4 full cartons, and each serving uses 1/8 of a carton. We need to find how many 1/8 portions fit into 4 cartons.
2
Step 2: Set up the calculation: This is a division problem: total cartons ÷ cartons per person = number of people, so 4 ÷ (1/8).
3
Step 3: Solve the division: Dividing by a fraction is the same as multiplying by its reciprocal: 4 × 8/1 = 32.
4
Step 4: Verify with a picture: Draw 4 rectangles (cartons), divide each into 8 equal parts. Count all the parts: 4×8=32, which matches the calculation.
Knowledge Points Involved
1
Dividing Whole Numbers by Fractions
To divide a whole number by a fraction, multiply the whole number by the reciprocal of the fraction. The reciprocal of a fraction a/b is b/a, where a and b are non-zero integers. This method works because we are finding how many of the fractional parts fit into the whole quantity.
2
Modeling Fraction Division with Visuals
Using drawings (like dividing rectangles into equal parts) to represent division of whole numbers by fractions helps visualize the problem, confirm calculations, and understand the relationship between the whole quantity and fractional portions.
3
Real-World Fraction Applications
Applying fraction operations to real-life scenarios (like dividing resources into equal portions) to solve practical problems, which requires translating the word problem into a mathematical equation.
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