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Difficulty: MediumFraction Operations

A pottery studio has a storage bin containing 151415\frac{1}{4} pounds of dry clay. An instructor removes 4584\frac{5}{8} pounds of the clay for a beginner class and another 3123\frac{1}{2} pounds for an advanced class. Later that day, a new shipment arrives, and 5785\frac{7}{8} pounds of clay are added to the bin. How many pounds of clay are in the bin now?

Answer: 13 pounds

Answer

13
The correct answer is found by establishing a common denominator for all fractions, correctly borrowing a whole number to subtract the first amount of clay, subtracting the second amount, and then adding the final shipment to yield exactly 13 pounds.

Step-by-Step Solution

1
Find a common denominator for all fractions.
1514=152815\frac{1}{4} = 15\frac{2}{8} and 312=3483\frac{1}{2} = 3\frac{4}{8}.
Fractions must have the same denominator before they can be added or subtracted.
2
Subtract the amount of clay used for the beginner class from the total.
1528−458=14108−458=105815\frac{2}{8} - 4\frac{5}{8} = 14\frac{10}{8} - 4\frac{5}{8} = 10\frac{5}{8} pounds.
Since 28\frac{2}{8} is smaller than 58\frac{5}{8}, we borrow 1 from 15 to properly execute the subtraction.
3
Subtract the amount of clay used for the advanced class from the new total.
1058−348=71810\frac{5}{8} - 3\frac{4}{8} = 7\frac{1}{8} pounds.
This accounts for the second removal of clay.
4
Add the newly shipped clay to the remaining amount.
718+578=12887\frac{1}{8} + 5\frac{7}{8} = 12\frac{8}{8} pounds.
The new shipment increases the total inventory.
5
Simplify the final mixed number.
1313 pounds.
88\frac{8}{8} is equal to 1 whole, so 12+1=1312 + 1 = 13.

Key Concept

Addition and subtraction of mixed numbers with unlike denominators, requiring whole-number borrowing.
Estimated Time:1m 15s
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Topics

Fraction Operations

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