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Question

Difficulty: EasyFractions and Rational Numbers

A community library received a donation of 120120 new books. On Monday, 38\frac{3}{8} of the donated books were cataloged. On Tuesday, 13\frac{1}{3} of the remaining uncataloged books were cataloged. How many of the donated books remain to be cataloged?

Answer: 50 books

Answer

50 books remain to be cataloged.
First, find the number of books cataloged on Monday: 3/8 of 120 is 45 books. Subtracting 45 from 120 leaves 75 books uncataloged. On Tuesday, 1/3 of those remaining 75 books were cataloged, which is 25 books. Subtracting 25 from 75 gives 50 books remaining to be cataloged.

Step-by-Step Solution

1
Calculate the number of books cataloged on Monday.
45 books
Multiply the initial total of 120 books by the fraction cataloged on Monday, which is 3/8.
2
Calculate the uncataloged books remaining after Monday.
75 books
Subtract the 45 cataloged books from the initial 120 books.
3
Calculate the number of books cataloged on Tuesday.
25 books
Multiply the remaining 75 books by the fraction cataloged on Tuesday, which is 1/3.
4
Calculate the final number of uncataloged books.
50 books
Subtract the 25 books cataloged on Tuesday from the 75 uncataloged books remaining after Monday.

Key Concept

Fraction of a Remaining Quantity
Estimated Time:50s
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Topics

Fractions and Rational Numbers

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