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Difficulty: EasyFractions and Rational Numbers

At a certain technology company, 49\frac{4}{9} of the employees work in the sales department and 13\frac{1}{3} of the employees work in the engineering department. If all of the remaining employees work in the administration department, what fraction of the total employees works in the administration department?

  1. 29\frac{2}{9}Answer
  2. B
    79\frac{7}{9}
  3. C
    512\frac{5}{12}
  4. D
    49\frac{4}{9}
  5. E
    19\frac{1}{9}

Answer

29\frac{2}{9}
Expressing 13\frac{1}{3} as 39\frac{3}{9} allows direct addition with 49\frac{4}{9}, giving 79\frac{7}{9} for sales and engineering combined. Subtracting 79\frac{7}{9} from 1 leaves 29\frac{2}{9} for administration.

Step-by-Step Solution

1
Find the total fraction of employees working in sales and engineering.
49+13=49+39=79\frac{4}{9} + \frac{1}{3} = \frac{4}{9} + \frac{3}{9} = \frac{7}{9}
Convert 13\frac{1}{3} to an equivalent fraction with a common denominator of 9 before adding.
2
Subtract the combined fraction from 1 to find the remaining fraction.
1−79=99−79=291 - \frac{7}{9} = \frac{9}{9} - \frac{7}{9} = \frac{2}{9}
The sum of all departmental fractions must equal 1 whole.

Key Concept

Adding fractions with unlike denominators and determining the remaining part of a whole.
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Topics

Fractions and Rational Numbers

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