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5. How many of the following take integer values? (1)/(1) (11)/(1+1) (111)/(1+1+1) (1111)/(1+1+1+1) (11111)/(1+1+1+1+1) A 0 B 1 C 2 D 3 E 4

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5. How many of the following take integer values? (1)/(1) (11)/(1+1) (111)/(1+1+1) (1111)/(1+1+1+1) (11111)/(1+1+1+1+1) A 0 B 1 C 2 D 3 E 4

5. How many of the following take integer values? (1)/(1) (11)/(1+1) (111)/(1+1+1) (1111)/(1+1+1+1) (11111)/(1+1+1+1+1) A 0 B 1 C 2 D 3 E 4

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DwightMaster · Tutor for 5 years

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C 2.

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This question is asking us to consider five different numbers and answer how many of these numbers are integers. An integer is a number which can be specified without a fractional or decimal component. This means the number is either a whole number or the negative of a whole number.<br /><br />Let's calculate each of these fractions to see if they come out to be integers:<br />- $\frac{1}{1}=1$ which is an integer.<br />- $\frac{11}{1+1} = \frac{11}{2} = 5.5$ which is not an integer.<br />- $\frac{111}{1+1+1} =\frac{111}{3} =37$ which is an integer.<br />- $\frac{1111}{1+1+1+1} = \frac{1111}{4} = 277.75$ which is not an integer.<br />- $\frac{1111}{1+1+1+1+1} =\frac{1111}{5} =222.2$ which is not an integer.<br /><br />Clearly, only 1 (the first fraction) and 37 (the third fraction) are whole numbers.
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