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prealgebra intermediate

Problem

For positive numbers

x

and

y

the operation

♠ (x, y)

is defined as

♠ (x, y) = x - \frac{1}{y}

What is

♠ (2, ♠ (2, 2))

?

(A)

\frac{2}{3}

(B)

1

(C)

\frac{4}{3}

(D)

\frac{5}{3}

Solution

♠ (2, 2) = 2 - \frac{1}{2} = \frac{3}{2}

. Then,

♠ (2, \frac{3}{2})

is

2 - \frac{1}{\frac{3}{2}} = 2 - \frac{2}{3} = \frac{4}{3}

The answer is

\frac{4}{3}

Final answer

C