Official Guide Explanation:
Problem Solving #93




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Solution and Metadata

Question: 93
Page: 73
Difficulty: 4 (Moderately Easy)
Category 1: Arithmetic > Decimals >
Category 2: Arithmetic > Fractions >

Explanation: This wouldn't be too arduous if you chose to multiply (-1.5)(1.2) and (4.5)(0.4), but it's good to get in other habits. 4.5 is three times 1.5, so the numerator can be factored as follows:

(-1.5)(1.2) - (4.5)(0.4) = (1.5)(-1.2 - (3)(0.4))

Similarly, 0.4 can be factored out as well:

(1.5)(-1.2 - (3)(0.4)) = (1.5)(0.4)(-3 - 3) = (1.5)(0.4)(-6)

Now, that makes the fraction easier to work with:

(((1.5)(0.4)(-6))/30) = ((-(1.5)(0.4))/5) = ((-0.6)/5) = ((-6)/50) = ((-12)/100)= - 0.12, choice (B).

This method may involve more steps, but each step is faster, and since it avoids decimal multiplication whenever possible, it avoids many chances for careless mistakes.

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