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Question Video: Multiplication of Integers with Absolute Values Then Comparing Mathematics

Which of the following is true? [A] |−90| × 30 > 80 × |−90| [B] |−90| × 30 < 80 × |−90| [C] |−90| × 30 = 80 × |−90|

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Video Transcript

Which of the following is true? (A) The absolute value of negative 90 times 30 is greater than 80 times the absolute value of negative 90. (B) The absolute value of negative 90 times 30 is less than 80 times the absolute value of negative 90. Or (C) the absolute value of negative 90 times 30 is equal to 80 times the absolute value of negative 90.

All three of our options are comparing the same two expressions. The absolute value of negative 90 times 30 is being compared to 80 times the absolute value of negative 90. If we consider the absolute value of negative 90, this will be positive 90. And that means, on the left, we’ll have 90 times 30 and, on the right, we’ll have 80 times 90. That means that 30 is being multiplied by 90 and 80 is being multiplied by 90. Since we know that 30 is less than 80, 90 times 30 will be less than 80 times 90. And that means we’re looking for the inequality with the less than symbol. And that is option (B).

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