Video: Determining an Expression for Evaluating the Distance between Two Quantities

A fisherman on a boat spotted a fish 3 meters below sea level and a bird 4 meters above sea level. Which expression represents the distance between the fish and the bird? [A] |4 − 3| [B] −4 − 3 [C] −4 + 3 [D] |4 − (−3)| [E] 3 − 4

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Video Transcript

A fisherman on a boat spotted a fish three meters below sea level and a bird four meters above sea level. Which expression represents the distance between the fish and the bird? Is it (A) the absolute value of four minus three, (B) negative four minus three, (C) negative four plus three, (D) the absolute value of four minus negative three, or (E) three minus four?

The absolute value or modulus of a number is the distance between the number and zero. In this question, we will consider the sea level as zero. As the fish is three meters below sea level, it has a value of negative three. The bird, on the other hand, is four meters above sea level, so has a value of positive four or four. To find the difference or distance between these, we need to subtract them so we could have positive four minus negative three or negative three minus positive four.

As our answer is a distance, it has to be positive. Therefore, we need to find the absolute value or modulus of either one of these answers. We don’t need to include the positive sign in front of the four, so we have two correct answers, the absolute value of four minus negative three or the absolute value of negative three minus four. The option that corresponds to one of these is (D) the absolute value of four minus negative three. Whilst we don’t need to in this question, we could calculate this value. Subtracting a negative value is the same as adding that value. Four plus three is equal to seven, so we have the absolute value of seven.

Our second correct answer, negative three minus four, is equal to negative seven. So we’re left with the absolute value of negative seven. As the absolute value is the distance of a number from zero, both of these are equal to seven. If we look at the incorrect options, option (A) would be equal to one as four minus three is one and the absolute value of this is one. Option (B) gives us an answer of negative seven. Options (C) and (E) both give us an answer of negative one.

It is therefore clear that options (B), (C), and (E) cannot be correct as the distance must be positive. We can see from the number line that the correct answer should be seven.

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