# On vacation, Sierra hiked to the 9970-foot summit of Haleakala volcano in Hawaii. The next day, she went scuba diving at a depth of 47 feet below sea level. What is the difference between the elevation of the summit of Haleakala and the depth Sierra dove?

The difference in elevation is 10,017 feet.

We are given that Sierra hiked to the summit (top) of Haleakala volcano, which is at an elevation of 9,970 feet. (Note that elevation is understood to be the distance above sea level.) Later, Sierra dove to a depth of 47 feet below sea level. We are asked to find the difference in elevation between these points.

In terms of the sea level, we can write the two numbers as integers (signed whole numbers). We let distance above sea level be a positive number and depth below sea level a negative number. The word difference indicates subtraction.

(1) 9970 - (-47)

Subtraction means to add the opposite of the number, so 9970 + 47 = 10017

(2) We can think of a negative sign as taking a number times negative one. 9970 + (-1)(-47); a negative number times a negative number yields a positive number, so 9970 + 47 = 10017.

(3) If you drew a picture, you would have the distance from the surface of the ocean as 9970 feet for the summit. You would see a distance of 47 feet in the opposite direction for the dive.

-----------------9970----------------------------------------|--47--
So the total distance is 9970 + 47 = 10017.

(4) When subtracting two numbers of opposite sign, we can add the absolute value of the two numbers and apply the sign of the minuend (minuend - subtrahend = difference). For example, 3 - (-4) can be written as +(|3|+|-4|) = +(3 + 4) = 7, where -4-3 can be written as -(|-4|+|3|) = -(4 + 3) = -7.

So here, we have 9970 - (-47) = + (|9970|+|-47|)= +(9970 + 47) = 10017.

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