a driver was 54 feet below the surface of the ocean and then descented another 67 feet. he then rose 59 feet what integer represents the drivers new depth

Question

A -62 feet                                   C 46 feet

 

 

 

 

B -46 feet                                   D 62 feet  

Answer 1

First, words like "descend", "depth", and "below" are all clues for negative numbers and subtraction.  If the meaning is "at depth such and such" that means a negative number, if it is "go up" that means add, and "go down" means subtract. 

 

So 54 feet below means -54 feet, descend 67 means subtract 67, and rose 59 means add 59. 

 

Really, when they first taught this subject to you, they should have used depth examples, because it is easier to work out all the rules.  If you start 54 feet underwater and go down, then you should be getting more negative.  And here is where the phrase "absolute value" is really useful.  The absolute value is the distance from the surface of the water, regardless of whether you are above it or below it.  This starts at 54 and gets larger, which lets you know you need to add the 54 and 67 to get the greater absolute value, the bottom of the dive. 

 

So now the diver is at 121 feet below, or -121.

 

Now going the other direction, we're getting closer to the surface, so we have to subtract the absolute values.  That gets 121 - 59, or 62, and we're still below the water, so that is -62.

 

 

If you think about examples like this, you can get the following rules. 

 

subtracting a negative is adding, for example, 12 - (-4) = 12+4.

Once all the double negatives are eliminated you will only have two kinds of results:

     Both numbers have the same sign, for example, -4-8, 4+8.

     The numbers have opposite signs, for example, 4-8, -4+8, 8-4, -8+4.

If they're the same, add the absolute values and use the sign that both of them had,

     for example, -8-4 = -(8+4) = -12

If they're different, the one with the highest absolute value "wins" and you use that sign, and you subtract

     to find the absolute value, for example, in -8+4, the -8 wins, so the sign is negative.  You subtract 8-4 to get

     the absolute value, so the result is -4.

If no number wins (absolute values the same) the result is zero: 4-4 = -4+4 = 0