Two hot air balloons were flying at the same height. Then, balloon A ascended 15 feet, while balloon B descended 15 feet. If we represent these changes by integers, will they sum to zero?
The word “ascended” means increased or goes upwards, whereas the word “descended” means decrease or goes downwards. As balloon A ascended by 15 feet, we can say that the change in height for balloon A was positive 15. Likewise, as balloon B descended by 15 feet, its change in height will be negative 15.
We were asked to work out whether the sum of these changes is equal to zero. We could calculate the sum in one of two ways: either positive 15 minus 15 or negative 15 plus 15. Both of these calculations give us an answer of zero. We can therefore conclude that, yes, the changes in heights do sum to zero.
We can go one step further here and say that any two opposite quantities will always sum to zero. For example, the integer values negative three and three and eight, negative eight both sum to zero. The fractions two-fifths and negative two-fifths sum to zero. And the decimals negative 0.71 and 0.71 also sum to zero.
Even if the changes were not integers, if they were opposites, they would always sum to zero.