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