Question Video: Finding an Opposite Quantity to Make Zero Mathematics • 6th Grade

In a game, the white counters count as +1 and the blue counters count as −1. Pick the move that would result in a total score of zero. [A] add one white counter. [B] add one blue counter. [C] subtract two white counters. [D] add two blue counters. [E] subtract two blue counters.

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Video Transcript

In a game, the white counters count as positive one and the blue counters count as negative one. Pick the move that would result in a total score of zero? Is it A) add one white counter B) add one blue counter, C) subtract two white counters, D) add two blue counters, or E) subtract two blue counters?

Each white counter counts as positive one. At present, we have four of them. This means that the total points for white counters is positive four. Each blue counter counts as negative one, and there are currently five blue counters. This gives us a total score of negative five. In order to get a result where the total score is zero, we need the white and blue to be opposites of each other. For example, positive four and negative four or positive five and negative five.

Option E suggested subtracting two blue counters. This would still give us a white total of positive four, but a blue total of negative three as there would be three blue counters. This result is equal to one, therefore it is not equal to zero. Option D, adding two blue counters, would still leave us with four white counters, giving us positive four, but would now give us seven blue counters, giving us negative seven. Once again, this is not equal to zero as positive four minus seven equals negative three.

Option C suggested subtracting two white counters. This would leave us with two white counters and five blue counters, positive two for the whites and negative five for the blues. This is equal to negative three. So once again, it is not equal to zero. Adding one blue counter would leave us with four white counters and six blue counters, positive four for white and negative six for blue. Once again this gives us a nonzero answer of negative two.

Finally, option A asked us to add one more white counter. This would give us five white counters and five blue counters, a score of positive five for white and a score of negative five for blue. Positive five minus five is equal to zero. We can therefore say that adding one white counter would result in a score of zero. As white counters counted as positive one and blue counters counted as negative one, we need the same number of white counters and blue counters.

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