Download Lesson #2 Practice Set C

Opposite Quantities Combine to Make Zero
Practice Set C
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Date:
1. Explain how zero pairs can help you when adding a positive and negative
number.
2. Does this apply to all rational numbers (fractions and decimals)? Justify your
answer with examples.
3. Does this apply to problems with more than two addends.
with examples.
Justify your answer
Opposite Quantities Combine to Make Zero
Practice Set C Answer Key
1. Explain how zero pairs can help you when adding a positive and negative
number.
Positives and negatives have opposite values. When you have the same quantity of
positives and negatives, they combine to make zero pairs, or zero.
So, when
adding a positives and negatives you can just look to see which group has more
(greater absolute value)? That will tell you if the answer is positive or negative.
The difference between positives and negatives tells the exact value.
2. Does this apply to all rational numbers (fractions and decimals)? Justify your
answer with examples.
Yes, it applies to all rational numbers because all rational numbers have opposites
and opposites combine to make zero. For example, the opposite of 1.3 is -1.3, and
if those two numbers were added together, the sum would be zero because they are
equally far from zero. The same holds true for fractions.
The opposite of ½ is -½
and when they are added together the result is zero, which lays in between the two
numbers on the number line. They don’t have to be zero pairs though. You could
have 1.4 + -0.2 and also get a sum between the addends. The -0.2 would create a
zero pair with 0.2, leaving only 1.2 as the sum, which lays between the addends on
the number line. The same holds true for fractions.
3. Does this apply to problems with more than two addends?
Justify your answer
with examples.
Yes, it applies when there are more than two addends. What you are looking for is
the net difference. You can group all the positives together and all the negatives
together. Then just find the difference of the absolute values of those totals,
because that is what will be left over after positives and negatives create zero pairs.
1.2 + -3.5
1.2 will join with its opposite (-1.2) to create zero pairs, this
leaves -2.3 for the sum.
This is the same thing as 3.5 - 1.2 = -2.3 (the difference
of the addend’s absolute values).
¾ + -¼
The negative ¼ will join with a positive ¼ to make zero pairs.
This leaves 2/4 or ½.
This is the same thing as ¾ - ¼ = ½ (the difference of their
absolute values). This works because of zero pairs. After they match up and cancel
each other out, left over is the sum or difference (difference of absolute values).