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Glacius
FoundationsConcept reference

Adding signed numbers

The sum of two signed integers combines their signed unit amounts.

1 min read1 figureSources & further reading
On this page 8 sections
  1. Overview
  2. Adding a signed integer changes a starting value
  3. Check your understanding
  4. Check your understanding
  5. Key takeaway
  6. Further questions
  7. Sources & further reading
  8. Concept connections

01Adding a signed integer changes a starting value#

Adding a signed integer changes a starting value. For −2+5-2+5, start at −2-2 and move five unit intervals right. You pass zero and finish at 33.

On a unit-spaced number line, a directed move from -2 to 3 is labeled add +5.On a unit-spaced number line, a directed move from -2 to 3 is labeled add +5.
Figure 1On a unit-spaced number line, a directed move from -2 to 3 is labeled add +5.
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A positive addend moves right; a negative addend moves left. So 3+(−5)3+(-5) moves five units left from 33, ending at −2-2. The sign of an addend tells you the movement, not the sign of the final value.

You can also cancel pairs: one +1+1 and one −1-1 make zero. In −6+4-6+4, four pairs cancel and two negative units remain. In −2+(−3)-2+(-3), all five units are negative.

−6+4=−2-6+4=-2
Check your reasoning

Calculate −4+7-4+7.

Show answer and explanation
3

Four negative units cancel four of the seven positives, leaving 33.

02Check your understanding#

Check your reasoning

Which move adds −3-3?

  1. AMove three units right
  2. BMake every result negative
  3. CMove three units left
Show answer and explanation
Move three units left

Move three units left. The result may stay positive.

03Check your understanding#

Check your reasoning

A temperature starts at 22 degrees and changes by −6-6 degrees. What is the final temperature, in degrees?

Show answer and explanation
-4

Start at 2 and move six units left: 2+(−6)=−42+(-6)=-4.

Key takeaway

Adding a positive moves right; adding a negative moves left.

  • Add two signed integers

Further questions

Does adding a negative always give a negative?
No. For example, 8 plus negative 3 is 5. The start and the change both matter.

Sources & further reading

  1. [1]

Reference this concept

Link to this page, a section, or an individual figure.

Glacius. “Adding signed numbers.” Math behind ML. /learn/f-add-signed