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Glacius
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Subtracting signed numbers

Subtracting a signed integer is equivalent to adding its additive opposite.

1 min read1 figureSources & further reading
On this page 8 sections
  1. Overview
  2. Subtracting a number undoes adding it
  3. Check your understanding
  4. Check your understanding
  5. Key takeaway
  6. Further questions
  7. Sources & further reading
  8. Concept connections

01Subtracting a number undoes adding it#

Subtracting a number undoes adding it. Adding −4-4 moves four units left, so subtracting −4-4 moves four units right. Starting at −2-2, you finish at 22.

On a unit-spaced number line, a directed move from -2 to 2 is labeled subtract −4.On a unit-spaced number line, a directed move from -2 to 2 is labeled subtract −4.
Figure 1On a unit-spaced number line, a directed move from -2 to 2 is labeled subtract −4.
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Replace subtraction with addition of the opposite. Keep the first number and change the second number’s sign. For −2−(−4)-2-(-4), add +4+4 to −2-2 to get 22.

−2−(−4)=2-2-(-4)=2

Subtracting a positive also follows this rule. For −2−4-2-4, add −4-4: move four units left and reach −6-6. Parentheses make the sign of the second number easy to see.

−2−4=−6-2-4=-6
Check your reasoning

Calculate 3−(−5)3-(-5).

Show answer and explanation
8

Keep 3 and add the opposite of −5: 3+5=83+5=8.

02Check your understanding#

Check your reasoning

Which addition is equal to −4−(−2)-4-(-2)?

  1. A4+24+2
  2. B−4+2-4+2
  3. C−4+(−2)-4+(-2)
Show answer and explanation
−4+2-4+2

Keep −4. The opposite of −2 is +2.

03Check your understanding#

Check your reasoning

A sensor reads −3-3 and its reference reads −7-7. The error is reading minus reference. What is the signed error?

Show answer and explanation
4

Subtract the reference: −3−(−7)=−3+7=4-3-(-7)=-3+7=4.

Key takeaway

Keep the first number and add the opposite of the second.

  • Subtract one signed integer from another

Further questions

Why do two nearby minus signs become a plus?
Only the pattern subtract a negative becomes add a positive. Keep the first number unchanged; do not erase every minus sign.

Sources & further reading

  1. [1]

Reference this concept

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

Glacius. “Subtracting signed numbers.” Math behind ML. /learn/f-subtract-signed