Subtracting Integers

Integers are subtracted in the same fashion as whole numbers, except that certain rules should be applied.

  • If you subtract negative integer from positive then just add numbers ignoring any minuses, i.e $$${\color{blue}{{{a}-{\left(-{b}\right)}={a}+{b}}}}$$$.
  • If you subtract positive integer from negative, add numbers ignoring any minuses and then place minus in front of result, i.e. $$${\color{green}{{-{a}-{b}=-{\left({a}+{b}\right)}}}}$$$.

Example 1. Find $$${46}-{\left(-{21}\right)}$$$.


So, $$${46}-{\left(-{21}\right)}={67}$$$ .

Next example.

Example 2. Find $$$-{35}-{21}$$$.


So, $$$-{35}-{21}=-{56}$$$.

  • If you subtract positive integer from positive, then you are actually subtracting whole numbers.
  • If you subtract two negative numbers use following rule: $$${\color{blue}{{-{a}-{\left(-{b}\right)}=-{a}+{b}={b}-{a}}}}$$$.

Example 3. Find $$${23}-{51}$$$.


Another example.

Example 4. Find $$$-{48}-{\left(-{19}\right)}$$$.


So, $$$-{48}-{\left(-{19}\right)}=-{29}$$$ .

Final example shows how to subtract more than two integers.

Example 5. Find $$$-{48}-{\left(-{45}\right)}-{34}$$$.

We do such problems step-by-step.

First find $$$-{48}-{\left(-{45}\right)}$$$. $$$-{48}-{\left(-{45}\right)}=-{48}+{45}=-{3}$$$.

Now we are left with $$$-{3}-{34}$$$. $$$-{3}-{34}=-{\left({3}+{34}\right)}=-{37}$$$.

So, $$$-{48}-{\left(-{45}\right)}-{34}=-{37}$$$.

Now, it's your turn. Take pen and paper and solve following problems.

Exercise 1. Find 36-(-21).

Answer: 57.

Exercise 2. Find -57-60.

Answer: -117.

Exercise 3. Find 100-69.

Answer: 31.

Exercise 4. Find -45-(-60).

Answer: 15.

Exercise 5. Find 65-(-34)-(-35)-21-(-45)-100.

Answer: 58.