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 $$${46}-{\left(-{21}\right)}$$$.
$$${46}-{\left(-{21}\right)}={46}+{21}={67}$$$.
So, $$${46}-{\left(-{21}\right)}={67}$$$ .
Next example.
Example 2. Find $$$-{35}-{21}$$$.
$$$-{35}-{21}=-{\left({35}+{21}\right)}=-{56}$$$.
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 $$${23}-{51}$$$.
$$${23}-{51}=-{28}$$$.
Another example.
Example 4. Find $$$-{48}-{\left(-{19}\right)}$$$.
$$$-{48}-{\left(-{19}\right)}=-{48}+{19}={19}-{48}=-{29}$$$.
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.