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).

Exercise 2. Find -57-60.