# Adding Integers

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

If you **add integers with different signs**, i.e. one is positive and another is negative, then subtract negative number without minus from positive number.

Note, that if **you add negative number and positive**, you'are actually subtract negative integer without minus from positive integer, that is $$${\color{blue}{{{a}+{\left(-{b}\right)}={a}-{b}}}}$$$.

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

We actually want to subtract 21 from 46: $$${46}-{21}={35}$$$.

So,** $$${46}+{\left(-{21}\right)}={35}$$$ **.

Next example.

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

We actually want to subtract 35 from 21: $$${21}-{35}=-{14}$$$.

If you're not comfortable with subtracting bigger number from smaller then change sign of each number: now we want to find 35-21=14.

And change sign back: 14 transforms into -14.

So,** $$$-{35}+{21}=-{14}$$$.**

- If you
**add two positive numbers**, you're actually adding whole numbers. - If you
**add two negative numbers**, add numbers without minus and then place minus in front of result, i.e. $$${\color{green}{{-{a}-{b}=-{\left({a}+{b}\right)}}}}$$$.

**Example 3.** Find $$${23}+{51}$$$.

$$${23}+{51}={74}$$$.

Another example.

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

Ignore minuses: $$${48}+{19}={67}$$$. Place minus in front of result: -67.

So,** $$$-{48}+{\left(-{19}\right)}={67}$$$ **.

Final example shows how to add more than two integers.

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

We do such problems step-by-step.

First find $$$-{48}+{\left(-{45}\right)}$$$. Ignore minuses: $$${48}+{45}={93}$$$. Set minus in front of result: -93.

Now we are left with $$$-{93}+{34}$$$. Change sign of every number: $$${93}-{34}={59}$$$.

Change sign back: -59.

So,** $$$-{48}+{\left(-{45}\right)}+{34}=-{59}$$$.**

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

**Exercise 1**. Find 36+(-21).

**Answer**: 15.

**Exercise 2**. Find -57+60.

**Answer**: 3.

**Exercise 3**. Find -100+69.

**Answer**: -31.

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

**Answer**: -105.

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

**Answer**: -58.