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.