Prerequisites
Arithmetic | 2 of 17
Prerequisites: Numbers and Place Value. Enables: Subtraction, Multiplication.
Addition combines quantities.
For two numbers:
where:
$a$ and $b$ are addends
$c$ is the sum
Properties of addition
| Property | Rule |
|---|---|
| Commutative property | $a + b = b + a$ |
| Associative property | $(a + b) + c = a + (b + c)$ |
| Additive identity | $a + 0 = a$ |
| Additive inverse | $a + (-a) = 0$ |
Adding whole numbers
Line up digits by place value.
Example:
Add ones:
Regroup $14$ ones as $1$ ten and $4$ ones. Write $4$ in the ones place and carry $1$ ten to the tens column.
Add tens:
Regroup $12$ tens as $1$ hundred and $2$ tens. Write $2$ in the tens place and carry $1$ hundred to the hundreds column.
Add hundreds:
Therefore:
Adding decimals
Line up decimal points before adding.
Example:
Rewrite as:
Then:
Adding quantities with the same units
Only quantities with the same units should be added directly.
Example:
Combining symbolic terms such as $3x+5x$ belongs to Like terms in Algebra.
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