From Arithmetic to Algebra: Practice

The equation swaps the order of the two numbers being added without changing the sum.

$a + b = b + a$

Changing the order (commuting) the numbers is the commutative law of addition.

The terms stay in the same order; only the grouping (the parentheses) moves.

$(2 + x) + 5 = 2 + (x + 5)$

Regrouping the same terms is the associative law of addition.

Multiplying any number by $1$ leaves it unchanged, because $1$ is the multiplicative identity.

$7 \cdot 1 = 7$

An equation joins two expressions with an equals sign; an expression alone has none.

$n + 4 = 9$

The other three name a value but make no claim, so they are expressions.

Substitute $4$ for $x$ and add.

$4 + 6 = 10$

Multiply the $3$ across both parts of the sum.

$3(x + 2) = 3x + 6$

Distribute the $2$ to each term inside the parentheses.

$2(n + 5) = 2n + 10$

An identity holds no matter what number the variable stands for.

$a + 0 = a$

This is true for every $a$, which is what makes it an identity.

The commutative law of multiplication swaps the order of the factors.

$xy = yx$

The other choices show the commutative law of addition, the distributive law, and the identity law.

An equals sign asserts that the expressions on its two sides name the same value.

$n + 4 = 9$

This says $n + 4$ and $9$ are the same number.

Multiplying by $1$ returns the same number.

$a \cdot 1 = a$

So $1$ is the multiplicative identity.

"Multiplied by $7$" means $7$ times the number.

$7n$