Real Numbers - ACT Math

1. A number plus its opposite equals zero.

1. The opposite changes the sign of a number.

Commutative Property of Addition. Addition order doesn't affect the sum.

1. $\sqrt{4} + \sqrt{9} = 2 + 3 = 5$.

1. Zero is the unique real number that is neither positive nor negative.

1. Exponent means repeated multiplication: $2 \times 2 \times 2 = 8$.

1. Multiplying any real number by $1$ gives the original number.

$\frac{a^n}{b^n}$. Distribute exponent to numerator and denominator.

$(a+b)+c=a+(b+c)$. Addition grouping doesn't affect the result.

$a^{mn}$. Multiply exponents when raising power to power.

$\frac{1}{5}$. The reciprocal multiplied by the original number equals $1$.

Multiplicative Identity Property. Multiplying by $1$ preserves the original value.

-1. Odd power of negative number stays negative.

${0,1,2,3,\dots}$. Natural numbers plus zero.

$a^{-n}=\frac{1}{a^n}$. Negative exponent means reciprocal of positive power.

Undefined. Division by zero is not allowed in real numbers.

1. Multiplying 2 by itself three times: $2^3 = 8$.

1. Zero is neither positive nor negative.

$\sqrt{10}$. $\sqrt{10} \approx 3.16$, which is greater than 3.

1. Multiplying 2 by itself three times: $2^3 = 8$.

$\frac{1}{5}$. Reciprocal means $\frac{1}{\text{original number}}$.

1. Absolute value is always non-negative.

1. Common denominator makes addition straightforward.

Non-negative number. Squaring always produces a non-negative result.

1. The floor function gives the largest integer not exceeding the value.

1. The opposite changes the sign of a number.

Distributive Property. Multiplication distributes over addition.

Irrational. Pi cannot be expressed as a fraction of integers.

1. Adding a negative and positive: $-3 + 7 = 4$.