Chapter 1 matsh

Integers (Positive & Negative Numbers)
➕ Addition Rules:

Same signs: Add the numbers and keep the sign
Example: -4 + (-3) = -7
+5 + (+6) = +11
Different signs: Subtract smaller from bigger, take sign of the bigger number
Example: -6 + 10 = 4
8 + (-12) = -4
➖ Subtraction Rules:
Subtracting a negative = adding: -2 - (-5) = -2 + 5 = 3
Subtracting a positive is normal: 6 - 3 = 3; -4 - 2 = -6
Tip: a - (-b) = a + b

Multiplying & Dividing Integers
Same signs = Positive
Different signs = Negative
Examples:
-4 × -2 = +8
6 ÷ -3 = -2
Square & Cube Roots
Square Root (\sqrt):

Example: $\sqrt{64} = 8$ because 8 × 8 = 64
$\sqrt{111} ≈ 10.53$ → Nearest whole number = 11
Cube Root (\sqrt[3]):
Example: $\sqrt[3]{27} = 3$ because 3 × 3 × 3 = 27
$\sqrt[3]{100} ≈ 4.64$ → Nearest whole number = 5

Rounding to Nearest Whole Number (for Roots)
Check the first digit after the decimal:

5 or more → round up
Less than 5 → round down
Examples:
$\sqrt{111} ≈ 10.53$ → 11
$\sqrt[3]{825} ≈ 9.37$ → 9

Indices / Powers
Positive powers: $a^n = a × a × …$ (n times)
Example: $2^3 = 8$
Zero power: $a^0 = 1$ (as long as a ≠ 0)
Example: $5^0 = 1$
Negative powers: $a^{-n} = 1 / a^n$
Example: $3^{-2} = 1/9$
Working with Indices (Index Laws)
$a^m × a^n = a^{m+n}$
Example: $2^3 × 2^2 = 2^5 = 32$
$a^m ÷ a^n = a^{m−n}$
Example: $5^4 ÷ 5^2 = 5^2 = 25$
$(a^m)^n = a^{m×n}$
Example: $(3^2)^3 = 3^6 = 729$
$a^{-n} = 1 / a^n$
$a^0 = 1$