Chapter 1 matsh
Integers (Positive & Negative Numbers)
➕ Addition Rules:
Same signs: Add the numbers and keep the sign
Example: -4 + (-3) = -7
+5 + (+6) = +11Different 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 = -2Square & 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} = 1/9Working with Indices (Index Laws)
a^m × a^n = a^{m+n}
Example: 2^3 × 2^2 = 2^5 = 32a^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 = 729a^{-n} = 1 / a^n
a^0 = 1