🥋 Basic Math – White to Black Belt Mastery

Intro Quote

“Strong foundations build unshakable strength.”

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White Belt – Key Concept

Basic math is the language of physics.
It gives you the tools to measure, compare, and solve problems.

Core skills include:

• Addition and subtraction
• Multiplication and division
• Exponents and roots
• Order of operations

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Core Principles

1. Numbers represent quantities we measure.
2. Operations follow a set order: parentheses, exponents, multiplication/division, addition/subtraction (PEMDAS).
3. Negative numbers and fractions follow the same rules.
4. Rounding and significant figures show the precision of data.
5. Units must always be carried through calculations.

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Key Equations (SI Units)

• a + b = c (addition)
• a − b = c (subtraction)
• a × b = c (multiplication)
• a ÷ b = c (division)
• √a = b (square root)
• aⁿ = result of exponentiation

Symbols:

• a, b, c = numbers or measured values
• n = power or exponent

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Common Mistakes and Pitfalls

• Ignoring the order of operations.
• Dropping negative signs.
• Forgetting units.
• Rounding too early (wait until the final step).
• Mixing up square roots and squares.

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🥋 Sensei’s Shortcuts

• Always solve parentheses first.
• Write out every step, even simple ones.
• Carry units with your numbers.
• Round at the very end, not in the middle.

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Worked Example – Step by Step (White Belt)

Problem:
Calculate (8 + 4 × 2)².

Step 1. Order of operations
Inside parentheses: 4 × 2 = 8 → (8 + 8)²

Step 2. Simplify
= (16)²

Step 3. Final Answer
= 256

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Practice Drill (with answers)

1. (6 + 2 × 3)² = ?
   • Answer: 100
2. √(81 ÷ 9) = ?
   • Answer: 3

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Yellow Belt Extension – Deeper Skills

Problem:
A student multiplies 2.5 × 3.40. Show the answer with correct significant figures.

Solution Outline:

• Multiply: 2.5 × 3.40 = 8.50
• Least number of significant figures: 2 (from 2.5)
• Final Answer: 8.5

Extra Practice:
Round 123.456 to 3 significant figures.

• Answer: 123

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Black Belt Mastery – Exam Strategy and Challenge

Problem:
A measurement is recorded as 5.6789 m. You must use it in the calculation: (5.6789 × 2.13) ÷ √3.00. Report the answer with proper significant figures.

Solution:

1. Multiply: 5.6789 × 2.13 = 12.1
2. Divide: 12.1 ÷ √3.00 = 12.1 ÷ 1.73 = 7.00
3. Significant figures:
   • 5.6789 has 5 sig figs
   • 2.13 has 3 sig figs
   • 3.00 has 3 sig figs
     → Final Answer should have 3 sig figs

Final Answer:
7.00 m

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Sensei’s Final Words

“Math is not the obstacle — it is the training ground for your mind.”