📘 Math Cheat Sheet
1. Basic Algebra
Solving Equations (Moving Terms)
When moving a term to the other side of an equation, use the opposite operation:
Origina Become
l
s
+
−
−
+
×
÷
÷
×
Example:
x+2=5
x=5−2
x=3
Combining Like Terms
•
Only terms with the same variable and exponent can be combined.
Examples:
3x + 2x = 5x
4y − y = 3y
Distributive Property
Multiply the number outside the parentheses by each term inside.
Formula:
a(b + c) = ab + ac
Example:
3(x + 4) = 3x + 12
Solving One-Step Equations
Undo the operation attached to the variable.
Examples:
x − 7 = 10 → x = 17
4x = 20 → x = 5
x / 3 = 6 → x = 18
2. Fractions
Least Common Denominator (LCD)
Steps:
1.
List multiples of each denominator
2.
Choose the smallest common multiple
Example (4 and 6):
Multiples of 4: 4, 8, 12…
Multiples of 6: 6, 12…
LCD = 12
Simplifying Fractions
•
Divide numerator and denominator by their Greatest Common Factor (GCF)
Example:
6/8 = 3/4
Adding & Subtracting Fractions
Steps:
1.
Find the LCD
2.
Rewrite fractions with the LCD
3.
Add or subtract numerators
4.
Simplify
Example:
1/4 + 1/6
= 3/12 + 2/12
= 5/12
Multiplying Fractions
•
Multiply straight across
•
Simplify if possible
Example:
2/3 × 4/5 = 8/15
Dividing Fractions
Steps:
1.
Keep the rst fraction
2.
Change ÷ to ×
3.
Flip the second fraction
4.
Multiply
Example:
1/2 ÷ 1/3
= 1/2 × 3/1
= 3/2
3. Mixed Numbers
Convert Mixed Numbers to Improper Fractions
Formula:
fi
a
b
c
=
a
c
+
b
c
a \frac{b}{c} = \frac{ac + b}{c}
acb =cac+b
Example:
3 2/4 = 14/4 → 7/2
Adding Mixed Numbers
Method 1: Convert to Improper Fractions
Example:
1 1/2 + 3 2/4
1 1/2 = 3/2
3 2/4 = 7/2
3/2 + 7/2 = 10/2 = 5
Method 2: Add Parts Separately
Whole numbers:
1+3=4
Fractions:
1/2 + 2/4 = 1
Final Answer: 5
Subtracting Mixed Numbers
Borrow if needed.
Example:
4 1/3 − 2 2/3
4 1/3 → 3 4/3
3 4/3 − 2 2/3 = 1 2/3
4. Key Fraction Rules (Formulas)
•
Addition:
a/b + c/d = (ad + bc) / bd
•
Subtraction:
a/b − c/d = (ad − bc) / bd
•
Multiplication:
a/b × c/d = ac / bd
•
Division:
a/b ÷ c/d = a/b × d/c
5. Decimals & Percents (Often Tested)
Decimal ↔ Fraction
0.5 = 1/2
0.25 = 1/4
Percent ↔ Decimal
•
Percent → Decimal: divide by 100
•
Decimal → Percent: multiply by 100
Examples:
25% = 0.25
0.6 = 60%
Percent of a Number
Percent
×
Number
\text{Percent} \times \text{Number}
Percent×Number
Example:
20% of 50 = 0.20 × 50 = 10
6. Negative Numbers
•
Same signs → positive
•
Different signs → negative
Examples:
−3 × −2 = 6
−8 ÷ 4 = −2
7. Order of Operations (PEMDAS)
1.
Parentheses
2.
Exponents
3.
Multiplication & Division (left to right)
4.
Addition & Subtraction (left to right)
8. Absolute Value
•
Distance from zero
•
Always positive
Example:
|−5| = 5
✅ Test Tips
•
Always simplify answers
•
Convert mixed numbers when unsure
•
Watch negative signs
•
Double-check the operation being used