Every rule the plots and drills lean on. One board, no guessing.
| Signed addition | Same signs: add the sizes, keep the sign. Different signs: subtract the sizes, take the sign of the larger size. |
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| Signed subtraction | Subtracting a number is adding its opposite. |
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| Signed multiplication and division | Even count of negative signs: positive result. Odd count: negative result. |
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| Absolute value | Distance from zero. Never negative. |
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| Order of operations | Parentheses, then exponents, then multiply and divide left to right, then add and subtract left to right. |
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| Distributive property | a(b + c) = ab + ac. The outside multiplies every inside term. |
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| Like terms | Combine terms whose variable parts match exactly: add the coefficients. |
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| One-step equations | Undo the one operation with its opposite, on both sides. |
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| Two-step equations | Undo the add or subtract first, then undo the multiply or divide. |
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| Fraction addition | Match the denominators, add the numerators, simplify. |
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| Fraction multiplication | Multiply straight across, then reduce. |
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| GCF and LCM | GCF: the largest shared divisor. LCM: the smallest shared multiple. Their product equals the product of the two numbers. |
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| Decimal addition | Line up the points, add, bring the point straight down. |
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| Percent | Percent means per hundred. To find p percent of n, multiply n by p over one hundred. |
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| Ratio and unit rate | A ratio compares by division. A unit rate is the amount per exactly one. |
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| Proportion | Two equal ratios. Cross products are equal. |
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| Exponents and roots | An exponent counts repeated multiplication. A square root undoes a square. |
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| Perimeter and area of a rectangle | Perimeter: double the sum of length and width. Area: length times width. |
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| The coordinate plane | Ordered pairs read across then up. Quadrants count counterclockwise from where both are positive. |
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