Manipulating Equations
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Manipulating Equations Rules
- The order of reareanging is important.
- B E D M A S Brackets Exponents Division Multiplication Addition Subtraction
- Solve -----> B E D M A S <----- Rearrange
- Use the opposite both sides.
- Every function has an opposite function.
- \(+ \; to \; -\)
- \(\times \; to \; \div\)
- \(x^2 \; to\; \sqrt{x} \)
- \(Sin \; to \;Sin^{-1}\)
- Whatever you do to one side of the equation you must do to the other side.
| Manipulating Equations | ||||
|---|---|---|---|---|
| Formulas w/2 | Formulas w/3 | Formulas w/4 | Formulas w/5 | Formulas w/6 |
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\(\large{ a = b \; c }\) \(\large{ b = \frac { a }{ c } }\) \(\large{ c = \frac { a }{ b } }\) |
\(\large{ a = b \; c \; d }\) \(\large{ b = \frac{ a }{ c \; d } }\) \(\large{ c = \frac{ a }{ b \; d } }\) \(\large{ d = \frac{ a }{ b \; c } }\) |
\(\large{ a = b \; c \; d \; e }\) \(\large{ b = \frac{ a }{ c \; d \; e } }\) \(\large{ c = \frac{ a }{ b \; d \; e } }\) \(\large{ d = \frac{ a }{ b \; c \; e } }\) \(\large{ e = \frac{ a }{ b \; c \; d } }\) |
\(\large{ a = b \; c \; d \; e \; f }\) \(\large{ b = \frac{ a }{ c \; d \; e \; f } }\) \(\large{ c = \frac{ a }{ b \; d \; e \; f } }\) \(\large{ d = \frac{ a }{ b \; c \; e \; f } }\) \(\large{ e = \frac{ a }{ b \; c \; d \; f } }\) \(\large{ f = \frac{ a }{ b \; c \; d \; e } }\) |
\(\large{ a = b \; c \; d \; e \; f \; g }\) \(\large{ b = \frac{ a }{ c \; d \; e \; f \; g} }\) \(\large{ c = \frac{ a }{ b \; d \; e \; f \; g} }\) \(\large{ d = \frac{ a }{ b \; c \; e \; f \; g } }\) \(\large{ e = \frac{ a }{ b \; c \; d \; f \; g} }\) \(\large{ f = \frac{ a }{ b \; c \; d \; e \; g } }\) \(\large{ g = \frac{ a }{ b \; c \; d \; e \; f } }\) |
| Manipulating Equations with Fraction | ||||
|---|---|---|---|---|
| Formulas w/1 | Formulas w/2 | Formulas w/3 | Formulas w/4 | Formulas w/5 |
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\(\large{ a = \frac{ b }{c} }\) \(\large{ b = a\;c }\) \(\large{ c = \frac{ b }{a} }\) |
\(\large{ a = \frac{ b\;c }{d} }\) \(\large{ b = \frac{ a\;d }{c} }\) \(\large{ c = \frac{ a\;d }{b} }\) \(\large{ d = \frac{ b\;c }{a} }\) |
\(\large{ a = \frac{ b\;c\;d }{e} }\) \(\large{ b = \frac{ a\;e }{c\;d} }\) \(\large{ c = \frac{ a\;e }{b\;d} }\) \(\large{ d = \frac{ a\;e }{b\;c} }\) \(\large{ e = \frac{ b\;c\;d }{a} }\) |
\(\large{ a = \frac{ b\;c\;d\;e }{ f } }\) \(\large{ b = \frac{ a\;f }{ c\;d\;e } }\) \(\large{ c = \frac{ a\;f }{ b\;d\;e } }\) \(\large{ d = \frac{ a\;f }{ b\;c\;e } }\) \(\large{ e = \frac{ a\;f }{ b\;c\;d } }\) \(\large{ f = \frac{ b\;c\;d\;e }{ a } }\) |
\(\large{ a = \frac{ b\;c\;d\;e\;f }{ g } }\) \(\large{ b = \frac{ a\;g }{ c\;d\;e\;f } }\) \(\large{ c = \frac{ a\;g }{ b\;d\;e\;f } }\) \(\large{ d = \frac{ a\;g }{ b\;c\;e\;f } }\) \(\large{ e = \frac{ a\;g }{ b\;c\;d\;f } }\) \(\large{ f = \frac{ a\;g }{ b\;c\;d\;e } }\) \(\large{ g = \frac{ b\;c\;d\;e\;f }{ a } }\) |
| Manipulating Equations with \(\large{ \frac{1}{2} }\) | ||||
|---|---|---|---|---|
| Formula | Formula | Formula | Formula | Formula |
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\(\large{ a = \frac{1}{2} \; b + c }\) \(\large{ b = 2\;a - c }\) \(\large{ c = 2\;a - b }\) |
\(\large{ a = \frac{1}{2} \; b \; c^2 }\) \(\large{ b = \frac{ 2\;a }{ c^2 } }\) \(\large{ c = \sqrt{ \frac{ 2\;a }{ b } } }\) |
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| Manipulating Equations | ||||
|---|---|---|---|---|
| Formula | Formula | Formula | Formula | Formula |
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\(\large{ a = b - c }\) \(\large{ b = a + c }\) \(\large{ c = b - a }\) |
\(\large{ a = b + c\;d }\) \(\large{ b = a - c\;d }\) \(\large{ c = \frac{ a - b }{ d } }\) \(\large{ d = \frac{ a - b }{ c } }\) |
\(\large{ a = - b \left( c - d \right) }\) \(\large{ b = \frac{ a }{ c \;-\; d } }\) \(\large{ c = d \;- \; \frac{ a }{ b } }\) \(\large{ d = \frac{ a }{ b } + c }\) |
\(\large{ a = \frac{ b\;-\;c }{ d } }\) \(\large{ b = a\;d + c }\) \(\large{ c = b - a\;d }\) \(\large{ d = \frac{ b\;-\;c }{ a } }\) |
\(\large{ a = \frac{ b\;+\;c }{ d } }\) \(\large{ b = a \; d - c }\) \(\large{ c = b \; c - b }\) \(\large{ d = \frac{ b\;+\;c }{ a } }\) |
| Manipulating Equations | ||||
|---|---|---|---|---|
| Formula | Formula | Formula | Formula | Formula |
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\(\large{ a = b\; \sqrt{ c\; d } }\) \(\large{ b = \frac{a}{ \sqrt{ c\; d } } }\) \(\large{ c = \frac{1}{d} \; \left( \frac{a}{b} \right)^2 }\) \(\large{ d = \frac{1}{c} \; \left( \frac{a}{b} \right)^2 }\) |
\(\large{ a = b\;c\; \sqrt{2\; d\; e } }\) \(\large{ b = \frac{a}{c\; \sqrt{2\; d\; e } } }\) \(\large{ c = \frac{a}{b\; \sqrt{2\; d\; e } } }\) \(\large{ d = \frac{\left( \frac{a}{b\;c} \right)^2 }{2\;e } }\) \(\large{ e = \frac{\left( \frac{a}{b\;c} \right)^2 }{2\;d } }\) |
\(\large{ a = 2\; \sqrt{ b^2 - c^2 } }\) \(\large{ b = \sqrt{ \frac{a^2}{4} + c^2 } }\) \(\large{ c = \sqrt{ \frac{a^2}{4} - b^2 } }\) |
\(\large{a = \sqrt{\frac{b\;c}{d} } }\) \(\large{b = \frac{a^2\;d}{c} }\) \(\large{c = \frac{a^2\;d}{b} }\) \(\large{d = \frac{b\;c}{a^2} }\) |
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| Manipulating Equations | ||||
|---|---|---|---|---|
| Formula | Formula | Formula | Formula | Formula |
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\(\large{ a = \frac{ b^2\;c }{ d } }\) \(\large{ b = \sqrt{ \frac{ a \; d }{ c } } }\) \(\large{ c = \frac{ a \; d }{ b^2 } }\) \(\large{ d = \frac{ b^2\;c }{ a } }\) |
\(\large{ a = \frac{ b^2\;c\;d }{e} }\) \(\large{ b = \sqrt{ \frac{ a \; e }{ c \; d } } }\) \(\large{ c = \frac{ a \; e }{ b^2 \; d } }\) \(\large{ d = \frac{ a \; e }{ b^2 \; c } }\) \(\large{ e = \frac{ b^2\;c\;d }{ a } }\) |
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| Manipulating Equations | ||||
|---|---|---|---|---|
| Formula | Formula | Formula | Formula | Formula |
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\(\large{ a = \frac{b}{\sqrt{ c\; d } } }\) \(\large{ b = a\; \sqrt{ c\; d } }\) \(\large{ c = \frac{b^2}{a^2\;d } }\) \(\large{ d = \frac{b^2}{a^2\;c } }\) |
\(\large{ a = \frac{ b\;-\;c }{c\; \left( d\;-\;e \right) } }\) \(\large{ b = a \; c\; \left( d\;-\;e \right) + c }\) \(\large{ c = \frac{ b }{ a\; \left( d\;-\;e \right) \;+\;1 } }\) \(\large{ d = \frac{ d\;-\;e }{ a\;c } + c }\) \(\large{ e = b - \frac{ d\;-\;e }{ a\;c } }\) |
\(\large{ a = \frac{ b\;c\;d }{ e } + f }\) \(\large{ b = a - f \; \frac{ e }{ c\;d } }\) \(\large{ c = a - f \; \frac{ e }{ b\;d } }\) \(\large{ d = a - f \; \frac{ e }{ b\;c } }\) \(\large{ e = \frac{ b\;c\;d }{ a \;-\; f } }\) \(\large{ f = a - \; \frac{ b\;c\;d }{ e } }\) |
\(\large{ a = \frac{ b \;-\; c }{ d \;\left( \frac{ b }{ c } \right) } }\) \(\large{ a = \frac{ b \;-\; c }{ d \; b \;-\; d \; c } }\) |
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