KEY CONCEPTS

Formulas can be rearranged to isolate different variables.A formula describes an algebraic relationship between two or more variables

To rearrange a formula in terms of a variable,Isolate the term that contains the variableIsolate the variable

EXAMPLE 1 Re-Arranging Formulas in One Step

(a) In geometry, an exterior angle of a triangle is equal to the sum of the two opposite interior angles, such that d = a + b

(i) Express a in terms of b and d (ii) Express b in terms of a and d

To rearrange a formula in terms of a variable,Isolate the term that contains the variableIsolate the variable

d = a + bd – b = a

Isolate aSubtract b

d = a + bd – a = b

Isolate bSubtract a

hh

EXAMPLE 1 Re-Arranging Formulas in One Step

To rearrange a formula in terms of a variable,Isolate the term that contains the variableIsolate the variable

(b) The area of a parallelogram is given by the formula A = bh. Re-arrange the formula to isolate b.

(c) The area of a square is given by the formula A = s2 (where s represents the length of a side). Re-arrange the formula to express s in terms of A.

bhA Leave this alone!Isolate bDivide both sides by h

bh

A

2sA To isolate a squaredvariable, we have to take the square root of both sides!

2sA

sA

xx

EXAMPLE 2 Re-Arranging Formulas Using Multiple Steps

To rearrange a formula in terms of a variable,Isolate the term that contains the variableIsolate the variable

(a) The equation in slope and y-intercept form is y = mx + b. Re-arrange the formula to isolate m.

(b) The area of a circle is given by the formula A = r2. Re-arrange the formula to isolate r.

bmxy mxby

mx

by

Leave this term alone (until the final step)!First, subtract b*Divide both sides by x

2rA Leave this term alone (until the final step)!First, divide both sides by

2rA

2rA

rA

To isolate a squaredvariable, we have to take the square rootof both sides!

RR

EXAMPLE 2 Re-Arranging Formulas Using Multiple Steps

To rearrange a formula in terms of a variable,Isolate the term that contains the variableIsolate the variable

(c) The formula for resistance in a circuit is given by the formula I

VR

(i) Re-arrange the formula to (ii) Re-arrange the formula to isolate V isolate I

I

VR

II

VIR

VIR

Leave this term alone!* Get rid of the fractionMultiply both sides by I

I

VR

* Get rid of the fractionMultiply both sides by II

I

VIR

VIR

R

VI

Leave the I alone!Divide both sides by R

Homework:

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