Why ReFormat?

Say we know the measures of the perimeter and the base of a rectangle. We need to find the height.

We could substitute the given values into the formula for Perimeter, using h to represent the height, and then solve for h.

P = 2(b + h),

When P = 28 cm. and b = 9 cm.

We get 28 = 2(9 + h) —> 14 = 9 + h therefore h = 5

A more efficient way to do it is to REFORMAT the Perimeter formula to express h in terms of the perimeter and base measures. Then substitute the given measures for the perimeter and base, to get h.

P = 2(b + h), becomes ½(P) = b + h

therefore h = ½(P) – b

When P = 28 cm. and b = 9 cm.

h = ½(28) – 9 = 5 cm.

This approach makes us more efficient and precise on our calculators because we don't round the answer after each calculation -- we do it all in a single calculation.

How Do We ReFormat?

To reformat any given formula, we solve for (isolate) the unknown variable by performing the inverse operations. We UNDO the operations to UNDRESS the desired variable.

We divided by 2 to change
P = 2(b + h) into ½(P) = b + h

Then we transposed b to get
h = ½(P) – b

The formula for simple interest is:

A = P + Prt

where A = the Amount in the fund, P = the Principal ($), r = the interest rate, t = time.

Say we invested $1000, and after 5 years there's $1100 in the fund.
We want to know the interest rate.
We reformat the formula to express r in terms of A, P and t.

We want to isolate r on the right side,
A = P + Prt becomes A – P = Prt
now we divide by Pt to get

(A – P)/ Pt = r
so r = (1100 – 1000) ÷ 5(1000) = 1/50 = 0.02 = 2%.

Practice

A)

1) The formula for the surface area of a trapezoid is A = ½ h(b₁ + b₂)

a) solve for h, ................... b) solve for b₂.

2) The Pythagorean theorem says: c² = a² + b², solve it for a.

3) The formula for the surface area of a cylinder is: .

a) solve for h, ................... b) solve for r. (hint: use the quadratic formula)

4) The formula for the volume of a sphere is: , solve it for r.

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B) These formulae come from physics, chemistry and engineering.
Solve for the indicated variable.

1) Given the formula: mg – T = mf,
a) solve for T, ................... b) solve for m. ................... c) solve for f.

2) Given the formula: ,

a) solve for m, ................... b) solve for M. ................... c) solve for v.

3) Given the formula: ,

a) solve for E, ................... b) solve for R. ................... c) solve for n.

Solutions:

1) The formula for the surface area of a trapezoid is A = ½ h(b₁ + b₂)

a) solve for h: ................... b) solve for b₂: .

_______________________________________________________

2) The Pythagorean theorem says: c² = a² + b², solve it for a.

Transpose b² to get a² = c² – b², therefore

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3) The formula for the surface area of a cylinder is: .

a) solve for h:

b) solve for r. (hint: use the quadratic formula)

is a trinomial in r.

using the quadratic formula with a = 1, b = h, and , we get

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4) The formula for the volume of a sphere is: , solve it for r.

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B) Solve for the indicated variable.

1) Given the formula: mg – T = mf,
a) T = mg – mf ................... b) m = T / ( g – f ) . ................... c) f = ( mg – T ) / m.

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2) Given the formula: ,

a) solve for m:
multiply to get Mu + mu = mv,
so

b) solve for M:
from Mu + mu = mv, we get Mu = mv – mu
so by division.

c) solve for v:
from Mu + mu = mv, we get v = ( Mu + mu ) / m by division.

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3) Given the formula: ,

a) solve for E:
multiply to get: nE = C( nR + r )
by division, .

b) solve for R:
from nE = C( nR + r ), we get CnR = nE – Cr,
by division,

c) solve for n:
from CnR = nE – Cr, we get, n ( E – CR ) = Cr
by division,

.

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