ReFormatting Formulas |

**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

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

The formula for simple interest is:

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

We want to **isolate r **on the right side,

A = P + P

now we divide by Pt to get

(A – P)/ Pt = *r*

so ** r** = (1100 – 1000) ÷ 5(1000) = 1/50 = 0.02 =

**Practice**

A)

1) The formula for the surface area of a trapezoid is *A* = ½ *h*(*b*_{1} + *b*_{2})

- a) solve for

2) The Pythagorean theorem says: *c*² = *a*² + *b*², solve it for *a*.

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

- a) solve for

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

- _______________________________________________________

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

3) Given the formula: ,

- a) solve for

**Solutions:**

1) The formula for the surface area of a trapezoid is *A* = ½ *h*(*b*_{1} + *b*_{2})

- a) solve for

- _______________________________________________________

2) The Pythagorean theorem says: *c*² = *a*² + *b*², solve it for *a*.

- Transpose

- _______________________________________________________

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

- a) solve for

- b) solve for

- is a trinomial in

- using the quadratic formula with

- _______________________________________________________

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

- _______________________________________________________

B) **Solve **for the indicated variable.

1) Given the formula: *mg* – *T = mf*,

a) ** T = mg – mf **................... b)

- _______________________________________________________

2) Given the formula: ,

- a) solve for

multiply to get

so

- b) solve for

from

so by division.

- c) solve for

from

- _______________________________________________________

3) Given the formula: ,

- a) solve for

multiply to get:

by division,

- b) solve for

from

by division,

- c) solve for

from

by division,

.

(*all content **© MathRoom Learning Service; 2004 - *).