156. Formulas

Learning Intentions

For the formula $P = 2 l + 2 w$ , identify the formula, the rule and the subject.

Use the formula $P = 2 l + 2 w$ to find $P$ when $l = 5$ and $w = 3$ .

Use the formula $A = l w$ to find $A$ when $l = 8$ and $w = 6$ .

Use the formula $C = 5 n + 2$ to find $C$ when $n = 4$ .

Use the formula $d = r t$ to find $d$ when $r = 7$ and $t = 3$ .

Use the formula $V = l w h$ to find $V$ when $l = 4$ , $w = 2$ and $h = 5$ .

For the formula $A = 2 x + 7$ , identify the formula, the rule and the subject.

Use the formula $P = 2 l + 2 w$ to find $P$ when $l = 9$ and $w = 4$ .

Use the formula $A = l w$ to find $A$ when $l = 7$ and $w = 5$ .

Use the formula $C = 5 n + 2$ to find $C$ when $n = 6$ .

Use the formula $d = r t$ to find $d$ when $r = 9$ and $t = 4$ .

Use the formula $V = l w h$ to find $V$ when $l = 3$ , $w = 6$ and $h = 2$ .

For each formula, state the subject.
a) $P = 3 a + b$
b) $A = l w$
c) $d = r t$
For each statement, decide whether it describes a formula, a rule or a subject.
a) the letter written alone on one side of a formula
b) an algebraic relationship used to calculate a quantity
c) the instruction showing how one quantity is found from others
Use each formula to find the unknown value.
a) $A = l w$ when $l = 9$ and $w = 2$
b) $P = 2 l + 2 w$ when $l = 4$ and $w = 7$
c) $d = r t$ when $r = 6$ and $t = 5$
Use each formula to find the unknown value.
a) $C = 4 n + 1$ when $n = 3$
b) $M = 7 p - 2$ when $p = 8$
c) $y = 3 x + 5$ when $x = 6$
Use each formula to find the unknown value.
a) $V = l w h$ when $l = 2$ , $w = 3$ , $h = 4$
b) $k = a b$ when $a = 5$ , $b = 9$
c) $T = 2 m + 6$ when $m = 11$
Write the values into the formula, then simplify.
a) $A = 3 x + 4$ when $x = 7$
b) $B = 2 p - 5$ when $p = 9$
c) $N = m n + 3$ when $m = 4$ , $n = 6$
A rectangle has length $10$ cm and width $3$ cm. Use $P = 2 l + 2 w$ to find its perimeter.
A car travels at $80$ km/h for $3$ hours. Use $d = r t$ to find the distance travelled.

Explain the difference between a formula, a rule and a subject.
A student says that in the formula $A = l w$ , the subject is $l$ because it comes first on the right-hand side. Explain the error.
Noah substitutes into $P = 2 l + 2 w$ with $l = 5$ and $w = 4$ and writes $P = 2 + 5 + 2 + 4$ . Explain why this is incorrect.
Explain why order of operations matters when using a formula such as $C = 5 n + 2$ .

The perimeter of a rectangle is found using $P = 2 l + 2 w$ . Find the perimeter when the length is $12$ m and the width is $5$ m.
The cost of hiring a bike is given by the rule $C = 8 h + 3$ , where $h$ is the number of hours. Find the cost when the bike is hired for $4$ hours.
The distance travelled is given by $d = r t$ . Find the distance when the speed is $14$ m/s and the time is $6$ s.
The volume of a box is given by $V = l w h$ . Find the volume when the box has length $5$ cm, width $4$ cm and height $3$ cm.

Thinking a formula and a rule are completely different ideas rather than closely related
Believing that the subject is any variable in the formula, instead of the one written alone on one side
Confusing the subject with the first variable named in the formula
Forgetting to substitute the given values into every relevant variable
Replacing a variable incorrectly when more than one variable appears in the formula
Ignoring order of operations when simplifying after substitution
Leaving the answer in unsimplified form after substitution
Forgetting to include units when interpreting the value found from a formula
Thinking that applying a formula means solving for a different subject, rather than using the given subject to calculate its value