156. Formulas

Learning Intentions

• To know the meaning of the terms formula, rule and subject
• Apply a formula to Solve an unknown value

Pre-requisite Summary

• A variable or pronumeral can represent a quantity
• An equation shows that two expressions are equal
• A formula is a rule written Use algebraic symbols
• Substitution means replacing a variable with a given value
• The subject of a formula is the variable written alone on one side
• Order of operations must be followed when evaluating a formula
• Units should be included when interpreting answers in context

Worked Examples

Worked Example 1

For the formula , Identify the formula, the rule and the subject.

Worked Example 2

Use the formula to find when and .

Worked Example 3

Use the formula to find when and .

Worked Example 4

Use the formula to find when .

Worked Example 5

Use the formula to find when and .

Worked Example 6

Use the formula to find when , and .

Problems

Problem 1

For the formula , identify the formula, the rule and the subject.

Problem 2

Use the formula to find when and .

Problem 3

Use the formula to find when and .

Problem 4

Use the formula to find when .

Problem 5

Use the formula to find when and .

Problem 6

Use the formula to find when , and .

Exercises

Understanding and Fluency

Exercise 1.

For each formula, State the subject.

a)

b)

c)

Exercise 2.

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

Exercise 3.

Use each formula to find the unknown value.

a) when and

b) when and

c) when and

Exercise 4.

Use each formula to find the unknown value.

a) when

b) when

c) when

Exercise 5.

Use each formula to find the unknown value.

a) when , ,

b) when ,

c) when

Exercise 6.

Write the values into the formula, then Simplify.

a) when

b) when

c) when ,

Exercise 7.

A rectangle has length cm and width cm. Use to find its perimeter.

Exercise 8.

A car travels at km/h for hours. Use to find the distance travelled.

Reasoning

Exercise 9.

Explain the difference between a formula, a rule and a subject.

Exercise 10.

A student says that in the formula , the subject is because it comes first on the right-hand side. Explain the error.

Exercise 11.

Noah substitutes into with and and writes . Explain why this is incorrect.

Exercise 12.

Explain why order of operations matters when using a formula such as .

Problem-solving

Exercise 13.

The perimeter of a rectangle is found using . Find the perimeter when the length is m and the width is m.

Exercise 14.

The cost of hiring a bike is given by the rule , where is the number of hours. Find the cost when the bike is hired for hours.

Exercise 15.

The distance travelled is given by . Find the distance when the speed is m/s and the time is s.

Exercise 16.

The volume of a box is given by . Find the volume when the box has length cm, width cm and height cm.

Potential Misunderstandings

• 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

Next: 157. Solving Real-World Problems with Equations