A1 · Apply and rearrange practical measurement and finance formulas

Alberta Grade 11 Mathematics

Algebra

Use measurement and finance formulas to find unknown values

What you will learn

• Identify known values and the unknown quantity in a practical problem.
• Choose and use a formula that connects the quantities in a problem.
• Rearrange a formula with inverse operations to isolate an unknown.
• Check units and decide whether an answer is reasonable.

Choose a formula and track units

• Name the unknown before calculating.
• Write known values with units.
• Choose a formula that connects the known values to the unknown.

Substitute and check

• Put each known value in the matching place in the formula.
• Use units in the calculation and in the final answer.
• Check that the result makes sense in context.

Rearrange by undoing operations

• Use inverse operations to isolate the requested variable.
• Apply the same operation to both sides.
• Check the result in the original formula.

Apply a simple-interest formula

• Simple interest is based on the original principal.
• Convert a percent rate to a decimal before substituting.
• Match the time unit to the rate’s time basis.

Worked example

Find the volume of a storage bin

1. Choose the formula
   The bin is a rectangular prism. Its volume is the product of its length, width, and height.
   $$V=lwh$$
2. Substitute and calculate
   All three dimensions are in centimetres, so the volume is in cubic centimetres.
   $$V=(60\text{ cm})(35\text{ cm})(40\text{ cm})=84\,000\text{ cm}^3$$
3. Check the result
   The answer is positive and represents the space inside the bin. Multiplying three lengths gives cubic units.
   $$60\times35\times40=84\,000$$

Worked example

Find a missing dimension by rearranging

1. Write the relationship
   The volume of a rectangular prism is length multiplied by width multiplied by height. The height is the unknown.
   $$V=lwh$$
2. Isolate the height
   The height is multiplied by the length and width. Divide both sides by their product to undo those multiplications.
   $$h=\frac{V}{lw}$$
3. Substitute and calculate
   Use the given measurements. Dividing cubic metres by square metres leaves metres, the correct unit for height.
   $$h=\frac{2.4\text{ m}^3}{(2\text{ m})(0.8\text{ m})}=1.5\text{ m}$$
4. Check in the original formula
   Multiply the three dimensions. The result matches the given volume.
   $$(2\text{ m})(0.8\text{ m})(1.5\text{ m})=2.4\text{ m}^3$$

Worked example

Calculate hypothetical simple interest

1. Choose the formula
   The principal is CAD 800, the annual rate is 3%, and the time is 2 years. The question asks for interest, not the final balance.
   $$I=Prt$$
2. Convert the rate
   A percent means an amount out of 100. Divide 3 by 100 to write the rate as a decimal.
   $$3\%=0.03$$
3. Substitute and calculate
   The rate is annual and time is in years, so the time units match.
   $$I=(800)(0.03)(2)=48$$
4. Check the size
   At this practice rate, one year’s interest is CAD 24. Two years of simple interest is CAD 48.
   $$24+24=48$$

Common mistakes and how to avoid them

Lesson summary

• Choose a formula that links the known values to the unknown.
• Substitute carefully and keep units with measurements.
• Rearrange with inverse operations, applying the same operation to both sides.
• Check units, context, and reasonableness before reporting an answer.

Check your understanding

Key terms

Variable

A letter used to stand for a quantity.

Substitution

Replacing a variable in a formula with a known value.

Rearranging

Changing a formula’s form to isolate a different variable while keeping the relationship true.

Principal

The starting amount of money used in an interest calculation.

Simple interest

Interest calculated on the original principal only.

Continue through Math 20-3

View the complete Math 20-3 Alberta Grade 11 Mathematics curriculum and lessons

• N5 · Compare credit-card and loan options in context
• A2 · Interpret slope as rise over run and as a constant rate
• A3 · Solve proportional problems using unit analysis
• M2 · Solve volume and capacity problems with SI and imperial units
• G1 · Solve problems involving two or three right triangles
• G2 · Solve practical scale and scale-diagram problems

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برای مبحث A1 · فرمول‌های کاربردیِ اندازه‌گیری و امور مالی را به کار ببرید و بازآرایی کنید در درس Math 20-3، سؤال و تلاش خود را همراه بیاورید. در جلسه می‌توانید گام‌های تلاش خود را نشان دهید و آن را با یک نمونهٔ حل‌شده مقایسه کنید. راهنمای معلم ریاضی را ببینید یا جلسهٔ معارفهٔ رایگان ۳۰ دقیقه‌ای درخواست کنید. زمان جلسه پس از پذیرش معلم قطعی می‌شود.

About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Alberta Grade 11 Mathematics (Math 20-3), expectation A1. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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