Chapter 57: Value for Money, Sales, and Reward Programs
Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.
What this chapter covers
This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.
57.1 Unit price
Unit price is the cost for one item or one unit of measure and is useful for comparing value. In this section, the focus is Unit price.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Unit price. Show the important steps, include units when needed, and explain how you checked the answer.
57.2 Best value
Best value is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Best value. Show the important steps, include units when needed, and explain how you checked the answer.
57.3 Sale price
Sale price is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Sale price. Show the important steps, include units when needed, and explain how you checked the answer.
57.4 Discounts
Discounts is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Discounts. Show the important steps, include units when needed, and explain how you checked the answer.
57.5 Coupons
Coupons is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Coupons. Show the important steps, include units when needed, and explain how you checked the answer.
57.6 Reward points
A point represents an exact location and has no length, width, or height. In this section, the focus is Reward points.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find the supplementary angle to 35°.
- Supplementary angles total 180°.
- 180° - 35° = 145°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 145°
Worked Example 2
Problem: Find the supplementary angle to 48°.
- Supplementary angles total 180°.
- 180° - 48° = 132°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 132°
Worked Example 3
Problem: Find the supplementary angle to 67°.
- Supplementary angles total 180°.
- 180° - 67° = 113°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 113°
Worked Example 4
Problem: Find the supplementary angle to 72°.
- Supplementary angles total 180°.
- 180° - 72° = 108°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 108°
Worked Example 5
Problem: Find the supplementary angle to 110°.
- Supplementary angles total 180°.
- 180° - 110° = 70°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 70°
Worked Example 6
Problem: Find the supplementary angle to 25°.
- Supplementary angles total 180°.
- 180° - 25° = 155°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 155°
Worked Example 7
Problem: Find the supplementary angle to 58°.
- Supplementary angles total 180°.
- 180° - 58° = 122°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 122°
Worked Example 8
Problem: Find the supplementary angle to 83°.
- Supplementary angles total 180°.
- 180° - 83° = 97°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 97°
Worked Example 9
Problem: Find the supplementary angle to 95°.
- Supplementary angles total 180°.
- 180° - 95° = 85°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 85°
Worked Example 10
Problem: Find the supplementary angle to 120°.
- Supplementary angles total 180°.
- 180° - 120° = 60°.
Very beginner explanation: Angles on a straight line are supplementary.
Answer: 60°
Practice exercise
Create one new Grade 8 problem involving Reward points. Show the important steps, include units when needed, and explain how you checked the answer.
57.7 Cash-back programs
Cash-back programs is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 50 cm
Worked Example 2
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 120 cm
Worked Example 3
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 275 cm
Worked Example 4
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 360 cm
Worked Example 5
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 405 cm
Worked Example 6
Problem: Convert 5.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 5.5 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 550 cm
Worked Example 7
Problem: Convert 7.25 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 7.25 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 725 cm
Worked Example 8
Problem: Convert 8.8 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 8.8 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 880 cm
Worked Example 9
Problem: Convert 10.1 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 10.1 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 1,010 cm
Worked Example 10
Problem: Convert 12.45 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 12.45 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 1,245 cm
Practice exercise
Create one new Grade 8 problem involving Cash-back programs. Show the important steps, include units when needed, and explain how you checked the answer.
57.8 Membership fees
Membership fees is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Membership fees. Show the important steps, include units when needed, and explain how you checked the answer.
57.9 Comparing reward programs
Comparing reward programs is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Convert 0.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 0.5 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 50 cm
Worked Example 2
Problem: Convert 1.2 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 1.2 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 120 cm
Worked Example 3
Problem: Convert 2.75 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 2.75 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 275 cm
Worked Example 4
Problem: Convert 3.6 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 3.6 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 360 cm
Worked Example 5
Problem: Convert 4.05 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 4.05 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 405 cm
Worked Example 6
Problem: Convert 5.5 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 5.5 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 550 cm
Worked Example 7
Problem: Convert 7.25 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 7.25 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 725 cm
Worked Example 8
Problem: Convert 8.8 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 8.8 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 880 cm
Worked Example 9
Problem: Convert 10.1 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 10.1 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 1,010 cm
Worked Example 10
Problem: Convert 12.45 metres to centimetres.
- Use 1 m = 100 cm.
- Multiply 12.45 by 100.
Very beginner explanation: Metric conversions use powers of 10, so decimal movement corresponds to multiplying or dividing by 10, 100, or 1000.
Answer: 1,245 cm
Practice exercise
Create one new Grade 8 problem involving Comparing reward programs. Show the important steps, include units when needed, and explain how you checked the answer.
57.10 Sales tax
Sales tax is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Sales tax. Show the important steps, include units when needed, and explain how you checked the answer.
57.11 Tips
Tips is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Tips. Show the important steps, include units when needed, and explain how you checked the answer.
57.12 Multi-step purchase comparisons
Multi-step purchase comparisons is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Multi-step purchase comparisons: Explain Multi-step purchase comparisons in one simple sentence.
- Look at the words in “Multi-step purchase comparisons”.
- State what the idea is used for.
- Give one small mathematical example.
Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.
Answer: Multi-step purchase comparisons is a Grade 8 math idea used to describe or solve a specific mathematical relationship.
Worked Example 2
Problem: Multi-step purchase comparisons: A student says, “I can use Multi-step purchase comparisons without checking units or labels.” Is that a good method?
- Read the statement.
- Ask whether units, signs, labels, or conditions matter.
- Decide whether the method is safe.
Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.
Answer: No. Important units, labels, signs, and conditions must be checked.
Worked Example 3
Problem: Multi-step purchase comparisons: What is the first step when solving a problem about Multi-step purchase comparisons?
- Read the whole question.
- Underline the known information.
- Identify what must be found.
Very beginner explanation: This prevents you from calculating before you understand the problem.
Answer: Identify the given information and the unknown before choosing a rule.
Worked Example 4
Problem: Multi-step purchase comparisons: After solving a Multi-step purchase comparisons problem, what should you do before accepting the answer?
- Estimate the expected size or direction.
- Check units and signs.
- Use an inverse method if possible.
Very beginner explanation: Checking is part of solving, not an optional extra.
Answer: Check whether the answer is reasonable and consistent with the problem.
Worked Example 5
Problem: Multi-step purchase comparisons: Give one way Multi-step purchase comparisons could appear outside a textbook.
- Think about money, measurements, data, maps, geometry, or technology.
- Connect the topic to one of those situations.
Very beginner explanation: Connecting math to real situations makes the rule easier to remember.
Answer: Multi-step purchase comparisons can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.
Worked Example 6
Problem: Multi-step purchase comparisons: Which representation could help explain Multi-step purchase comparisons: a table, graph, diagram, equation, or number line?
- Choose the representation that makes the relationship easiest to see.
- Label it clearly.
Very beginner explanation: Different representations show different features of the same mathematics.
Answer: Use the representation that best matches the problem; more than one may be valid.
Worked Example 7
Problem: Multi-step purchase comparisons: A student gets an answer for Multi-step purchase comparisons but cannot explain the steps. What should be improved?
- Rewrite the solution one step at a time.
- Name the rule used at each important step.
Very beginner explanation: A correct final number without reasoning may hide an error.
Answer: The reasoning should be shown so the solution can be checked.
Worked Example 8
Problem: Multi-step purchase comparisons: Why can estimation help before a detailed Multi-step purchase comparisons calculation?
- Round or use benchmark values.
- Predict the approximate answer.
- Compare the exact result with the estimate.
Very beginner explanation: If the exact answer is far from the estimate, recheck the work.
Answer: Estimation gives a target range for the final answer.
Worked Example 9
Problem: Multi-step purchase comparisons: How can you test whether your rule for Multi-step purchase comparisons works?
- Choose a very small easy example.
- Apply the rule.
- Check the result another way.
Very beginner explanation: Small examples expose mistakes quickly.
Answer: Test the rule on a simple case whose answer can be verified.
Worked Example 10
Problem: Multi-step purchase comparisons: How would you teach Multi-step purchase comparisons to someone seeing it for the first time?
- Define the idea.
- Show one easy example.
- Explain every step.
- Then let the learner try a similar problem.
Very beginner explanation: This sequence reduces memorization without understanding.
Answer: Teach meaning first, then a small worked example, then guided practice.
Practice exercise
Create one new Grade 8 problem involving Multi-step purchase comparisons. Show the important steps, include units when needed, and explain how you checked the answer.
57.13 Consumer decision-making
Consumer decision-making is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: An item costs $50.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 50.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $6.50
Worked Example 2
Problem: An item costs $100.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 100.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $13.00
Worked Example 3
Problem: An item costs $75.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 75.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $9.75
Worked Example 4
Problem: An item costs $120.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 120.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $15.60
Worked Example 5
Problem: An item costs $200.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 200.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $26.00
Worked Example 6
Problem: An item costs $150.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 150.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $19.50
Worked Example 7
Problem: An item costs $250.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 250.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $32.50
Worked Example 8
Problem: An item costs $80.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 80.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $10.40
Worked Example 9
Problem: An item costs $300.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 300.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $39.00
Worked Example 10
Problem: An item costs $60.00. Find 13% sales tax.
- Convert 13% to 0.13.
- Tax = 60.00×0.13.
Very beginner explanation: Tax is a percentage of the purchase price and is added to the price when required.
Answer: $7.80
Practice exercise
Create one new Grade 8 problem involving Consumer decision-making. Show the important steps, include units when needed, and explain how you checked the answer.
Chapter 57 Review Questions and Answers
Q1. What is important to remember about Unit price?
Answer: Unit price is the cost for one item or one unit of measure and is useful for comparing value. In this section, the focus is Unit price.
Q2. What is important to remember about Best value?
Answer: Best value is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q3. What is important to remember about Sale price?
Answer: Sale price is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q4. What is important to remember about Discounts?
Answer: Discounts is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q5. What is important to remember about Coupons?
Answer: Coupons is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Reward points?
Answer: A point represents an exact location and has no length, width, or height. In this section, the focus is Reward points.
Q7. What is important to remember about Cash-back programs?
Answer: Cash-back programs is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Membership fees?
Answer: Membership fees is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q9. What is important to remember about Comparing reward programs?
Answer: Comparing reward programs is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about Sales tax?
Answer: Sales tax is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q11. What is important to remember about Tips?
Answer: Tips is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q12. What is important to remember about Multi-step purchase comparisons?
Answer: Multi-step purchase comparisons is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q13. What is important to remember about Consumer decision-making?
Answer: Consumer decision-making is an important Grade 8 concept in Value for Money, Sales, and Reward Programs. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.
Q14. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q15. Why is estimation useful?
Answer: Estimation helps you judge whether a calculated answer is reasonable.
Q16. Why do units matter?
Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.
Q17. When should you round?
Answer: Usually round near the end unless the question specifically asks for earlier rounding.
Q18. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the mathematical relationship connecting them.
Q20. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q21. What should you do if an answer seems unreasonable?
Answer: Re-read the question and check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, rates, relationships, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer was obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.
Q26. When is a calculator useful?
Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.
Q27. Why compare more than one strategy?
Answer: Different strategies may make a problem easier and provide a way to verify the result.
Q28. What is mathematical communication?
Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.
Q29. What is mathematical modelling?
Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.
Q30. Why should assumptions be stated?
Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.