Chapter 16: Percent Applications
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Percent Applications with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Percent (a ratio out of 100)
- Estimate (a close approximation used to check whether an answer is reasonable)
- Solution (a value or result that satisfies the problem)
- Representation (a way to show mathematics using symbols, diagrams, tables, graphs, or words)
- Reasonableness (whether an answer makes sense in the context of the problem)
How to Learn This Chapter
Read the explanation first, follow the examples one step at a time, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
16.1 Discounts
A discount is an amount taken off an original price, usually expressed as a percent. This topic focuses on Discounts .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: $80 item with 10% discount. Find sale price.
- Discount = 0.1×80 = 8.00.
- Sale price = 80-8.00.
Very beginner explanation: A discount is an amount taken off an original price, usually expressed as a percent. This topic focuses on Discounts .
Answer: $72.00
Worked Example 2
Problem: $60 item with 25% discount. Find sale price.
- Discount = 0.25×60 = 15.00.
- Sale price = 60-15.00.
Very beginner explanation: A discount is an amount taken off an original price, usually expressed as a percent. This topic focuses on Discounts .
Answer: $45.00
Worked Example 3
Problem: $120 item with 15% discount. Find sale price.
- Discount = 0.15×120 = 18.00.
- Sale price = 120-18.00.
Very beginner explanation: A discount is an amount taken off an original price, usually expressed as a percent. This topic focuses on Discounts .
Answer: $102.00
Worked Example 4
Problem: $250 item with 5% discount. Find sale price.
- Discount = 0.05×250 = 12.50.
- Sale price = 250-12.50.
Very beginner explanation: A discount is an amount taken off an original price, usually expressed as a percent. This topic focuses on Discounts .
Answer: $237.50
Worked Example 5
Problem: $75 item with 13% discount. Find sale price.
- Discount = 0.13×75 = 9.75.
- Sale price = 75-9.75.
Very beginner explanation: A discount is an amount taken off an original price, usually expressed as a percent. This topic focuses on Discounts .
Answer: $65.25
Worked Example 6
Problem: An item costs $90. It is discounted 10%. Find the sale price.
- Discount = 0.1 × 90 = 9.00.
- Sale price = 90 - 9.00.
Very beginner explanation: A discount removes a percentage of the original price.
Answer: $81.00
Worked Example 7
Problem: An item costs $64. It is discounted 25%. Find the sale price.
- Discount = 0.25 × 64 = 16.00.
- Sale price = 64 - 16.00.
Very beginner explanation: A discount removes a percentage of the original price.
Answer: $48.00
Worked Example 8
Problem: An item costs $140. It is discounted 15%. Find the sale price.
- Discount = 0.15 × 140 = 21.00.
- Sale price = 140 - 21.00.
Very beginner explanation: A discount removes a percentage of the original price.
Answer: $119.00
Worked Example 9
Problem: An item costs $260. It is discounted 5%. Find the sale price.
- Discount = 0.05 × 260 = 13.00.
- Sale price = 260 - 13.00.
Very beginner explanation: A discount removes a percentage of the original price.
Answer: $247.00
Worked Example 10
Problem: An item costs $75. It is discounted 20%. Find the sale price.
- Discount = 0.2 × 75 = 15.00.
- Sale price = 75 - 15.00.
Very beginner explanation: A discount removes a percentage of the original price.
Answer: $60.00
Practice Exercise
Create one new question about Discounts. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.2 Sale price
Sale price is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: $80 item with 10% discount. Find sale price.
- Discount = 0.1×80 = 8.00.
- Sale price = 80-8.00.
Very beginner explanation: Sale price is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $72.00
Worked Example 2
Problem: $60 item with 25% discount. Find sale price.
- Discount = 0.25×60 = 15.00.
- Sale price = 60-15.00.
Very beginner explanation: Sale price is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $45.00
Worked Example 3
Problem: $120 item with 15% discount. Find sale price.
- Discount = 0.15×120 = 18.00.
- Sale price = 120-18.00.
Very beginner explanation: Sale price is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $102.00
Worked Example 4
Problem: $250 item with 5% discount. Find sale price.
- Discount = 0.05×250 = 12.50.
- Sale price = 250-12.50.
Very beginner explanation: Sale price is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $237.50
Worked Example 5
Problem: $75 item with 13% discount. Find sale price.
- Discount = 0.13×75 = 9.75.
- Sale price = 75-9.75.
Very beginner explanation: Sale price is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $65.25
Worked Example 6
Problem: An item costs $90. It is discounted 10%. Find the sale price.
- Discount = 0.1 × 90 = 9.00.
- Sale price = 90 - 9.00.
Very beginner explanation: A discount removes a percentage of the original price.
Answer: $81.00
Worked Example 7
Problem: An item costs $64. It is discounted 25%. Find the sale price.
- Discount = 0.25 × 64 = 16.00.
- Sale price = 64 - 16.00.
Very beginner explanation: A discount removes a percentage of the original price.
Answer: $48.00
Worked Example 8
Problem: An item costs $140. It is discounted 15%. Find the sale price.
- Discount = 0.15 × 140 = 21.00.
- Sale price = 140 - 21.00.
Very beginner explanation: A discount removes a percentage of the original price.
Answer: $119.00
Worked Example 9
Problem: An item costs $260. It is discounted 5%. Find the sale price.
- Discount = 0.05 × 260 = 13.00.
- Sale price = 260 - 13.00.
Very beginner explanation: A discount removes a percentage of the original price.
Answer: $247.00
Worked Example 10
Problem: An item costs $75. It is discounted 20%. Find the sale price.
- Discount = 0.2 × 75 = 15.00.
- Sale price = 75 - 15.00.
Very beginner explanation: A discount removes a percentage of the original price.
Answer: $60.00
Practice Exercise
Create one new question about Sale price. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.3 Markups
A markup is an amount added to a cost to obtain a selling price. This topic focuses on Markups .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of $80.
- Convert 10% to 0.1.
- Multiply by 80.
Very beginner explanation: A markup is an amount added to a cost to obtain a selling price. This topic focuses on Markups .
Answer: $8.00
Worked Example 2
Problem: Find 25% of $60.
- Convert 25% to 0.25.
- Multiply by 60.
Very beginner explanation: A markup is an amount added to a cost to obtain a selling price. This topic focuses on Markups .
Answer: $15.00
Worked Example 3
Problem: Find 15% of $120.
- Convert 15% to 0.15.
- Multiply by 120.
Very beginner explanation: A markup is an amount added to a cost to obtain a selling price. This topic focuses on Markups .
Answer: $18.00
Worked Example 4
Problem: Find 5% of $250.
- Convert 5% to 0.05.
- Multiply by 250.
Very beginner explanation: A markup is an amount added to a cost to obtain a selling price. This topic focuses on Markups .
Answer: $12.50
Worked Example 5
Problem: Find 13% of $75.
- Convert 13% to 0.13.
- Multiply by 75.
Very beginner explanation: A markup is an amount added to a cost to obtain a selling price. This topic focuses on Markups .
Answer: $9.75
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Markups. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.4 Sales tax
Sales tax is a percentage added to the selling price of taxable goods or services. This topic focuses on Sales tax .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of $80.
- Convert 10% to 0.1.
- Multiply by 80.
Very beginner explanation: Sales tax is a percentage added to the selling price of taxable goods or services. This topic focuses on Sales tax .
Answer: $8.00
Worked Example 2
Problem: Find 25% of $60.
- Convert 25% to 0.25.
- Multiply by 60.
Very beginner explanation: Sales tax is a percentage added to the selling price of taxable goods or services. This topic focuses on Sales tax .
Answer: $15.00
Worked Example 3
Problem: Find 15% of $120.
- Convert 15% to 0.15.
- Multiply by 120.
Very beginner explanation: Sales tax is a percentage added to the selling price of taxable goods or services. This topic focuses on Sales tax .
Answer: $18.00
Worked Example 4
Problem: Find 5% of $250.
- Convert 5% to 0.05.
- Multiply by 250.
Very beginner explanation: Sales tax is a percentage added to the selling price of taxable goods or services. This topic focuses on Sales tax .
Answer: $12.50
Worked Example 5
Problem: Find 13% of $75.
- Convert 13% to 0.13.
- Multiply by 75.
Very beginner explanation: Sales tax is a percentage added to the selling price of taxable goods or services. This topic focuses on Sales tax .
Answer: $9.75
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Sales tax. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.5 Tips
A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Tips .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of $80.
- Convert 10% to 0.1.
- Multiply by 80.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Tips .
Answer: $8.00
Worked Example 2
Problem: Find 25% of $60.
- Convert 25% to 0.25.
- Multiply by 60.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Tips .
Answer: $15.00
Worked Example 3
Problem: Find 15% of $120.
- Convert 15% to 0.15.
- Multiply by 120.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Tips .
Answer: $18.00
Worked Example 4
Problem: Find 5% of $250.
- Convert 5% to 0.05.
- Multiply by 250.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Tips .
Answer: $12.50
Worked Example 5
Problem: Find 13% of $75.
- Convert 13% to 0.13.
- Multiply by 75.
Very beginner explanation: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Tips .
Answer: $9.75
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Tips. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.6 Commission introduction
Commission introduction is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of $80.
- Convert 10% to 0.1.
- Multiply by 80.
Very beginner explanation: Commission introduction is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $8.00
Worked Example 2
Problem: Find 25% of $60.
- Convert 25% to 0.25.
- Multiply by 60.
Very beginner explanation: Commission introduction is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $15.00
Worked Example 3
Problem: Find 15% of $120.
- Convert 15% to 0.15.
- Multiply by 120.
Very beginner explanation: Commission introduction is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $18.00
Worked Example 4
Problem: Find 5% of $250.
- Convert 5% to 0.05.
- Multiply by 250.
Very beginner explanation: Commission introduction is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $12.50
Worked Example 5
Problem: Find 13% of $75.
- Convert 13% to 0.13.
- Multiply by 75.
Very beginner explanation: Commission introduction is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: $9.75
Worked Example 6
Problem: Find 10% of $90.
- Convert 10% to 0.1.
- Multiply by 90.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $9.00
Worked Example 7
Problem: Find 25% of $64.
- Convert 25% to 0.25.
- Multiply by 64.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $16.00
Worked Example 8
Problem: Find 15% of $140.
- Convert 15% to 0.15.
- Multiply by 140.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $21.00
Worked Example 9
Problem: Find 5% of $260.
- Convert 5% to 0.05.
- Multiply by 260.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $13.00
Worked Example 10
Problem: Find 20% of $75.
- Convert 20% to 0.2.
- Multiply by 75.
Very beginner explanation: Percent of an amount is found by multiplying the amount by the percent written as a decimal.
Answer: $15.00
Practice Exercise
Create one new question about Commission introduction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.7 Percent increase
Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent increase .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of 80.
- 10% = 0.1.
- 0.1×80=8.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent increase .
Answer: 8
Worked Example 2
Problem: Find 25% of 60.
- 25% = 0.25.
- 0.25×60=15.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent increase .
Answer: 15
Worked Example 3
Problem: Find 15% of 120.
- 15% = 0.15.
- 0.15×120=18.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent increase .
Answer: 18
Worked Example 4
Problem: Find 5% of 250.
- 5% = 0.05.
- 0.05×250=12.5.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent increase .
Answer: 12.5
Worked Example 5
Problem: Find 13% of 75.
- 13% = 0.13.
- 0.13×75=9.75.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent increase .
Answer: 9.75
Worked Example 6
Problem: Find 10% of 90.
- 10% = 0.1.
- 0.1 × 90 = 9.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 9
Worked Example 7
Problem: Find 25% of 64.
- 25% = 0.25.
- 0.25 × 64 = 16.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 16
Worked Example 8
Problem: Find 15% of 140.
- 15% = 0.15.
- 0.15 × 140 = 21.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 21
Worked Example 9
Problem: Find 5% of 260.
- 5% = 0.05.
- 0.05 × 260 = 13.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 13
Worked Example 10
Problem: Find 20% of 75.
- 20% = 0.2.
- 0.2 × 75 = 15.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 15
Practice Exercise
Create one new question about Percent increase. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.8 Percent decrease
Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent decrease .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of 80.
- 10% = 0.1.
- 0.1×80=8.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent decrease .
Answer: 8
Worked Example 2
Problem: Find 25% of 60.
- 25% = 0.25.
- 0.25×60=15.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent decrease .
Answer: 15
Worked Example 3
Problem: Find 15% of 120.
- 15% = 0.15.
- 0.15×120=18.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent decrease .
Answer: 18
Worked Example 4
Problem: Find 5% of 250.
- 5% = 0.05.
- 0.05×250=12.5.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent decrease .
Answer: 12.5
Worked Example 5
Problem: Find 13% of 75.
- 13% = 0.13.
- 0.13×75=9.75.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent decrease .
Answer: 9.75
Worked Example 6
Problem: Find 10% of 90.
- 10% = 0.1.
- 0.1 × 90 = 9.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 9
Worked Example 7
Problem: Find 25% of 64.
- 25% = 0.25.
- 0.25 × 64 = 16.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 16
Worked Example 8
Problem: Find 15% of 140.
- 15% = 0.15.
- 0.15 × 140 = 21.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 21
Worked Example 9
Problem: Find 5% of 260.
- 5% = 0.05.
- 0.05 × 260 = 13.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 13
Worked Example 10
Problem: Find 20% of 75.
- 20% = 0.2.
- 0.2 × 75 = 15.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 15
Practice Exercise
Create one new question about Percent decrease. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.9 Original amount
Original amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Locate (2,3).
- Move 2 units right.
- Move 3 units up.
Very beginner explanation: Original amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Quadrant I
Worked Example 2
Problem: Locate (-4,5).
- Move 4 units left.
- Move 5 units up.
Very beginner explanation: Original amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Quadrant II
Worked Example 3
Problem: Locate (-3,-2).
- Move 3 units left.
- Move 2 units down.
Very beginner explanation: Original amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Quadrant III
Worked Example 4
Problem: Locate (6,-1).
- Move 6 units right.
- Move 1 units down.
Very beginner explanation: Original amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: Quadrant IV
Worked Example 5
Problem: Locate (0,4).
- Move 0 units right.
- Move 4 units up.
Very beginner explanation: Original amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: on an axis
Worked Example 6
Problem: Explain Original amount in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Original amount becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Original amount and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Original amount becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Original amount using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Original amount becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Original amount problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Original amount becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Original amount could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Original amount becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Original amount. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.10 New amount
New amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: New amount: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: New amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 2
Problem: New amount: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: New amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 3
Problem: New amount: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: New amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 4
Problem: New amount: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: New amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 5
Problem: New amount: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: New amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: A correct response must satisfy the definition or rule and include a check.
Worked Example 6
Problem: Explain New amount in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: New amount becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy New amount and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: New amount becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show New amount using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: New amount becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a New amount problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: New amount becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where New amount could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: New amount becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about New amount. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.11 Multi-step shopping problems
Multi-step shopping problems is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Circle radius 3 cm. Find circumference.
- Use C=2πr.
- C≈18.85.
Very beginner explanation: Multi-step shopping problems is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 18.85 cm
Worked Example 2
Problem: Circle radius 4 cm. Find circumference.
- Use C=2πr.
- C≈25.13.
Very beginner explanation: Multi-step shopping problems is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 25.13 cm
Worked Example 3
Problem: Circle radius 5 cm. Find circumference.
- Use C=2πr.
- C≈31.42.
Very beginner explanation: Multi-step shopping problems is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 31.42 cm
Worked Example 4
Problem: Circle radius 6 cm. Find circumference.
- Use C=2πr.
- C≈37.70.
Very beginner explanation: Multi-step shopping problems is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 37.70 cm
Worked Example 5
Problem: Circle radius 7 cm. Find circumference.
- Use C=2πr.
- C≈43.98.
Very beginner explanation: Multi-step shopping problems is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 43.98 cm
Worked Example 6
Problem: Explain Multi-step shopping problems in one simple sentence.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Multi-step shopping problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: State the meaning, then give one small example.
Worked Example 7
Problem: Give one example that does not satisfy Multi-step shopping problems and explain why.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Multi-step shopping problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Identify the rule or condition that fails.
Worked Example 8
Problem: Show Multi-step shopping problems using a table, diagram, number line, graph, or equation.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Multi-step shopping problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Choose the representation that makes the relationship easiest to see.
Worked Example 9
Problem: After solving a Multi-step shopping problems problem, how can you check the answer?
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Multi-step shopping problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Use estimation, an inverse operation, substitution, or a second representation.
Worked Example 10
Problem: Give one real-life situation where Multi-step shopping problems could be useful.
- Read the definition of the topic.
- Use the definition to build the response.
- Check that the response matches every important condition.
Very beginner explanation: Multi-step shopping problems becomes easier to understand when you connect its definition to examples, non-examples, and representations.
Answer: Connect the idea to money, measurement, data, design, or technology.
Practice Exercise
Create one new question about Multi-step shopping problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.12 Percent in statistics
Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in statistics .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of 80.
- 10% = 0.1.
- 0.1×80=8.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in statistics .
Answer: 8
Worked Example 2
Problem: Find 25% of 60.
- 25% = 0.25.
- 0.25×60=15.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in statistics .
Answer: 15
Worked Example 3
Problem: Find 15% of 120.
- 15% = 0.15.
- 0.15×120=18.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in statistics .
Answer: 18
Worked Example 4
Problem: Find 5% of 250.
- 5% = 0.05.
- 0.05×250=12.5.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in statistics .
Answer: 12.5
Worked Example 5
Problem: Find 13% of 75.
- 13% = 0.13.
- 0.13×75=9.75.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in statistics .
Answer: 9.75
Worked Example 6
Problem: Find 10% of 90.
- 10% = 0.1.
- 0.1 × 90 = 9.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 9
Worked Example 7
Problem: Find 25% of 64.
- 25% = 0.25.
- 0.25 × 64 = 16.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 16
Worked Example 8
Problem: Find 15% of 140.
- 15% = 0.15.
- 0.15 × 140 = 21.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 21
Worked Example 9
Problem: Find 5% of 260.
- 5% = 0.05.
- 0.05 × 260 = 13.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 13
Worked Example 10
Problem: Find 20% of 75.
- 20% = 0.2.
- 0.2 × 75 = 15.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 15
Practice Exercise
Create one new question about Percent in statistics. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.13 Percent in everyday decisions
Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in everyday decisions .
Beginner Note
Identify what is given, what must be found, choose the correct rule or representation, work one step at a time, and check whether the result makes sense.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find 10% of 80.
- 10% = 0.1.
- 0.1×80=8.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in everyday decisions .
Answer: 8
Worked Example 2
Problem: Find 25% of 60.
- 25% = 0.25.
- 0.25×60=15.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in everyday decisions .
Answer: 15
Worked Example 3
Problem: Find 15% of 120.
- 15% = 0.15.
- 0.15×120=18.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in everyday decisions .
Answer: 18
Worked Example 4
Problem: Find 5% of 250.
- 5% = 0.05.
- 0.05×250=12.5.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in everyday decisions .
Answer: 12.5
Worked Example 5
Problem: Find 13% of 75.
- 13% = 0.13.
- 0.13×75=9.75.
Very beginner explanation: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in everyday decisions .
Answer: 9.75
Worked Example 6
Problem: Find 10% of 90.
- 10% = 0.1.
- 0.1 × 90 = 9.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 9
Worked Example 7
Problem: Find 25% of 64.
- 25% = 0.25.
- 0.25 × 64 = 16.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 16
Worked Example 8
Problem: Find 15% of 140.
- 15% = 0.15.
- 0.15 × 140 = 21.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 21
Worked Example 9
Problem: Find 5% of 260.
- 5% = 0.05.
- 0.05 × 260 = 13.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 13
Worked Example 10
Problem: Find 20% of 75.
- 20% = 0.2.
- 0.2 × 75 = 15.
Very beginner explanation: Percent means per hundred, so converting the percent to a decimal makes multiplication straightforward.
Answer: 15
Practice Exercise
Create one new question about Percent in everyday decisions. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
Chapter Notes, Practice, and Common Mistakes
Chapter Notes
- Read the complete question before choosing an operation, formula, graph, or model.
- Write technical words together with their meaning until you are comfortable using them.
- Show all important steps so another student can follow your reasoning.
- Keep units, labels, signs, axes, variables, and mathematical symbols clear.
- Estimate before or after calculating when an estimate can help check reasonableness.
- For real-life problems, explain what the final number means in the situation.
Extra Practice
- Create and solve a new question about Discounts . Show your reasoning and check your answer.
- Create and solve a new question about Sale price . Show your reasoning and check your answer.
- Create and solve a new question about Markups . Show your reasoning and check your answer.
- Create and solve a new question about Sales tax . Show your reasoning and check your answer.
- Create and solve a new question about Tips . Show your reasoning and check your answer.
- Create and solve a new question about Commission introduction . Show your reasoning and check your answer.
- Create and solve a new question about Percent increase . Show your reasoning and check your answer.
- Create and solve a new question about Percent decrease . Show your reasoning and check your answer.
- Create and solve a new question about Original amount . Show your reasoning and check your answer.
- Create and solve a new question about New amount . Show your reasoning and check your answer.
- Create and solve a new question about Multi-step shopping problems . Show your reasoning and check your answer.
- Create and solve a new question about Percent in statistics . Show your reasoning and check your answer.
Common Mistakes
- Changing only one part of an equivalent fraction or ratio.
- Moving a decimal point without a mathematical reason.
- Using the new amount instead of the original amount for percent change.
- Mixing units when comparing rates or scale.
30 Review Questions and Answers
Q1. What is important to remember about Discounts?
Answer: A discount is an amount taken off an original price, usually expressed as a percent. This topic focuses on Discounts.
Q2. What is important to remember about Sale price?
Answer: Sale price is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q3. What is important to remember about Markups?
Answer: A markup is an amount added to a cost to obtain a selling price. This topic focuses on Markups.
Q4. What is important to remember about Sales tax?
Answer: Sales tax is a percentage added to the selling price of taxable goods or services. This topic focuses on Sales tax.
Q5. What is important to remember about Tips?
Answer: A tip is an extra amount, often calculated as a percent of a bill. This topic focuses on Tips.
Q6. What is important to remember about Commission introduction?
Answer: Commission introduction is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q7. What is important to remember about Percent increase?
Answer: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent increase.
Q8. What is important to remember about Percent decrease?
Answer: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent decrease.
Q9. What is important to remember about Original amount?
Answer: Original amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q10. What is important to remember about New amount?
Answer: New amount is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q11. What is important to remember about Multi-step shopping problems?
Answer: Multi-step shopping problems is an important Grade 7 idea in Percent Applications. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q12. What is important to remember about Percent in statistics?
Answer: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in statistics.
Q13. What is important to remember about Percent in everyday decisions?
Answer: Percent means per hundred, so 35% means 35 out of 100. This topic focuses on Percent in everyday decisions.
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 final answer is reasonable before accepting it.
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 of a calculation 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 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, check copied values, signs, units, formulas, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships between lengths, angles, areas, and other quantities.
Q23. Why are tables useful?
Answer: Tables organize values and help reveal patterns, relationships, rates, and missing information.
Q24. Why should you explain your reasoning?
Answer: Reasoning shows why a method works, not just what answer you obtained.
Q25. How do mistakes help learning?
Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent the same error later.
Q26. How should you study this chapter?
Answer: Review definitions, redo worked examples without looking, practise mixed questions, and explain solutions in your own words.
Q27. When is a calculator useful?
Answer: A calculator is useful for lengthy arithmetic after you understand the mathematical setup and can estimate the expected size of the answer.
Q28. Why compare more than one strategy?
Answer: Different strategies can make a problem easier and provide a way to verify the result.
Q29. What is a mathematical model?
Answer: It is a simplified mathematical representation of a real situation used to analyze, explain, or predict.
Q30. Why should assumptions be stated?
Answer: Assumptions show what conditions the solution depends on and help readers judge whether the model is reasonable.