Chapter 18: Rates and Unit Rates
Learn Grade 7 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Rates and Unit Rates with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Unit Rate (a rate per one unit)
- Circle Graph (a graph using sectors of a circle to show parts of a whole)
- Exchange Rate (the value of one currency expressed in another currency)
- Interest Rate (percentage used to calculate interest)
- 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.
18.1 Meaning of rate
A rate compares two quantities measured in different units. This topic focuses on Meaning of rate .
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: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Meaning of rate .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Meaning of rate .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Meaning of rate .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Meaning of rate .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Meaning of rate .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Meaning of rate. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.2 Unit rate
A rate compares two quantities measured in different units. This topic focuses on Unit rate .
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: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Unit rate .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Unit rate .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Unit rate .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Unit rate .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Unit rate .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Unit rate. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.3 Speed
Speed is an important Grade 7 idea in Rates and Unit Rates. 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: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: Speed is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: Speed is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: Speed is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: Speed is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: Speed is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Speed. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.4 Price per item
Price per item is an important Grade 7 idea in Rates and Unit Rates. 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: Price per item: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Price per item is an important Grade 7 idea in Rates and Unit Rates. 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: Price per item: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Price per item is an important Grade 7 idea in Rates and Unit Rates. 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: Price per item: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Price per item is an important Grade 7 idea in Rates and Unit Rates. 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: Price per item: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Price per item is an important Grade 7 idea in Rates and Unit Rates. 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: Price per item: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Price per item is an important Grade 7 idea in Rates and Unit Rates. 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 Price per item 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: Price per item 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 Price per item 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: Price per item 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 Price per item 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: Price per item 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 Price per item 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: Price per item 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 Price per item 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: Price per item 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 Price per item. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.5 Cost per kilogram
Cost per kilogram is an important Grade 7 idea in Rates and Unit Rates. 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: Convert 3.6 m to cm.
- Use the metric relationship and multiply or divide by a power of 10.
Very beginner explanation: Cost per kilogram is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 360 cm
Worked Example 2
Problem: Convert 2.5 km to m.
- Use the metric relationship and multiply or divide by a power of 10.
Very beginner explanation: Cost per kilogram is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2500 m
Worked Example 3
Problem: Convert 7500 g to kg.
- Use the metric relationship and multiply or divide by a power of 10.
Very beginner explanation: Cost per kilogram is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7.5 kg
Worked Example 4
Problem: Convert 1.8 L to mL.
- Use the metric relationship and multiply or divide by a power of 10.
Very beginner explanation: Cost per kilogram is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1800 mL
Worked Example 5
Problem: Convert 450 mm to cm.
- Use the metric relationship and multiply or divide by a power of 10.
Very beginner explanation: Cost per kilogram is an important Grade 7 idea in Rates and Unit Rates. 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 cm
Worked Example 6
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.
Answer: 50 cm
Worked Example 7
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.
Answer: 120 cm
Worked Example 8
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.
Answer: 275 cm
Worked Example 9
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.
Answer: 360 cm
Worked Example 10
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.
Answer: 405 cm
Practice Exercise
Create one new question about Cost per kilogram. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.6 Cost per litre
Cost per litre is an important Grade 7 idea in Rates and Unit Rates. 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: Convert 3.6 m to cm.
- Use the metric relationship and multiply or divide by a power of 10.
Very beginner explanation: Cost per litre is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 360 cm
Worked Example 2
Problem: Convert 2.5 km to m.
- Use the metric relationship and multiply or divide by a power of 10.
Very beginner explanation: Cost per litre is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 2500 m
Worked Example 3
Problem: Convert 7500 g to kg.
- Use the metric relationship and multiply or divide by a power of 10.
Very beginner explanation: Cost per litre is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 7.5 kg
Worked Example 4
Problem: Convert 1.8 L to mL.
- Use the metric relationship and multiply or divide by a power of 10.
Very beginner explanation: Cost per litre is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 1800 mL
Worked Example 5
Problem: Convert 450 mm to cm.
- Use the metric relationship and multiply or divide by a power of 10.
Very beginner explanation: Cost per litre is an important Grade 7 idea in Rates and Unit Rates. 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 cm
Worked Example 6
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.
Answer: 50 cm
Worked Example 7
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.
Answer: 120 cm
Worked Example 8
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.
Answer: 275 cm
Worked Example 9
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.
Answer: 360 cm
Worked Example 10
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.
Answer: 405 cm
Practice Exercise
Create one new question about Cost per litre. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.7 Distance per unit time
Distance per unit time is an important Grade 7 idea in Rates and Unit Rates. 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: Distance per unit time: Identify a correct example.
- State the definition and show why the example fits.
- Show all important reasoning.
Very beginner explanation: Distance per unit time is an important Grade 7 idea in Rates and Unit Rates. 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: Distance per unit time: Identify a non-example.
- Explain which requirement is missing.
- Show all important reasoning.
Very beginner explanation: Distance per unit time is an important Grade 7 idea in Rates and Unit Rates. 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: Distance per unit time: Compare two cases.
- State one similarity and one difference.
- Show all important reasoning.
Very beginner explanation: Distance per unit time is an important Grade 7 idea in Rates and Unit Rates. 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: Distance per unit time: Apply the idea in a real situation.
- Translate the situation into mathematical language.
- Show all important reasoning.
Very beginner explanation: Distance per unit time is an important Grade 7 idea in Rates and Unit Rates. 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: Distance per unit time: Create and check your own example.
- Use the definition, then verify each condition.
- Show all important reasoning.
Very beginner explanation: Distance per unit time is an important Grade 7 idea in Rates and Unit Rates. 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 Distance per unit time 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: Distance per unit time 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 Distance per unit time 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: Distance per unit time 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 Distance per unit time 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: Distance per unit time 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 Distance per unit time 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: Distance per unit time 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 Distance per unit time 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: Distance per unit time 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 Distance per unit time. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.8 Comparing unit rates
A rate compares two quantities measured in different units. This topic focuses on Comparing unit rates .
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: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Comparing unit rates .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Comparing unit rates .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Comparing unit rates .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Comparing unit rates .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Comparing unit rates .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Comparing unit rates. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.9 Best-buy problems
Best-buy problems is an important Grade 7 idea in Rates and Unit Rates. 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: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: Best-buy problems is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: Best-buy problems is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: Best-buy problems is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: Best-buy problems is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: Best-buy problems is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Answer: 70 km/h
Worked Example 6
Problem: Explain Best-buy 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: Best-buy 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 Best-buy 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: Best-buy 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 Best-buy 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: Best-buy 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 Best-buy 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: Best-buy 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 Best-buy 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: Best-buy 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 Best-buy problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.10 Converting units in rates
A rate compares two quantities measured in different units. This topic focuses on Converting units in rates .
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: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Converting units in rates .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Converting units in rates .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Converting units in rates .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Converting units in rates .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Converting units in rates .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Converting units in rates. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.11 Rate tables
A rate compares two quantities measured in different units. This topic focuses on Rate tables .
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: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Rate tables .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Rate tables .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Rate tables .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Rate tables .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Rate tables .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Rate tables. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.12 Graphs of constant rates
A rate compares two quantities measured in different units. This topic focuses on Graphs of constant rates .
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: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Graphs of constant rates .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Graphs of constant rates .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Graphs of constant rates .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Graphs of constant rates .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Graphs of constant rates .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Graphs of constant rates. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
18.13 Real-life rate problems
A rate compares two quantities measured in different units. This topic focuses on Real-life rate problems .
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: 120 km in 2 h. Find the unit rate.
- Use rate = distance ÷ time.
- 120÷2=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Real-life rate problems .
Answer: 60 km/h
Worked Example 2
Problem: 180 km in 3 h. Find the unit rate.
- Use rate = distance ÷ time.
- 180÷3=60.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Real-life rate problems .
Answer: 60 km/h
Worked Example 3
Problem: 250 km in 5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 250÷5=50.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Real-life rate problems .
Answer: 50 km/h
Worked Example 4
Problem: 72 km in 1.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 72÷1.5=48.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Real-life rate problems .
Answer: 48 km/h
Worked Example 5
Problem: 315 km in 4.5 h. Find the unit rate.
- Use rate = distance ÷ time.
- 315÷4.5=70.
Very beginner explanation: A rate compares two quantities measured in different units. This topic focuses on Real-life rate problems .
Answer: 70 km/h
Worked Example 6
Problem: 120 km are travelled in 2 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 120 ÷ 2 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 7
Problem: 180 km are travelled in 3 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 180 ÷ 3 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 8
Problem: 240 km are travelled in 4 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 240 ÷ 4 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 9
Problem: 300 km are travelled in 5 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 300 ÷ 5 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Worked Example 10
Problem: 360 km are travelled in 6 hours. Find the unit rate.
- Use rate = distance ÷ time.
- 360 ÷ 6 = 60.
Very beginner explanation: A unit rate compares a quantity with exactly one unit of another quantity.
Answer: 60 km/h
Practice Exercise
Create one new question about Real-life rate problems. 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 Meaning of rate . Show your reasoning and check your answer.
- Create and solve a new question about Unit rate . Show your reasoning and check your answer.
- Create and solve a new question about Speed . Show your reasoning and check your answer.
- Create and solve a new question about Price per item . Show your reasoning and check your answer.
- Create and solve a new question about Cost per kilogram . Show your reasoning and check your answer.
- Create and solve a new question about Cost per litre . Show your reasoning and check your answer.
- Create and solve a new question about Distance per unit time . Show your reasoning and check your answer.
- Create and solve a new question about Comparing unit rates . Show your reasoning and check your answer.
- Create and solve a new question about Best-buy problems . Show your reasoning and check your answer.
- Create and solve a new question about Converting units in rates . Show your reasoning and check your answer.
- Create and solve a new question about Rate tables . Show your reasoning and check your answer.
- Create and solve a new question about Graphs of constant rates . 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 Meaning of rate?
Answer: A rate compares two quantities measured in different units. This topic focuses on Meaning of rate.
Q2. What is important to remember about Unit rate?
Answer: A rate compares two quantities measured in different units. This topic focuses on Unit rate.
Q3. What is important to remember about Speed?
Answer: Speed is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q4. What is important to remember about Price per item?
Answer: Price per item is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q5. What is important to remember about Cost per kilogram?
Answer: Cost per kilogram is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q6. What is important to remember about Cost per litre?
Answer: Cost per litre is an important Grade 7 idea in Rates and Unit Rates. 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 Distance per unit time?
Answer: Distance per unit time is an important Grade 7 idea in Rates and Unit Rates. Identify what is known, what must be found, choose an appropriate strategy, show the important steps, and check whether the result is reasonable.
Q8. What is important to remember about Comparing unit rates?
Answer: A rate compares two quantities measured in different units. This topic focuses on Comparing unit rates.
Q9. What is important to remember about Best-buy problems?
Answer: Best-buy problems is an important Grade 7 idea in Rates and Unit Rates. 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 Converting units in rates?
Answer: A rate compares two quantities measured in different units. This topic focuses on Converting units in rates.
Q11. What is important to remember about Rate tables?
Answer: A rate compares two quantities measured in different units. This topic focuses on Rate tables.
Q12. What is important to remember about Graphs of constant rates?
Answer: A rate compares two quantities measured in different units. This topic focuses on Graphs of constant rates.
Q13. What is important to remember about Real-life rate problems?
Answer: A rate compares two quantities measured in different units. This topic focuses on Real-life rate problems.
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.