Chapter 16: Subtracting Decimal Numbers to Hundredths
Learn Grade 5 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Subtracting Decimal Numbers to Hundredths with simple language, step-by-step reasoning, and original worked examples. Technical words are explained in plain language.
Key Technical Terms
- Aligning decimal points for subtraction (a Grade 5 idea used in this chapter)
- Subtracting tenths (a Grade 5 idea used in this chapter)
- Subtracting hundredths (a Grade 5 idea used in this chapter)
- Adding trailing zeros (a Grade 5 idea used in this chapter)
- Regrouping with decimals (a Grade 5 idea used in this chapter)
- Using compensation (a Grade 5 idea used in this chapter)
- Estimating decimal differences (a Grade 5 idea used in this chapter)
- Money subtraction (a Grade 5 idea used in this chapter)
- Measurement subtraction (a Grade 5 idea used in this chapter)
- Checking decimal subtraction (a Grade 5 idea used in this chapter)
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 Aligning decimal points for subtraction
Aligning decimal points for subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Aligning decimal points for subtraction?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Aligning decimal points for subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Aligning decimal points for subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Worked Example 2
Problem: What should you identify first before solving a problem about Aligning decimal points for subtraction?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Aligning decimal points for subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Aligning decimal points for subtraction.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Aligning decimal points for subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Aligning decimal points for subtraction problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Aligning decimal points for subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Aligning decimal points for subtraction.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Aligning decimal points for subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Aligning decimal points for subtraction can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Calculate 3.75 - 1.2.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 2.55
Worked Example 7
Problem: Calculate 8.4 - 0.6.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 7.8
Worked Example 8
Problem: Calculate 12.05 - 2.5.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 9.55
Worked Example 9
Problem: Calculate 0.96 - 0.4.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 0.56
Worked Example 10
Problem: Calculate 5.125 - 1.25.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 3.875
Practice Exercise
Create one new question about Aligning decimal points for subtraction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.2 Subtracting tenths
Subtracting tenths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Subtracting tenths?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Subtracting tenths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Subtracting tenths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Worked Example 2
Problem: What should you identify first before solving a problem about Subtracting tenths?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Subtracting tenths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Subtracting tenths.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Subtracting tenths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Subtracting tenths problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Subtracting tenths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Subtracting tenths.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Subtracting tenths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Subtracting tenths can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Calculate 3.75 - 1.2.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 2.55
Worked Example 7
Problem: Calculate 8.4 - 0.6.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 7.8
Worked Example 8
Problem: Calculate 12.05 - 2.5.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 9.55
Worked Example 9
Problem: Calculate 0.96 - 0.4.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 0.56
Worked Example 10
Problem: Calculate 5.125 - 1.25.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 3.875
Practice Exercise
Create one new question about Subtracting tenths. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.3 Subtracting hundredths
Subtracting hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Subtracting hundredths?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Subtracting hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Subtracting hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Worked Example 2
Problem: What should you identify first before solving a problem about Subtracting hundredths?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Subtracting hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Subtracting hundredths.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Subtracting hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Subtracting hundredths problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Subtracting hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Subtracting hundredths.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Subtracting hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Subtracting hundredths can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Calculate 3.75 - 1.2.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 2.55
Worked Example 7
Problem: Calculate 8.4 - 0.6.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 7.8
Worked Example 8
Problem: Calculate 12.05 - 2.5.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 9.55
Worked Example 9
Problem: Calculate 0.96 - 0.4.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 0.56
Worked Example 10
Problem: Calculate 5.125 - 1.25.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 3.875
Practice Exercise
Create one new question about Subtracting hundredths. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.4 Adding trailing zeros
Adding trailing zeros is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Adding trailing zeros?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Adding trailing zeros is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Adding trailing zeros is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Adding trailing zeros?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Adding trailing zeros is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Adding trailing zeros.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Adding trailing zeros is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Adding trailing zeros problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Adding trailing zeros is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Adding trailing zeros.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Adding trailing zeros is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Adding trailing zeros can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Adding trailing zeros 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: Adding trailing zeros 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 Adding trailing zeros 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: Adding trailing zeros 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 Adding trailing zeros 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: Adding trailing zeros 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 Adding trailing zeros 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: Adding trailing zeros 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 Adding trailing zeros 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: Adding trailing zeros 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 Adding trailing zeros. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.5 Regrouping with decimals
Regrouping with decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Regrouping with decimals?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Regrouping with decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Regrouping with decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Worked Example 2
Problem: What should you identify first before solving a problem about Regrouping with decimals?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Regrouping with decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Regrouping with decimals.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Regrouping with decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Regrouping with decimals problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Regrouping with decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Regrouping with decimals.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Regrouping with decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Regrouping with decimals can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 3.8
Worked Example 7
Problem: Round 8.4 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 8.4
Worked Example 8
Problem: Round 12.05 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 12.1
Worked Example 9
Problem: Round 0.96 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 1
Worked Example 10
Problem: Round 5.125 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 5.1
Practice Exercise
Create one new question about Regrouping with decimals. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.6 Using compensation
Using compensation is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Using compensation?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Using compensation is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Using compensation is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Worked Example 2
Problem: What should you identify first before solving a problem about Using compensation?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Using compensation is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Using compensation.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Using compensation is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Using compensation problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Using compensation is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Using compensation.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Using compensation is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Answer: Using compensation can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Using compensation 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: Using compensation 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 Using compensation 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: Using compensation 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 Using compensation 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: Using compensation 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 Using compensation 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: Using compensation 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 Using compensation 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: Using compensation 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 Using compensation. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.7 Estimating decimal differences
Estimating decimal differences uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Estimating decimal differences?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Estimating decimal differences uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Estimating decimal differences uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Worked Example 2
Problem: What should you identify first before solving a problem about Estimating decimal differences?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Estimating decimal differences uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Estimating decimal differences.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Estimating decimal differences uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Estimating decimal differences problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Estimating decimal differences uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Estimating decimal differences.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Estimating decimal differences uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Estimating decimal differences can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Round 3.75 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 3.8
Worked Example 7
Problem: Round 8.4 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 8.4
Worked Example 8
Problem: Round 12.05 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 12.1
Worked Example 9
Problem: Round 0.96 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 1
Worked Example 10
Problem: Round 5.125 to the nearest tenth.
- Find the tenths digit.
- Look at the hundredths digit.
- Round up if the hundredths digit is 5 or more.
Very beginner explanation: Rounding uses the next digit to decide whether the target digit stays or increases.
Answer: 5.1
Practice Exercise
Create one new question about Estimating decimal differences. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.8 Money subtraction
Money subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Money subtraction?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Money subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Money subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Worked Example 2
Problem: What should you identify first before solving a problem about Money subtraction?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Money subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Money subtraction.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Money subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Money subtraction problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Money subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Money subtraction.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Money subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Money subtraction can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Money subtraction 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: Money subtraction 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 Money subtraction 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: Money subtraction 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 Money subtraction 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: Money subtraction 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 Money subtraction 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: Money subtraction 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 Money subtraction 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: Money subtraction 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 Money subtraction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.9 Measurement subtraction
Measurement subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Measurement subtraction?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Measurement subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Measurement subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Worked Example 2
Problem: What should you identify first before solving a problem about Measurement subtraction?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Measurement subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Measurement subtraction.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Measurement subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Measurement subtraction problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Measurement subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Measurement subtraction.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Measurement subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Answer: Measurement subtraction can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Explain Measurement subtraction 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: Measurement subtraction 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 Measurement subtraction 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: Measurement subtraction 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 Measurement subtraction 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: Measurement subtraction 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 Measurement subtraction 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: Measurement subtraction 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 Measurement subtraction 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: Measurement subtraction 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 Measurement subtraction. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
16.10 Checking decimal subtraction
Checking decimal subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Beginner Note
Begin with meaning and a visual or concrete example. Work one step at a time and check the answer before moving on.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: In your own words, what is the main idea of Checking decimal subtraction?
- Read the topic name carefully.
- Identify the quantity, relationship, shape, or process it describes.
- Explain the idea without using a memorized sentence.
Very beginner explanation: Checking decimal subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Checking decimal subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Worked Example 2
Problem: What should you identify first before solving a problem about Checking decimal subtraction?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Checking decimal subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Checking decimal subtraction.
- Decide whether a model, number line, table, graph, diagram, equation, or labelled calculation best fits the idea.
- Label the representation clearly.
- Check that it matches the mathematical relationship.
Very beginner explanation: Checking decimal subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Use the representation that makes the important relationship easiest to see and check.
Worked Example 4
Problem: A learner gets an answer in a Checking decimal subtraction problem. How can the learner check it?
- Estimate the expected size or direction of the answer.
- Check units, labels, signs, and place values.
- Use an inverse operation or a second method when possible.
Very beginner explanation: Checking decimal subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: The answer should agree with an estimate, the problem conditions, and a second check.
Worked Example 5
Problem: Give a real-life use for Checking decimal subtraction.
- Think about money, measurement, data, patterns, design, or everyday quantities.
- Choose a situation where the topic helps compare, calculate, measure, predict, or organize.
- Explain the connection in one sentence.
Very beginner explanation: Checking decimal subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Checking decimal subtraction can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Calculate 3.75 - 1.2.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 2.55
Worked Example 7
Problem: Calculate 8.4 - 0.6.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 7.8
Worked Example 8
Problem: Calculate 12.05 - 2.5.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 9.55
Worked Example 9
Problem: Calculate 0.96 - 0.4.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 0.56
Worked Example 10
Problem: Calculate 5.125 - 1.25.
- Align decimal points.
- Add trailing zeros if helpful.
- Subtract by place value.
Very beginner explanation: Trailing zeros can be added without changing a decimal value.
Answer: 3.875
Practice Exercise
Create one new question about Checking decimal subtraction. 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 question before calculating.
- Represent the mathematics with a model, table, graph, diagram, number line, or equation when useful.
- Show the reasoning and check the final answer with a second method when possible.
Extra Practice
- Create and solve one original problem about Aligning decimal points for subtraction.
- Create and solve one original problem about Subtracting tenths.
- Create and solve one original problem about Subtracting hundredths.
- Create and solve one original problem about Adding trailing zeros.
- Create and solve one original problem about Regrouping with decimals.
- Create and solve one original problem about Using compensation.
Common Mistakes
- Skipping the meaning and trying to memorize a rule only.
- Using the wrong operation because the question was not read completely.
- Ignoring units, labels, place values, or the context of the problem.
- Not estimating or checking whether the final answer is reasonable.
30 Review Questions and Answers
Q1. What is the key idea in Aligning decimal points for subtraction?
Answer: Aligning decimal points for subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Q2. What is the key idea in Subtracting tenths?
Answer: Subtracting tenths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Q3. What is the key idea in Subtracting hundredths?
Answer: Subtracting hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Q4. What is the key idea in Adding trailing zeros?
Answer: Adding trailing zeros is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q5. What is the key idea in Regrouping with decimals?
Answer: Regrouping with decimals uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Q6. What is the key idea in Using compensation?
Answer: Using compensation is an important Grade 5 mathematics idea. Learn its meaning first, then connect it to a representation, a worked example, and a real-life use.
Q7. What is the key idea in Estimating decimal differences?
Answer: Estimating decimal differences uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Q8. What is the key idea in Money subtraction?
Answer: Money subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Q9. What is the key idea in Measurement subtraction?
Answer: Measurement subtraction develops accurate calculation and problem solving. Learners choose a strategy, show the steps, estimate when useful, and check the result with an inverse operation or another method.
Q10. What is the key idea in Checking decimal subtraction?
Answer: Checking decimal subtraction uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Q11. Why should you estimate before or after a calculation?
Answer: Estimation gives a reasonable range and can reveal place-value or operation mistakes.
Q12. Why are labels and units important?
Answer: They show what a number represents and help prevent mixing unlike quantities.
Q13. How can a diagram help solve a problem?
Answer: A diagram makes quantities and relationships visible before calculation.
Q14. How can inverse operations check an answer?
Answer: An inverse operation reverses the original operation and should recover the starting value when the work is correct.
Q15. Why should you show steps?
Answer: Showing steps makes reasoning clear and helps find where an error happened.
Q16. What should you do after making a mistake?
Answer: Find the step where the reasoning changed, correct it, and try a similar problem again.
Q17. How can a number line support reasoning?
Answer: It shows order, distance, relative size, fractions, decimals, and inequality solutions visually.
Q18. When is a table useful?
Answer: A table organizes related values so patterns and comparisons are easier to see.
Q19. When is a graph useful?
Answer: A graph makes trends, comparisons, locations, or data patterns visible.
Q20. How do you decide which operation to use?
Answer: Use the meaning of the situation: combine, compare, find a difference, form equal groups, or find how many groups fit.
Q21. Why should you check place value?
Answer: A digit or decimal has a different value depending on its position.
Q22. What makes an answer reasonable?
Answer: It fits the context, has the expected size and units, and agrees with an estimate or second method.
Q23. How can you explain mathematical reasoning clearly?
Answer: Name the information, the rule or operation, the steps, and why the final answer fits the problem.
Q24. Why can more than one strategy be correct?
Answer: Different valid strategies can represent the same mathematical relationship and lead to the same result.
Q25. How should you approach a difficult Grade 5 problem?
Answer: Break it into smaller parts, solve one part at a time, and check each result before continuing.
Q26. How can you practise Subtracting Decimal Numbers to Hundredths effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q27. How can you practise Subtracting Decimal Numbers to Hundredths effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q28. How can you practise Subtracting Decimal Numbers to Hundredths effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q29. How can you practise Subtracting Decimal Numbers to Hundredths effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.
Q30. How can you practise Subtracting Decimal Numbers to Hundredths effectively?
Answer: Work a small example, explain every step, check the answer, then try a similar problem without looking at the first solution.