Chapter 15: Adding Decimal Numbers to Hundredths
Learn Grade 5 mathematics from very beginner explanations through worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Adding 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 (a Grade 5 idea used in this chapter)
- Adding tenths (a Grade 5 idea used in this chapter)
- Adding hundredths (a Grade 5 idea used in this chapter)
- Adding decimals with different numbers of places (a Grade 5 idea used in this chapter)
- Adding three decimal numbers (a Grade 5 idea used in this chapter)
- Using place-value models (a Grade 5 idea used in this chapter)
- Using compensation (a Grade 5 idea used in this chapter)
- Estimating decimal sums (a Grade 5 idea used in this chapter)
- Decimal addition word problems (a Grade 5 idea used in this chapter)
- Checking decimal addition (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.
15.1 Aligning decimal points
Aligning decimal points 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?
- 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 uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Aligning decimal points 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?
- 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 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.
- 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 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 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 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.
- 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 uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Aligning decimal points 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 Aligning decimal points. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
15.2 Adding tenths
Adding 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 Adding 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: Adding tenths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Adding 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 Adding tenths?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Adding 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 Adding 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: Adding 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 Adding 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: Adding 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 Adding 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: Adding tenths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Adding 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 by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 4.95
Worked Example 7
Problem: Calculate 8.4 + 0.6.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 9
Worked Example 8
Problem: Calculate 12.05 + 2.5.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 14.55
Worked Example 9
Problem: Calculate 0.96 + 0.4.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 1.36
Worked Example 10
Problem: Calculate 5.125 + 1.25.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 6.375
Practice Exercise
Create one new question about Adding tenths. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
15.3 Adding hundredths
Adding 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 Adding 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: Adding hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Adding 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 Adding hundredths?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Adding 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 Adding 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: Adding 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 Adding 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: Adding 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 Adding 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: Adding hundredths uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Adding 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 by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 4.95
Worked Example 7
Problem: Calculate 8.4 + 0.6.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 9
Worked Example 8
Problem: Calculate 12.05 + 2.5.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 14.55
Worked Example 9
Problem: Calculate 0.96 + 0.4.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 1.36
Worked Example 10
Problem: Calculate 5.125 + 1.25.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 6.375
Practice Exercise
Create one new question about Adding hundredths. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
15.4 Adding decimals with different numbers of places
Adding decimals with different numbers of places 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 Adding decimals with different numbers of places?
- 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 decimals with different numbers of places uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Adding decimals with different numbers of places 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 Adding decimals with different numbers of places?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Adding decimals with different numbers of places 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 Adding decimals with different numbers of places.
- 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 decimals with different numbers of places 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 Adding decimals with different numbers of places 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 decimals with different numbers of places 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 Adding decimals with different numbers of places.
- 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 decimals with different numbers of places uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Adding decimals with different numbers of places 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 by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 4.95
Worked Example 7
Problem: Calculate 8.4 + 0.6.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 9
Worked Example 8
Problem: Calculate 12.05 + 2.5.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 14.55
Worked Example 9
Problem: Calculate 0.96 + 0.4.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 1.36
Worked Example 10
Problem: Calculate 5.125 + 1.25.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 6.375
Practice Exercise
Create one new question about Adding decimals with different numbers of places. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
15.5 Adding three decimal numbers
Adding three decimal numbers 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 Adding three decimal numbers?
- 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 three decimal numbers uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Adding three decimal numbers 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 Adding three decimal numbers?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Adding three decimal numbers 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 Adding three decimal numbers.
- 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 three decimal numbers 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 Adding three decimal numbers 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 three decimal numbers 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 Adding three decimal numbers.
- 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 three decimal numbers uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Adding three decimal numbers 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 by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 4.95
Worked Example 7
Problem: Calculate 8.4 + 0.6.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 9
Worked Example 8
Problem: Calculate 12.05 + 2.5.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 14.55
Worked Example 9
Problem: Calculate 0.96 + 0.4.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 1.36
Worked Example 10
Problem: Calculate 5.125 + 1.25.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 6.375
Practice Exercise
Create one new question about Adding three decimal numbers. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
15.6 Using place-value models
Using place-value models uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
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 place-value models?
- 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 place-value models uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
Answer: Using place-value models uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
Worked Example 2
Problem: What should you identify first before solving a problem about Using place-value models?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Using place-value models uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
Answer: Identify the known information and the unknown before choosing an operation or rule.
Worked Example 3
Problem: Choose a useful representation for Using place-value models.
- 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 place-value models uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
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 place-value models 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 place-value models uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
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 place-value models.
- 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 place-value models uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
Answer: Using place-value models can be used in a real situation where mathematics helps make a clear calculation, comparison, measurement, prediction, or decision.
Worked Example 6
Problem: Tile a floor
- Write a simple rule: area = length × width.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Estimate tile quantity and include a small waste allowance.
Worked Example 7
Problem: Plan monthly savings
- Write a simple rule: total = starting amount + monthly deposit × months.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Predict when the savings goal is reached.
Worked Example 8
Problem: Simulate a die
- Write a simple rule: generate a random whole number from 1 to 6.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Repeat many times and compare frequencies.
Worked Example 9
Problem: Translate a point
- Write a simple rule: new x = x + 3; new y = y - 2.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Apply the same rule to every point.
Worked Example 10
Problem: Estimate paint needed
- Write a simple rule: paint = wall area ÷ coverage per can.
- State any assumptions.
- Use the rule on sample values.
- Check whether the result is realistic.
Very beginner explanation: Coding and modelling organize a real situation into clear steps, variables, rules, and checks.
Answer: Round up because a partial can may not be enough.
Practice Exercise
Create one new question about Using place-value models. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
15.7 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.
15.8 Estimating decimal sums
Estimating decimal sums 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 sums?
- 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 sums uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Estimating decimal sums 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 sums?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Estimating decimal sums 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 sums.
- 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 sums 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 sums 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 sums 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 sums.
- 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 sums uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Estimating decimal sums 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 sums. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
15.9 Decimal addition word problems
Decimal addition word problems 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 Decimal addition word problems?
- 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: Decimal addition word problems uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Decimal addition word problems 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 Decimal addition word problems?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Decimal addition word problems 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 Decimal addition word problems.
- 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: Decimal addition word problems 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 Decimal addition word problems 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: Decimal addition word problems 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 Decimal addition word problems.
- 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: Decimal addition word problems uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Decimal addition word problems 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 by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 4.95
Worked Example 7
Problem: Calculate 8.4 + 0.6.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 9
Worked Example 8
Problem: Calculate 12.05 + 2.5.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 14.55
Worked Example 9
Problem: Calculate 0.96 + 0.4.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 1.36
Worked Example 10
Problem: Calculate 5.125 + 1.25.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 6.375
Practice Exercise
Create one new question about Decimal addition word problems. Solve it step by step, include units or labels when needed, and check whether your answer is reasonable.
15.10 Checking decimal addition
Checking decimal addition 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 addition?
- 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 addition uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Checking decimal addition 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 addition?
- Read the complete problem.
- Mark the information that is given.
- Identify exactly what the question asks you to find.
Very beginner explanation: Checking decimal addition 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 addition.
- 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 addition 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 addition 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 addition 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 addition.
- 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 addition uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Answer: Checking decimal addition 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 by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 4.95
Worked Example 7
Problem: Calculate 8.4 + 0.6.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 9
Worked Example 8
Problem: Calculate 12.05 + 2.5.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 14.55
Worked Example 9
Problem: Calculate 0.96 + 0.4.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 1.36
Worked Example 10
Problem: Calculate 5.125 + 1.25.
- Align decimal points.
- Add by place value.
Very beginner explanation: Aligning decimal points keeps tenths with tenths and hundredths with hundredths.
Answer: 6.375
Practice Exercise
Create one new question about Checking decimal addition. 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.
- Create and solve one original problem about Adding tenths.
- Create and solve one original problem about Adding hundredths.
- Create and solve one original problem about Adding decimals with different numbers of places.
- Create and solve one original problem about Adding three decimal numbers.
- Create and solve one original problem about Using place-value models.
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?
Answer: Aligning decimal points 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 Adding tenths?
Answer: Adding 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 Adding hundredths?
Answer: Adding 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 decimals with different numbers of places?
Answer: Adding decimals with different numbers of places uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Q5. What is the key idea in Adding three decimal numbers?
Answer: Adding three decimal numbers 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 place-value models?
Answer: Using place-value models uses mathematics to simplify a real situation, test possible solutions, and explain a reasonable recommendation.
Q7. 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.
Q8. What is the key idea in Estimating decimal sums?
Answer: Estimating decimal sums uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Q9. What is the key idea in Decimal addition word problems?
Answer: Decimal addition word problems uses place value to describe parts smaller than one. Keeping decimal places aligned makes comparisons and calculations easier to understand.
Q10. What is the key idea in Checking decimal addition?
Answer: Checking decimal addition 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 Adding 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 Adding 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 Adding 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 Adding 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 Adding 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.