Chapter 7: Equivalent Fractions, Comparison, and Ordering
Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Equivalent Fractions, Comparison, and Ordering in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
Key Technical Terms
- Generating equivalent fractions (A fraction represents equal parts of a whole, set, or quantity.)
- Simplest form (Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Common denominators (The denominator tells how many equal parts make one whole.)
- Comparing fractions with equal numerators (The numerator tells how many equal parts are being considered.)
- Comparing mixed numbers (Comparing mixed numbers is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Ordering mixed numbers (Ordering mixed numbers is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
How to Learn This Chapter
Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
7.1 Generating equivalent fractions
A fraction represents equal parts of a whole, set, or quantity. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: The fraction bar means division.
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: The fraction bar means division.
Answer: 0.667
Worked Example 3
Problem: Write 3/5 as a decimal.
- Divide 3 by 5.
Very beginner explanation: The fraction bar means division.
Answer: 0.6
Worked Example 4
Problem: Write 5/8 as a decimal.
- Divide 5 by 8.
Very beginner explanation: The fraction bar means division.
Answer: 0.625
Worked Example 5
Problem: Write 7/10 as a decimal.
- Divide 7 by 10.
Very beginner explanation: The fraction bar means division.
Answer: 0.7
Worked Example 6
Problem: Write 4/9 as a decimal.
- Divide 4 by 9.
Very beginner explanation: The fraction bar means division.
Answer: 0.444
Worked Example 7
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: The fraction bar means division.
Answer: 0.833
Worked Example 8
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: The fraction bar means division.
Answer: 0.75
Worked Example 9
Problem: Write 2/5 as a decimal.
- Divide 2 by 5.
Very beginner explanation: The fraction bar means division.
Answer: 0.4
Worked Example 10
Problem: Write 7/12 as a decimal.
- Divide 7 by 12.
Very beginner explanation: The fraction bar means division.
Answer: 0.583
Practice Exercise
Create one new Grade 6 problem about Generating equivalent fractions. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is combining numerators and denominators without first applying the correct fraction rule.
7.2 Simplest form
Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Use Simplest form to analyze the values 3 and 2. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 2
Problem: Use Simplest form to analyze the values 29 and 6. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 3
Problem: Use Simplest form to analyze the values 3 and 9. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 4
Problem: Use Simplest form to analyze the values 25 and 17. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 5
Problem: Use Simplest form to analyze the values 20 and 17. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 6
Problem: Use Simplest form to analyze the values 15 and 17. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 7
Problem: Use Simplest form to analyze the values 15 and 12. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 8
Problem: Use Simplest form to analyze the values 24 and 7. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 9
Problem: Use Simplest form to analyze the values 21 and 8. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 10
Problem: Use Simplest form to analyze the values 8 and 19. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Practice Exercise
Create one new Grade 6 problem about Simplest form. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
7.3 Common denominators
The denominator tells how many equal parts make one whole. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: The fraction bar means division.
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: The fraction bar means division.
Answer: 0.667
Worked Example 3
Problem: Write 3/5 as a decimal.
- Divide 3 by 5.
Very beginner explanation: The fraction bar means division.
Answer: 0.6
Worked Example 4
Problem: Write 5/8 as a decimal.
- Divide 5 by 8.
Very beginner explanation: The fraction bar means division.
Answer: 0.625
Worked Example 5
Problem: Write 7/10 as a decimal.
- Divide 7 by 10.
Very beginner explanation: The fraction bar means division.
Answer: 0.7
Worked Example 6
Problem: Write 4/9 as a decimal.
- Divide 4 by 9.
Very beginner explanation: The fraction bar means division.
Answer: 0.444
Worked Example 7
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: The fraction bar means division.
Answer: 0.833
Worked Example 8
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: The fraction bar means division.
Answer: 0.75
Worked Example 9
Problem: Write 2/5 as a decimal.
- Divide 2 by 5.
Very beginner explanation: The fraction bar means division.
Answer: 0.4
Worked Example 10
Problem: Write 7/12 as a decimal.
- Divide 7 by 12.
Very beginner explanation: The fraction bar means division.
Answer: 0.583
Practice Exercise
Create one new Grade 6 problem about Common denominators. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
7.4 Comparing fractions with equal denominators
The denominator tells how many equal parts make one whole. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 1/2 and 1/3.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 1/2 > 1/3
Worked Example 2
Problem: Compare 2/3 and 1/4.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/3 > 1/4
Worked Example 3
Problem: Compare 3/5 and 2/7.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/5 > 2/7
Worked Example 4
Problem: Compare 5/8 and 1/6.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/8 > 1/6
Worked Example 5
Problem: Compare 7/10 and 3/5.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/10 > 3/5
Worked Example 6
Problem: Compare 4/9 and 5/12.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 4/9 > 5/12
Worked Example 7
Problem: Compare 5/6 and 1/8.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/6 > 1/8
Worked Example 8
Problem: Compare 3/4 and 7/9.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/4 < 7/9
Worked Example 9
Problem: Compare 2/5 and 4/15.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/5 > 4/15
Worked Example 10
Problem: Compare 7/12 and 5/18.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/12 > 5/18
Practice Exercise
Create one new Grade 6 problem about Comparing fractions with equal denominators. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is combining numerators and denominators without first applying the correct fraction rule.
7.5 Comparing fractions with equal numerators
The numerator tells how many equal parts are being considered. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 1/2 and 1/3.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 1/2 > 1/3
Worked Example 2
Problem: Compare 2/3 and 1/4.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/3 > 1/4
Worked Example 3
Problem: Compare 3/5 and 2/7.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/5 > 2/7
Worked Example 4
Problem: Compare 5/8 and 1/6.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/8 > 1/6
Worked Example 5
Problem: Compare 7/10 and 3/5.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/10 > 3/5
Worked Example 6
Problem: Compare 4/9 and 5/12.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 4/9 > 5/12
Worked Example 7
Problem: Compare 5/6 and 1/8.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/6 > 1/8
Worked Example 8
Problem: Compare 3/4 and 7/9.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/4 < 7/9
Worked Example 9
Problem: Compare 2/5 and 4/15.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/5 > 4/15
Worked Example 10
Problem: Compare 7/12 and 5/18.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/12 > 5/18
Practice Exercise
Create one new Grade 6 problem about Comparing fractions with equal numerators. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is combining numerators and denominators without first applying the correct fraction rule.
7.6 Comparing fractions with unlike denominators
The denominator tells how many equal parts make one whole. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 1/2 and 1/3.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 1/2 > 1/3
Worked Example 2
Problem: Compare 2/3 and 1/4.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/3 > 1/4
Worked Example 3
Problem: Compare 3/5 and 2/7.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/5 > 2/7
Worked Example 4
Problem: Compare 5/8 and 1/6.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/8 > 1/6
Worked Example 5
Problem: Compare 7/10 and 3/5.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/10 > 3/5
Worked Example 6
Problem: Compare 4/9 and 5/12.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 4/9 > 5/12
Worked Example 7
Problem: Compare 5/6 and 1/8.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/6 > 1/8
Worked Example 8
Problem: Compare 3/4 and 7/9.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/4 < 7/9
Worked Example 9
Problem: Compare 2/5 and 4/15.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/5 > 4/15
Worked Example 10
Problem: Compare 7/12 and 5/18.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/12 > 5/18
Practice Exercise
Create one new Grade 6 problem about Comparing fractions with unlike denominators. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is combining numerators and denominators without first applying the correct fraction rule.
7.7 Comparing mixed numbers
Comparing mixed numbers is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 1/2 and 1/3.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 1/2 > 1/3
Worked Example 2
Problem: Compare 2/3 and 1/4.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/3 > 1/4
Worked Example 3
Problem: Compare 3/5 and 2/7.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/5 > 2/7
Worked Example 4
Problem: Compare 5/8 and 1/6.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/8 > 1/6
Worked Example 5
Problem: Compare 7/10 and 3/5.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/10 > 3/5
Worked Example 6
Problem: Compare 4/9 and 5/12.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 4/9 > 5/12
Worked Example 7
Problem: Compare 5/6 and 1/8.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/6 > 1/8
Worked Example 8
Problem: Compare 3/4 and 7/9.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/4 < 7/9
Worked Example 9
Problem: Compare 2/5 and 4/15.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/5 > 4/15
Worked Example 10
Problem: Compare 7/12 and 5/18.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/12 > 5/18
Practice Exercise
Create one new Grade 6 problem about Comparing mixed numbers. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
7.8 Using benchmark fractions
A fraction represents equal parts of a whole, set, or quantity. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: The fraction bar means division.
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: The fraction bar means division.
Answer: 0.667
Worked Example 3
Problem: Write 3/5 as a decimal.
- Divide 3 by 5.
Very beginner explanation: The fraction bar means division.
Answer: 0.6
Worked Example 4
Problem: Write 5/8 as a decimal.
- Divide 5 by 8.
Very beginner explanation: The fraction bar means division.
Answer: 0.625
Worked Example 5
Problem: Write 7/10 as a decimal.
- Divide 7 by 10.
Very beginner explanation: The fraction bar means division.
Answer: 0.7
Worked Example 6
Problem: Write 4/9 as a decimal.
- Divide 4 by 9.
Very beginner explanation: The fraction bar means division.
Answer: 0.444
Worked Example 7
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: The fraction bar means division.
Answer: 0.833
Worked Example 8
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: The fraction bar means division.
Answer: 0.75
Worked Example 9
Problem: Write 2/5 as a decimal.
- Divide 2 by 5.
Very beginner explanation: The fraction bar means division.
Answer: 0.4
Worked Example 10
Problem: Write 7/12 as a decimal.
- Divide 7 by 12.
Very beginner explanation: The fraction bar means division.
Answer: 0.583
Practice Exercise
Create one new Grade 6 problem about Using benchmark fractions. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is combining numerators and denominators without first applying the correct fraction rule.
7.9 Ordering fractions
A fraction represents equal parts of a whole, set, or quantity. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 1/2 and 1/3.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 1/2 > 1/3
Worked Example 2
Problem: Compare 2/3 and 1/4.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/3 > 1/4
Worked Example 3
Problem: Compare 3/5 and 2/7.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/5 > 2/7
Worked Example 4
Problem: Compare 5/8 and 1/6.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/8 > 1/6
Worked Example 5
Problem: Compare 7/10 and 3/5.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/10 > 3/5
Worked Example 6
Problem: Compare 4/9 and 5/12.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 4/9 > 5/12
Worked Example 7
Problem: Compare 5/6 and 1/8.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/6 > 1/8
Worked Example 8
Problem: Compare 3/4 and 7/9.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/4 < 7/9
Worked Example 9
Problem: Compare 2/5 and 4/15.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/5 > 4/15
Worked Example 10
Problem: Compare 7/12 and 5/18.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/12 > 5/18
Practice Exercise
Create one new Grade 6 problem about Ordering fractions. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is combining numerators and denominators without first applying the correct fraction rule.
7.10 Ordering mixed numbers
Ordering mixed numbers is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 1/2 and 1/3.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 1/2 > 1/3
Worked Example 2
Problem: Compare 2/3 and 1/4.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/3 > 1/4
Worked Example 3
Problem: Compare 3/5 and 2/7.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/5 > 2/7
Worked Example 4
Problem: Compare 5/8 and 1/6.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/8 > 1/6
Worked Example 5
Problem: Compare 7/10 and 3/5.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/10 > 3/5
Worked Example 6
Problem: Compare 4/9 and 5/12.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 4/9 > 5/12
Worked Example 7
Problem: Compare 5/6 and 1/8.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/6 > 1/8
Worked Example 8
Problem: Compare 3/4 and 7/9.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/4 < 7/9
Worked Example 9
Problem: Compare 2/5 and 4/15.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/5 > 4/15
Worked Example 10
Problem: Compare 7/12 and 5/18.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/12 > 5/18
Practice Exercise
Create one new Grade 6 problem about Ordering mixed numbers. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
7.11 Fraction number lines
A fraction represents equal parts of a whole, set, or quantity. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Write 1/2 as a decimal.
- Divide 1 by 2.
Very beginner explanation: The fraction bar means division.
Answer: 0.5
Worked Example 2
Problem: Write 2/3 as a decimal.
- Divide 2 by 3.
Very beginner explanation: The fraction bar means division.
Answer: 0.667
Worked Example 3
Problem: Write 3/5 as a decimal.
- Divide 3 by 5.
Very beginner explanation: The fraction bar means division.
Answer: 0.6
Worked Example 4
Problem: Write 5/8 as a decimal.
- Divide 5 by 8.
Very beginner explanation: The fraction bar means division.
Answer: 0.625
Worked Example 5
Problem: Write 7/10 as a decimal.
- Divide 7 by 10.
Very beginner explanation: The fraction bar means division.
Answer: 0.7
Worked Example 6
Problem: Write 4/9 as a decimal.
- Divide 4 by 9.
Very beginner explanation: The fraction bar means division.
Answer: 0.444
Worked Example 7
Problem: Write 5/6 as a decimal.
- Divide 5 by 6.
Very beginner explanation: The fraction bar means division.
Answer: 0.833
Worked Example 8
Problem: Write 3/4 as a decimal.
- Divide 3 by 4.
Very beginner explanation: The fraction bar means division.
Answer: 0.75
Worked Example 9
Problem: Write 2/5 as a decimal.
- Divide 2 by 5.
Very beginner explanation: The fraction bar means division.
Answer: 0.4
Worked Example 10
Problem: Write 7/12 as a decimal.
- Divide 7 by 12.
Very beginner explanation: The fraction bar means division.
Answer: 0.583
Practice Exercise
Create one new Grade 6 problem about Fraction number lines. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is combining numerators and denominators without first applying the correct fraction rule.
7.12 Real-life fraction comparisons
A fraction represents equal parts of a whole, set, or quantity. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Compare 1/2 and 1/3.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 1/2 > 1/3
Worked Example 2
Problem: Compare 2/3 and 1/4.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/3 > 1/4
Worked Example 3
Problem: Compare 3/5 and 2/7.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/5 > 2/7
Worked Example 4
Problem: Compare 5/8 and 1/6.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/8 > 1/6
Worked Example 5
Problem: Compare 7/10 and 3/5.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/10 > 3/5
Worked Example 6
Problem: Compare 4/9 and 5/12.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 4/9 > 5/12
Worked Example 7
Problem: Compare 5/6 and 1/8.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 5/6 > 1/8
Worked Example 8
Problem: Compare 3/4 and 7/9.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 3/4 < 7/9
Worked Example 9
Problem: Compare 2/5 and 4/15.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 2/5 > 4/15
Worked Example 10
Problem: Compare 7/12 and 5/18.
- Use a common denominator, decimal value, or benchmark fraction.
Very beginner explanation: Changing both fractions to comparable forms makes the comparison clear.
Answer: 7/12 > 5/18
Practice Exercise
Create one new Grade 6 problem about Real-life fraction comparisons. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is combining numerators and denominators without first applying the correct fraction rule.
30 Review Questions and Answers
Q1. What is important to understand about Generating equivalent fractions?
Answer: A fraction represents equal parts of a whole, set, or quantity.
Q2. What is important to understand about Simplest form?
Answer: Simplest form is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q3. What is important to understand about Common denominators?
Answer: The denominator tells how many equal parts make one whole.
Q4. What is important to understand about Comparing fractions with equal denominators?
Answer: The denominator tells how many equal parts make one whole.
Q5. What is important to understand about Comparing fractions with equal numerators?
Answer: The numerator tells how many equal parts are being considered.
Q6. What is important to understand about Comparing fractions with unlike denominators?
Answer: The denominator tells how many equal parts make one whole.
Q7. What is important to understand about Comparing mixed numbers?
Answer: Comparing mixed numbers is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q8. What is important to understand about Using benchmark fractions?
Answer: A fraction represents equal parts of a whole, set, or quantity.
Q9. What is important to understand about Ordering fractions?
Answer: A fraction represents equal parts of a whole, set, or quantity.
Q10. What is important to understand about Ordering mixed numbers?
Answer: Ordering mixed numbers is a Grade 6 mathematics idea in Equivalent Fractions, Comparison, and Ordering. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q11. What is important to understand about Fraction number lines?
Answer: A fraction represents equal parts of a whole, set, or quantity.
Q12. What is important to understand about Real-life fraction comparisons?
Answer: A fraction represents equal parts of a whole, set, or quantity.
Q13. Why should you show your steps?
Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.
Q14. Why is estimation useful?
Answer: Estimation helps you judge whether a final answer is reasonable before accepting it.
Q15. Why do units matter?
Answer: Units tell what a value measures and help prevent incompatible quantities from being mixed.
Q16. When should you round?
Answer: Usually round near the end unless the question specifically asks for earlier rounding.
Q17. How can you check an answer?
Answer: Use an inverse operation, substitution, estimation, a graph, a table, or a second method.
Q18. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the relationship connecting them.
Q19. What makes a final answer complete?
Answer: Give the value, correct units when needed, and a brief interpretation in context.
Q20. What should you do if an answer seems unreasonable?
Answer: Re-read the question and check copied values, operations, signs, units, rules, and calculations.
Q21. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships that are harder to see in words alone.
Q22. Why are tables useful?
Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.
Q23. Why are graphs useful?
Answer: Graphs make relationships, changes, trends, and comparisons visible.
Q24. Why should you explain your reasoning?
Answer: An explanation shows why a method works instead of only giving a final number.
Q25. Why can more than one strategy be correct?
Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.
Q26. What should you do before using a formula or rule?
Answer: Check what each quantity means and whether the rule matches the situation.
Q27. How does practice help in mathematics?
Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.
Q28. What is a good way to learn from a mistake?
Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.
Q29. Why should you compare an exact answer with an estimate?
Answer: The estimate gives a quick reasonableness check for the exact calculation.
Q30. What does representing mathematics mean?
Answer: It means showing an idea with numbers, symbols, words, diagrams, tables, graphs, or models.