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Chapter 6: Fraction and Mixed Number Foundations

Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 6Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
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Chapter Overview

This chapter teaches Fraction and Mixed Number Foundations in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

Key Technical Terms

  • Numerator and denominator (The numerator tells how many equal parts are being considered.)
  • Proper fractions (A fraction represents equal parts of a whole, set, or quantity.)
  • Mixed numbers (Mixed numbers is a Grade 6 mathematics idea in Fraction and Mixed Number Foundations. 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.

6.1 Numerator and denominator

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: Write 1/2 as a decimal.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. Divide 7 by 12.

Very beginner explanation: The fraction bar means division.

Answer: 0.583

Practice Exercise

Create one new Grade 6 problem about Numerator and denominator. 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.

6.2 Proper 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. Divide 7 by 12.

Very beginner explanation: The fraction bar means division.

Answer: 0.583

Practice Exercise

Create one new Grade 6 problem about Proper 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.

6.3 Improper 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: Convert 1 1/2 to an improper fraction.

  1. Multiply 1 × 2.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 3/2

Worked Example 2

Problem: Convert 1 1/3 to an improper fraction.

  1. Multiply 1 × 3.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 4/3

Worked Example 3

Problem: Convert 4 3/5 to an improper fraction.

  1. Multiply 4 × 5.
  2. Add the numerator 3.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 23/5

Worked Example 4

Problem: Convert 5 2/8 to an improper fraction.

  1. Multiply 5 × 8.
  2. Add the numerator 2.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 42/8

Worked Example 5

Problem: Convert 4 2/10 to an improper fraction.

  1. Multiply 4 × 10.
  2. Add the numerator 2.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 42/10

Worked Example 6

Problem: Convert 5 7/9 to an improper fraction.

  1. Multiply 5 × 9.
  2. Add the numerator 7.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 52/9

Worked Example 7

Problem: Convert 3 5/6 to an improper fraction.

  1. Multiply 3 × 6.
  2. Add the numerator 5.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 23/6

Worked Example 8

Problem: Convert 1 1/4 to an improper fraction.

  1. Multiply 1 × 4.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 5/4

Worked Example 9

Problem: Convert 1 2/5 to an improper fraction.

  1. Multiply 1 × 5.
  2. Add the numerator 2.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 7/5

Worked Example 10

Problem: Convert 5 6/12 to an improper fraction.

  1. Multiply 5 × 12.
  2. Add the numerator 6.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 66/12

Practice Exercise

Create one new Grade 6 problem about Improper 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.

6.4 Mixed numbers

Mixed numbers is a Grade 6 mathematics idea in Fraction and Mixed Number Foundations. 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: Convert 3 1/2 to an improper fraction.

  1. Multiply 3 × 2.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 7/2

Worked Example 2

Problem: Convert 5 1/3 to an improper fraction.

  1. Multiply 5 × 3.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 16/3

Worked Example 3

Problem: Convert 1 2/5 to an improper fraction.

  1. Multiply 1 × 5.
  2. Add the numerator 2.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 7/5

Worked Example 4

Problem: Convert 4 2/8 to an improper fraction.

  1. Multiply 4 × 8.
  2. Add the numerator 2.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 34/8

Worked Example 5

Problem: Convert 1 3/10 to an improper fraction.

  1. Multiply 1 × 10.
  2. Add the numerator 3.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 13/10

Worked Example 6

Problem: Convert 3 4/9 to an improper fraction.

  1. Multiply 3 × 9.
  2. Add the numerator 4.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 31/9

Worked Example 7

Problem: Convert 3 2/6 to an improper fraction.

  1. Multiply 3 × 6.
  2. Add the numerator 2.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 20/6

Worked Example 8

Problem: Convert 5 2/4 to an improper fraction.

  1. Multiply 5 × 4.
  2. Add the numerator 2.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 22/4

Worked Example 9

Problem: Convert 5 4/5 to an improper fraction.

  1. Multiply 5 × 5.
  2. Add the numerator 4.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 29/5

Worked Example 10

Problem: Convert 4 3/12 to an improper fraction.

  1. Multiply 4 × 12.
  2. Add the numerator 3.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 51/12

Practice Exercise

Create one new Grade 6 problem about 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.

6.5 Converting improper fractions to mixed numbers

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: Convert 1 1/2 to an improper fraction.

  1. Multiply 1 × 2.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 3/2

Worked Example 2

Problem: Convert 4 1/3 to an improper fraction.

  1. Multiply 4 × 3.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 13/3

Worked Example 3

Problem: Convert 3 1/5 to an improper fraction.

  1. Multiply 3 × 5.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 16/5

Worked Example 4

Problem: Convert 1 4/8 to an improper fraction.

  1. Multiply 1 × 8.
  2. Add the numerator 4.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 12/8

Worked Example 5

Problem: Convert 3 9/10 to an improper fraction.

  1. Multiply 3 × 10.
  2. Add the numerator 9.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 39/10

Worked Example 6

Problem: Convert 2 1/9 to an improper fraction.

  1. Multiply 2 × 9.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 19/9

Worked Example 7

Problem: Convert 3 5/6 to an improper fraction.

  1. Multiply 3 × 6.
  2. Add the numerator 5.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 23/6

Worked Example 8

Problem: Convert 2 2/4 to an improper fraction.

  1. Multiply 2 × 4.
  2. Add the numerator 2.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 10/4

Worked Example 9

Problem: Convert 5 4/5 to an improper fraction.

  1. Multiply 5 × 5.
  2. Add the numerator 4.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 29/5

Worked Example 10

Problem: Convert 3 3/12 to an improper fraction.

  1. Multiply 3 × 12.
  2. Add the numerator 3.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 39/12

Practice Exercise

Create one new Grade 6 problem about Converting improper fractions to mixed numbers. 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.

6.6 Converting mixed numbers to improper 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: Convert 4 1/2 to an improper fraction.

  1. Multiply 4 × 2.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 9/2

Worked Example 2

Problem: Convert 2 2/3 to an improper fraction.

  1. Multiply 2 × 3.
  2. Add the numerator 2.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 8/3

Worked Example 3

Problem: Convert 5 1/5 to an improper fraction.

  1. Multiply 5 × 5.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 26/5

Worked Example 4

Problem: Convert 1 6/8 to an improper fraction.

  1. Multiply 1 × 8.
  2. Add the numerator 6.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 14/8

Worked Example 5

Problem: Convert 3 1/10 to an improper fraction.

  1. Multiply 3 × 10.
  2. Add the numerator 1.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 31/10

Worked Example 6

Problem: Convert 5 5/9 to an improper fraction.

  1. Multiply 5 × 9.
  2. Add the numerator 5.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 50/9

Worked Example 7

Problem: Convert 5 5/6 to an improper fraction.

  1. Multiply 5 × 6.
  2. Add the numerator 5.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 35/6

Worked Example 8

Problem: Convert 2 3/4 to an improper fraction.

  1. Multiply 2 × 4.
  2. Add the numerator 3.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 11/4

Worked Example 9

Problem: Convert 3 2/5 to an improper fraction.

  1. Multiply 3 × 5.
  2. Add the numerator 2.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 17/5

Worked Example 10

Problem: Convert 5 4/12 to an improper fraction.

  1. Multiply 5 × 12.
  2. Add the numerator 4.
  3. Keep the same denominator.

Very beginner explanation: A mixed number combines whole groups and a fractional part.

Answer: 64/12

Practice Exercise

Create one new Grade 6 problem about Converting mixed numbers to improper 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.

6.7 Fractions of a set

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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. Divide 7 by 12.

Very beginner explanation: The fraction bar means division.

Answer: 0.583

Practice Exercise

Create one new Grade 6 problem about Fractions of a set. 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.

6.8 Fractions on 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. Divide 7 by 12.

Very beginner explanation: The fraction bar means division.

Answer: 0.583

Practice Exercise

Create one new Grade 6 problem about Fractions on 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.

6.9 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. Divide 7 by 12.

Very beginner explanation: The fraction bar means division.

Answer: 0.583

Practice Exercise

Create one new Grade 6 problem about 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.

6.10 Equivalent fractions introduction

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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. Divide 7 by 12.

Very beginner explanation: The fraction bar means division.

Answer: 0.583

Practice Exercise

Create one new Grade 6 problem about Equivalent fractions introduction. 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.

6.11 Simplifying 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. Divide 7 by 12.

Very beginner explanation: The fraction bar means division.

Answer: 0.583

Practice Exercise

Create one new Grade 6 problem about Simplifying 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.

6.12 Fraction word problems

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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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.

  1. 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 word problems. 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.

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30 Review Questions and Answers

Q1. What is important to understand about Numerator and denominator?

Answer: The numerator tells how many equal parts are being considered.

Q2. What is important to understand about Proper fractions?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q3. What is important to understand about Improper fractions?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q4. What is important to understand about Mixed numbers?

Answer: Mixed numbers is a Grade 6 mathematics idea in Fraction and Mixed Number Foundations. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.

Q5. What is important to understand about Converting improper fractions to mixed numbers?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q6. What is important to understand about Converting mixed numbers to improper fractions?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q7. What is important to understand about Fractions of a set?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q8. What is important to understand about Fractions on number lines?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q9. What is important to understand about Benchmark fractions?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q10. What is important to understand about Equivalent fractions introduction?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q11. What is important to understand about Simplifying fractions?

Answer: A fraction represents equal parts of a whole, set, or quantity.

Q12. What is important to understand about Fraction word problems?

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.