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Chapter 9: Adding and Subtracting Fractions

Learn Grade 8 Math from beginner foundations through advanced Grade 8 problem solving with detailed explanations, at least five examples per topic, practice exercises, and review questions.

Grade 8Beginner Friendly5+ Examples Per TopicPractice30 Q&A
Estimated reading time0% read
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What this chapter covers

This chapter contains 13 topics. Technical terms are followed by plain-language meanings where they first appear. Each topic includes at least five worked examples. Coding is included only where it naturally supports the Grade 8 coding expectations.

9.1 Like denominators

Like denominators is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 1/2 + 1/3.

  1. Use common denominator 6.
  2. 1/2 = 3/6.
  3. 1/3 = 2/6.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 5/6

Worked Example 2

Problem: Calculate 2/3 + 1/4.

  1. Use common denominator 12.
  2. 2/3 = 8/12.
  3. 1/4 = 3/12.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 11/12

Worked Example 3

Problem: Calculate 3/5 + 2/7.

  1. Use common denominator 35.
  2. 3/5 = 21/35.
  3. 2/7 = 10/35.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/35

Worked Example 4

Problem: Calculate 5/8 + 1/6.

  1. Use common denominator 48.
  2. 5/8 = 30/48.
  3. 1/6 = 8/48.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 19/24

Worked Example 5

Problem: Calculate 7/10 + 3/5.

  1. Use common denominator 50.
  2. 7/10 = 35/50.
  3. 3/5 = 30/50.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 13/10

Worked Example 6

Problem: Calculate 4/9 + 5/12.

  1. Use common denominator 108.
  2. 4/9 = 48/108.
  3. 5/12 = 45/108.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/36

Worked Example 7

Problem: Calculate 5/6 + 1/8.

  1. Use common denominator 48.
  2. 5/6 = 40/48.
  3. 1/8 = 6/48.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 23/24

Worked Example 8

Problem: Calculate 3/4 + 7/9.

  1. Use common denominator 36.
  2. 3/4 = 27/36.
  3. 7/9 = 28/36.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 55/36

Worked Example 9

Problem: Calculate 2/5 + 4/15.

  1. Use common denominator 75.
  2. 2/5 = 30/75.
  3. 4/15 = 20/75.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 2/3

Worked Example 10

Problem: Calculate 7/12 + 5/18.

  1. Use common denominator 216.
  2. 7/12 = 126/216.
  3. 5/18 = 60/216.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/36

Practice exercise

Create one new Grade 8 problem involving Like denominators. Show the important steps, include units when needed, and explain how you checked the answer.

9.2 Unlike denominators

Unlike denominators is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 1/2 + 1/3.

  1. Use common denominator 6.
  2. 1/2 = 3/6.
  3. 1/3 = 2/6.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 5/6

Worked Example 2

Problem: Calculate 2/3 + 1/4.

  1. Use common denominator 12.
  2. 2/3 = 8/12.
  3. 1/4 = 3/12.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 11/12

Worked Example 3

Problem: Calculate 3/5 + 2/7.

  1. Use common denominator 35.
  2. 3/5 = 21/35.
  3. 2/7 = 10/35.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/35

Worked Example 4

Problem: Calculate 5/8 + 1/6.

  1. Use common denominator 48.
  2. 5/8 = 30/48.
  3. 1/6 = 8/48.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 19/24

Worked Example 5

Problem: Calculate 7/10 + 3/5.

  1. Use common denominator 50.
  2. 7/10 = 35/50.
  3. 3/5 = 30/50.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 13/10

Worked Example 6

Problem: Calculate 4/9 + 5/12.

  1. Use common denominator 108.
  2. 4/9 = 48/108.
  3. 5/12 = 45/108.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/36

Worked Example 7

Problem: Calculate 5/6 + 1/8.

  1. Use common denominator 48.
  2. 5/6 = 40/48.
  3. 1/8 = 6/48.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 23/24

Worked Example 8

Problem: Calculate 3/4 + 7/9.

  1. Use common denominator 36.
  2. 3/4 = 27/36.
  3. 7/9 = 28/36.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 55/36

Worked Example 9

Problem: Calculate 2/5 + 4/15.

  1. Use common denominator 75.
  2. 2/5 = 30/75.
  3. 4/15 = 20/75.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 2/3

Worked Example 10

Problem: Calculate 7/12 + 5/18.

  1. Use common denominator 216.
  2. 7/12 = 126/216.
  3. 5/18 = 60/216.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/36

Practice exercise

Create one new Grade 8 problem involving Unlike denominators. Show the important steps, include units when needed, and explain how you checked the answer.

9.3 Least common denominator

Least common denominator is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide numerator 1 by denominator 2.
  2. 1 ÷ 2 = 0.5000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide numerator 2 by denominator 3.
  2. 2 ÷ 3 = 0.6667.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide numerator 3 by denominator 5.
  2. 3 ÷ 5 = 0.6000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide numerator 5 by denominator 8.
  2. 5 ÷ 8 = 0.6250.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide numerator 7 by denominator 10.
  2. 7 ÷ 10 = 0.7000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide numerator 4 by denominator 9.
  2. 4 ÷ 9 = 0.4444.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide numerator 5 by denominator 6.
  2. 5 ÷ 6 = 0.8333.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.8333

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide numerator 3 by denominator 4.
  2. 3 ÷ 4 = 0.7500.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide numerator 2 by denominator 5.
  2. 2 ÷ 5 = 0.4000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide numerator 7 by denominator 12.
  2. 7 ÷ 12 = 0.5833.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5833

Practice exercise

Create one new Grade 8 problem involving Least common denominator. Show the important steps, include units when needed, and explain how you checked the answer.

9.4 Adding fractions

A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Adding fractions.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 1/2 + 1/3.

  1. Use common denominator 6.
  2. 1/2 = 3/6.
  3. 1/3 = 2/6.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 5/6

Worked Example 2

Problem: Calculate 2/3 + 1/4.

  1. Use common denominator 12.
  2. 2/3 = 8/12.
  3. 1/4 = 3/12.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 11/12

Worked Example 3

Problem: Calculate 3/5 + 2/7.

  1. Use common denominator 35.
  2. 3/5 = 21/35.
  3. 2/7 = 10/35.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/35

Worked Example 4

Problem: Calculate 5/8 + 1/6.

  1. Use common denominator 48.
  2. 5/8 = 30/48.
  3. 1/6 = 8/48.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 19/24

Worked Example 5

Problem: Calculate 7/10 + 3/5.

  1. Use common denominator 50.
  2. 7/10 = 35/50.
  3. 3/5 = 30/50.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 13/10

Worked Example 6

Problem: Calculate 4/9 + 5/12.

  1. Use common denominator 108.
  2. 4/9 = 48/108.
  3. 5/12 = 45/108.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/36

Worked Example 7

Problem: Calculate 5/6 + 1/8.

  1. Use common denominator 48.
  2. 5/6 = 40/48.
  3. 1/8 = 6/48.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 23/24

Worked Example 8

Problem: Calculate 3/4 + 7/9.

  1. Use common denominator 36.
  2. 3/4 = 27/36.
  3. 7/9 = 28/36.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 55/36

Worked Example 9

Problem: Calculate 2/5 + 4/15.

  1. Use common denominator 75.
  2. 2/5 = 30/75.
  3. 4/15 = 20/75.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 2/3

Worked Example 10

Problem: Calculate 7/12 + 5/18.

  1. Use common denominator 216.
  2. 7/12 = 126/216.
  3. 5/18 = 60/216.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/36

Practice exercise

Create one new Grade 8 problem involving Adding fractions. Show the important steps, include units when needed, and explain how you checked the answer.

9.5 Subtracting fractions

A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Subtracting fractions.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 1/2 - 1/3.

  1. Use common denominator 6.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 1/6

Worked Example 2

Problem: Calculate 2/3 - 1/4.

  1. Use common denominator 12.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 5/12

Worked Example 3

Problem: Calculate 3/5 - 2/7.

  1. Use common denominator 35.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 11/35

Worked Example 4

Problem: Calculate 5/8 - 1/6.

  1. Use common denominator 48.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 11/24

Worked Example 5

Problem: Calculate 7/10 - 3/5.

  1. Use common denominator 50.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 1/10

Worked Example 6

Problem: Calculate 4/9 - 5/12.

  1. Use common denominator 108.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 1/36

Worked Example 7

Problem: Calculate 5/6 - 1/8.

  1. Use common denominator 48.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 17/24

Worked Example 8

Problem: Calculate 3/4 - 7/9.

  1. Use common denominator 36.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: -1/36

Worked Example 9

Problem: Calculate 2/5 - 4/15.

  1. Use common denominator 75.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 2/15

Worked Example 10

Problem: Calculate 7/12 - 5/18.

  1. Use common denominator 216.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 11/36

Practice exercise

Create one new Grade 8 problem involving Subtracting fractions. Show the important steps, include units when needed, and explain how you checked the answer.

9.6 Adding mixed numbers

Adding mixed numbers is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 1/2 + 1/3.

  1. Use common denominator 6.
  2. 1/2 = 3/6.
  3. 1/3 = 2/6.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 5/6

Worked Example 2

Problem: Calculate 2/3 + 1/4.

  1. Use common denominator 12.
  2. 2/3 = 8/12.
  3. 1/4 = 3/12.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 11/12

Worked Example 3

Problem: Calculate 3/5 + 2/7.

  1. Use common denominator 35.
  2. 3/5 = 21/35.
  3. 2/7 = 10/35.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/35

Worked Example 4

Problem: Calculate 5/8 + 1/6.

  1. Use common denominator 48.
  2. 5/8 = 30/48.
  3. 1/6 = 8/48.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 19/24

Worked Example 5

Problem: Calculate 7/10 + 3/5.

  1. Use common denominator 50.
  2. 7/10 = 35/50.
  3. 3/5 = 30/50.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 13/10

Worked Example 6

Problem: Calculate 4/9 + 5/12.

  1. Use common denominator 108.
  2. 4/9 = 48/108.
  3. 5/12 = 45/108.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/36

Worked Example 7

Problem: Calculate 5/6 + 1/8.

  1. Use common denominator 48.
  2. 5/6 = 40/48.
  3. 1/8 = 6/48.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 23/24

Worked Example 8

Problem: Calculate 3/4 + 7/9.

  1. Use common denominator 36.
  2. 3/4 = 27/36.
  3. 7/9 = 28/36.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 55/36

Worked Example 9

Problem: Calculate 2/5 + 4/15.

  1. Use common denominator 75.
  2. 2/5 = 30/75.
  3. 4/15 = 20/75.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 2/3

Worked Example 10

Problem: Calculate 7/12 + 5/18.

  1. Use common denominator 216.
  2. 7/12 = 126/216.
  3. 5/18 = 60/216.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/36

Practice exercise

Create one new Grade 8 problem involving Adding mixed numbers. Show the important steps, include units when needed, and explain how you checked the answer.

9.7 Subtracting mixed numbers

Subtracting mixed numbers is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 1/2 - 1/3.

  1. Use common denominator 6.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 1/6

Worked Example 2

Problem: Calculate 2/3 - 1/4.

  1. Use common denominator 12.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 5/12

Worked Example 3

Problem: Calculate 3/5 - 2/7.

  1. Use common denominator 35.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 11/35

Worked Example 4

Problem: Calculate 5/8 - 1/6.

  1. Use common denominator 48.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 11/24

Worked Example 5

Problem: Calculate 7/10 - 3/5.

  1. Use common denominator 50.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 1/10

Worked Example 6

Problem: Calculate 4/9 - 5/12.

  1. Use common denominator 108.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 1/36

Worked Example 7

Problem: Calculate 5/6 - 1/8.

  1. Use common denominator 48.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 17/24

Worked Example 8

Problem: Calculate 3/4 - 7/9.

  1. Use common denominator 36.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: -1/36

Worked Example 9

Problem: Calculate 2/5 - 4/15.

  1. Use common denominator 75.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 2/15

Worked Example 10

Problem: Calculate 7/12 - 5/18.

  1. Use common denominator 216.
  2. Rewrite both fractions with that denominator.
  3. Subtract the numerators and simplify.

Very beginner explanation: The denominator describes the size of each part, so the part sizes must match before subtracting.

Answer: 11/36

Practice exercise

Create one new Grade 8 problem involving Subtracting mixed numbers. Show the important steps, include units when needed, and explain how you checked the answer.

9.8 Regrouping mixed numbers

Regrouping mixed numbers is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide numerator 1 by denominator 2.
  2. 1 ÷ 2 = 0.5000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide numerator 2 by denominator 3.
  2. 2 ÷ 3 = 0.6667.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide numerator 3 by denominator 5.
  2. 3 ÷ 5 = 0.6000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide numerator 5 by denominator 8.
  2. 5 ÷ 8 = 0.6250.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide numerator 7 by denominator 10.
  2. 7 ÷ 10 = 0.7000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide numerator 4 by denominator 9.
  2. 4 ÷ 9 = 0.4444.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide numerator 5 by denominator 6.
  2. 5 ÷ 6 = 0.8333.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.8333

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide numerator 3 by denominator 4.
  2. 3 ÷ 4 = 0.7500.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide numerator 2 by denominator 5.
  2. 2 ÷ 5 = 0.4000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide numerator 7 by denominator 12.
  2. 7 ÷ 12 = 0.5833.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5833

Practice exercise

Create one new Grade 8 problem involving Regrouping mixed numbers. Show the important steps, include units when needed, and explain how you checked the answer.

9.9 Negative fractions

A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Negative fractions.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide numerator 1 by denominator 2.
  2. 1 ÷ 2 = 0.5000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide numerator 2 by denominator 3.
  2. 2 ÷ 3 = 0.6667.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide numerator 3 by denominator 5.
  2. 3 ÷ 5 = 0.6000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide numerator 5 by denominator 8.
  2. 5 ÷ 8 = 0.6250.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide numerator 7 by denominator 10.
  2. 7 ÷ 10 = 0.7000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide numerator 4 by denominator 9.
  2. 4 ÷ 9 = 0.4444.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide numerator 5 by denominator 6.
  2. 5 ÷ 6 = 0.8333.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.8333

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide numerator 3 by denominator 4.
  2. 3 ÷ 4 = 0.7500.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide numerator 2 by denominator 5.
  2. 2 ÷ 5 = 0.4000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide numerator 7 by denominator 12.
  2. 7 ÷ 12 = 0.5833.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5833

Practice exercise

Create one new Grade 8 problem involving Negative fractions. Show the important steps, include units when needed, and explain how you checked the answer.

9.10 Estimating fraction sums and differences

A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Estimating fraction sums and differences.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Calculate 1/2 + 1/3.

  1. Use common denominator 6.
  2. 1/2 = 3/6.
  3. 1/3 = 2/6.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 5/6

Worked Example 2

Problem: Calculate 2/3 + 1/4.

  1. Use common denominator 12.
  2. 2/3 = 8/12.
  3. 1/4 = 3/12.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 11/12

Worked Example 3

Problem: Calculate 3/5 + 2/7.

  1. Use common denominator 35.
  2. 3/5 = 21/35.
  3. 2/7 = 10/35.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/35

Worked Example 4

Problem: Calculate 5/8 + 1/6.

  1. Use common denominator 48.
  2. 5/8 = 30/48.
  3. 1/6 = 8/48.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 19/24

Worked Example 5

Problem: Calculate 7/10 + 3/5.

  1. Use common denominator 50.
  2. 7/10 = 35/50.
  3. 3/5 = 30/50.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 13/10

Worked Example 6

Problem: Calculate 4/9 + 5/12.

  1. Use common denominator 108.
  2. 4/9 = 48/108.
  3. 5/12 = 45/108.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/36

Worked Example 7

Problem: Calculate 5/6 + 1/8.

  1. Use common denominator 48.
  2. 5/6 = 40/48.
  3. 1/8 = 6/48.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 23/24

Worked Example 8

Problem: Calculate 3/4 + 7/9.

  1. Use common denominator 36.
  2. 3/4 = 27/36.
  3. 7/9 = 28/36.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 55/36

Worked Example 9

Problem: Calculate 2/5 + 4/15.

  1. Use common denominator 75.
  2. 2/5 = 30/75.
  3. 4/15 = 20/75.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 2/3

Worked Example 10

Problem: Calculate 7/12 + 5/18.

  1. Use common denominator 216.
  2. 7/12 = 126/216.
  3. 5/18 = 60/216.
  4. Add the numerators, then simplify.

Very beginner explanation: Fractions can only be added directly after the parts are the same size, which means using a common denominator.

Answer: 31/36

Practice exercise

Create one new Grade 8 problem involving Estimating fraction sums and differences. Show the important steps, include units when needed, and explain how you checked the answer.

9.11 Multi-step fraction calculations

A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Multi-step fraction calculations.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Write 1/2 as a decimal.

  1. Divide numerator 1 by denominator 2.
  2. 1 ÷ 2 = 0.5000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5

Worked Example 2

Problem: Write 2/3 as a decimal.

  1. Divide numerator 2 by denominator 3.
  2. 2 ÷ 3 = 0.6667.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6667

Worked Example 3

Problem: Write 3/5 as a decimal.

  1. Divide numerator 3 by denominator 5.
  2. 3 ÷ 5 = 0.6000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.6

Worked Example 4

Problem: Write 5/8 as a decimal.

  1. Divide numerator 5 by denominator 8.
  2. 5 ÷ 8 = 0.6250.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.625

Worked Example 5

Problem: Write 7/10 as a decimal.

  1. Divide numerator 7 by denominator 10.
  2. 7 ÷ 10 = 0.7000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.7

Worked Example 6

Problem: Write 4/9 as a decimal.

  1. Divide numerator 4 by denominator 9.
  2. 4 ÷ 9 = 0.4444.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4444

Worked Example 7

Problem: Write 5/6 as a decimal.

  1. Divide numerator 5 by denominator 6.
  2. 5 ÷ 6 = 0.8333.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.8333

Worked Example 8

Problem: Write 3/4 as a decimal.

  1. Divide numerator 3 by denominator 4.
  2. 3 ÷ 4 = 0.7500.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.75

Worked Example 9

Problem: Write 2/5 as a decimal.

  1. Divide numerator 2 by denominator 5.
  2. 2 ÷ 5 = 0.4000.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.4

Worked Example 10

Problem: Write 7/12 as a decimal.

  1. Divide numerator 7 by denominator 12.
  2. 7 ÷ 12 = 0.5833.

Very beginner explanation: A fraction bar means division, so numerator ÷ denominator gives the decimal form.

Answer: 0.5833

Practice exercise

Create one new Grade 8 problem involving Multi-step fraction calculations. Show the important steps, include units when needed, and explain how you checked the answer.

9.12 Word problems

Word problems is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Word problems: Explain Word problems in one simple sentence.

  1. Look at the words in “Word problems”.
  2. State what the idea is used for.
  3. Give one small mathematical example.

Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.

Answer: Word problems is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: Word problems: A student says, “I can use Word problems without checking units or labels.” Is that a good method?

  1. Read the statement.
  2. Ask whether units, signs, labels, or conditions matter.
  3. Decide whether the method is safe.

Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.

Answer: No. Important units, labels, signs, and conditions must be checked.

Worked Example 3

Problem: Word problems: What is the first step when solving a problem about Word problems?

  1. Read the whole question.
  2. Underline the known information.
  3. Identify what must be found.

Very beginner explanation: This prevents you from calculating before you understand the problem.

Answer: Identify the given information and the unknown before choosing a rule.

Worked Example 4

Problem: Word problems: After solving a Word problems problem, what should you do before accepting the answer?

  1. Estimate the expected size or direction.
  2. Check units and signs.
  3. Use an inverse method if possible.

Very beginner explanation: Checking is part of solving, not an optional extra.

Answer: Check whether the answer is reasonable and consistent with the problem.

Worked Example 5

Problem: Word problems: Give one way Word problems could appear outside a textbook.

  1. Think about money, measurements, data, maps, geometry, or technology.
  2. Connect the topic to one of those situations.

Very beginner explanation: Connecting math to real situations makes the rule easier to remember.

Answer: Word problems can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: Word problems: Which representation could help explain Word problems: a table, graph, diagram, equation, or number line?

  1. Choose the representation that makes the relationship easiest to see.
  2. Label it clearly.

Very beginner explanation: Different representations show different features of the same mathematics.

Answer: Use the representation that best matches the problem; more than one may be valid.

Worked Example 7

Problem: Word problems: A student gets an answer for Word problems but cannot explain the steps. What should be improved?

  1. Rewrite the solution one step at a time.
  2. Name the rule used at each important step.

Very beginner explanation: A correct final number without reasoning may hide an error.

Answer: The reasoning should be shown so the solution can be checked.

Worked Example 8

Problem: Word problems: Why can estimation help before a detailed Word problems calculation?

  1. Round or use benchmark values.
  2. Predict the approximate answer.
  3. Compare the exact result with the estimate.

Very beginner explanation: If the exact answer is far from the estimate, recheck the work.

Answer: Estimation gives a target range for the final answer.

Worked Example 9

Problem: Word problems: How can you test whether your rule for Word problems works?

  1. Choose a very small easy example.
  2. Apply the rule.
  3. Check the result another way.

Very beginner explanation: Small examples expose mistakes quickly.

Answer: Test the rule on a simple case whose answer can be verified.

Worked Example 10

Problem: Word problems: How would you teach Word problems to someone seeing it for the first time?

  1. Define the idea.
  2. Show one easy example.
  3. Explain every step.
  4. Then let the learner try a similar problem.

Very beginner explanation: This sequence reduces memorization without understanding.

Answer: Teach meaning first, then a small worked example, then guided practice.

Practice exercise

Create one new Grade 8 problem involving Word problems. Show the important steps, include units when needed, and explain how you checked the answer.

9.13 Checking answers

Checking answers is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

For a beginner, focus on the meaning before memorizing a procedure. Start with a small example, name the quantities and units, apply one rule at a time, and connect the result back to the question.

10 Worked Examples with Answers and Very-Beginner Explanations

Worked Example 1

Problem: Checking answers: Explain Checking answers in one simple sentence.

  1. Look at the words in “Checking answers”.
  2. State what the idea is used for.
  3. Give one small mathematical example.

Very beginner explanation: A beginner should first understand the meaning before memorizing a rule.

Answer: Checking answers is a Grade 8 math idea used to describe or solve a specific mathematical relationship.

Worked Example 2

Problem: Checking answers: A student says, “I can use Checking answers without checking units or labels.” Is that a good method?

  1. Read the statement.
  2. Ask whether units, signs, labels, or conditions matter.
  3. Decide whether the method is safe.

Very beginner explanation: Many math mistakes come from using a correct calculation on the wrong quantity.

Answer: No. Important units, labels, signs, and conditions must be checked.

Worked Example 3

Problem: Checking answers: What is the first step when solving a problem about Checking answers?

  1. Read the whole question.
  2. Underline the known information.
  3. Identify what must be found.

Very beginner explanation: This prevents you from calculating before you understand the problem.

Answer: Identify the given information and the unknown before choosing a rule.

Worked Example 4

Problem: Checking answers: After solving a Checking answers problem, what should you do before accepting the answer?

  1. Estimate the expected size or direction.
  2. Check units and signs.
  3. Use an inverse method if possible.

Very beginner explanation: Checking is part of solving, not an optional extra.

Answer: Check whether the answer is reasonable and consistent with the problem.

Worked Example 5

Problem: Checking answers: Give one way Checking answers could appear outside a textbook.

  1. Think about money, measurements, data, maps, geometry, or technology.
  2. Connect the topic to one of those situations.

Very beginner explanation: Connecting math to real situations makes the rule easier to remember.

Answer: Checking answers can be used in a real-life situation where quantities must be compared, measured, predicted, or calculated.

Worked Example 6

Problem: Checking answers: Which representation could help explain Checking answers: a table, graph, diagram, equation, or number line?

  1. Choose the representation that makes the relationship easiest to see.
  2. Label it clearly.

Very beginner explanation: Different representations show different features of the same mathematics.

Answer: Use the representation that best matches the problem; more than one may be valid.

Worked Example 7

Problem: Checking answers: A student gets an answer for Checking answers but cannot explain the steps. What should be improved?

  1. Rewrite the solution one step at a time.
  2. Name the rule used at each important step.

Very beginner explanation: A correct final number without reasoning may hide an error.

Answer: The reasoning should be shown so the solution can be checked.

Worked Example 8

Problem: Checking answers: Why can estimation help before a detailed Checking answers calculation?

  1. Round or use benchmark values.
  2. Predict the approximate answer.
  3. Compare the exact result with the estimate.

Very beginner explanation: If the exact answer is far from the estimate, recheck the work.

Answer: Estimation gives a target range for the final answer.

Worked Example 9

Problem: Checking answers: How can you test whether your rule for Checking answers works?

  1. Choose a very small easy example.
  2. Apply the rule.
  3. Check the result another way.

Very beginner explanation: Small examples expose mistakes quickly.

Answer: Test the rule on a simple case whose answer can be verified.

Worked Example 10

Problem: Checking answers: How would you teach Checking answers to someone seeing it for the first time?

  1. Define the idea.
  2. Show one easy example.
  3. Explain every step.
  4. Then let the learner try a similar problem.

Very beginner explanation: This sequence reduces memorization without understanding.

Answer: Teach meaning first, then a small worked example, then guided practice.

Practice exercise

Create one new Grade 8 problem involving Checking answers. Show the important steps, include units when needed, and explain how you checked the answer.

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Chapter 9 Review Questions and Answers

Q1. What is important to remember about Like denominators?

Answer: Like denominators is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q2. What is important to remember about Unlike denominators?

Answer: Unlike denominators is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q3. What is important to remember about Least common denominator?

Answer: Least common denominator is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q4. What is important to remember about Adding fractions?

Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Adding fractions.

Q5. What is important to remember about Subtracting fractions?

Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Subtracting fractions.

Q6. What is important to remember about Adding mixed numbers?

Answer: Adding mixed numbers is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q7. What is important to remember about Subtracting mixed numbers?

Answer: Subtracting mixed numbers is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q8. What is important to remember about Regrouping mixed numbers?

Answer: Regrouping mixed numbers is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q9. What is important to remember about Negative fractions?

Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Negative fractions.

Q10. What is important to remember about Estimating fraction sums and differences?

Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Estimating fraction sums and differences.

Q11. What is important to remember about Multi-step fraction calculations?

Answer: A fraction (a numerator over a denominator) can represent part of a whole, a quotient, a ratio, or a point on a number line. In this section, the focus is Multi-step fraction calculations.

Q12. What is important to remember about Word problems?

Answer: Word problems is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q13. What is important to remember about Checking answers?

Answer: Checking answers is an important Grade 8 concept in Adding and Subtracting Fractions. Start by identifying the quantities, relationships, units, or rules involved. Work with a small example first, show the important steps, and check whether the result is reasonable.

Q14. Why should you show your steps?

Answer: Showing steps makes reasoning easier to verify and helps locate mistakes.

Q15. Why is estimation useful?

Answer: Estimation helps you judge whether a calculated answer is reasonable.

Q16. Why do units matter?

Answer: Units tell what a value measures and prevent incompatible quantities from being mixed.

Q17. When should you round?

Answer: Usually round near the end unless the question specifically asks for earlier rounding.

Q18. How can you check an answer?

Answer: Use an inverse operation, substitution, estimation, a graph, or a second method.

Q19. What should you identify first in a word problem?

Answer: Identify what is known, what is unknown, and the mathematical relationship connecting them.

Q20. What makes a final answer complete?

Answer: Give the value, correct units when needed, and a brief interpretation in context.

Q21. What should you do if an answer seems unreasonable?

Answer: Re-read the question and check copied values, signs, units, formulas, and calculations.

Q22. Why are diagrams useful?

Answer: A labelled diagram can reveal relationships among lengths, angles, areas, and coordinates.

Q23. Why are tables useful?

Answer: Tables organize values and help reveal patterns, rates, relationships, and missing information.

Q24. Why should you explain your reasoning?

Answer: Reasoning shows why a method works, not just what answer was obtained.

Q25. How do mistakes help learning?

Answer: Analyzing a mistake identifies the misunderstood rule or step and helps prevent repetition.

Q26. When is a calculator useful?

Answer: A calculator helps with lengthy arithmetic after the mathematical setup is understood and estimated.

Q27. Why compare more than one strategy?

Answer: Different strategies may make a problem easier and provide a way to verify the result.

Q28. What is mathematical communication?

Answer: It is presenting ideas clearly with words, symbols, diagrams, tables, graphs, and justified steps.

Q29. What is mathematical modelling?

Answer: It is representing a real situation with mathematics, testing the model, and revising it if needed.

Q30. Why should assumptions be stated?

Answer: Assumptions show the conditions the model depends on and help readers judge whether it is reasonable.