EASYTUTORGUIDE

Practical tutorials, tools, courses, digital skills, and business promotion.

Free Learning
Google Translate — English / فارسی / العربية
EasyTutorGuide LogoLearn, Build, & Grow

Chapter 34: Variables, Expressions, and Equations

Learn Grade 4 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.

Grade 4Beginner Friendly10 Examples Per Topic30 Q&APractice + Review
Estimated reading time0% read
Advertisement area — AdSense / Auto Ads

Chapter Overview

This chapter teaches Variables, Expressions, and Equations in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.

34.1 Meaning of a variable

Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Solve n + 10 = 20.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 10

Worked Example 2

Problem: Solve n + 7 = 9.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 2

Worked Example 3

Problem: Solve n + 10 = 21.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 11

Worked Example 4

Problem: Solve n + 8 = 21.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 13

Worked Example 5

Problem: Solve n + 2 = 12.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 10

Worked Example 6

Problem: Solve n + 5 = 12.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 7

Worked Example 7

Problem: Solve n + 5 = 16.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 11

Worked Example 8

Problem: Solve n + 6 = 16.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 10

Worked Example 9

Problem: Solve n + 4 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 9

Worked Example 10

Problem: Solve n + 1 = 15.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 14

Practice Exercise

Create and solve one new example of Meaning of a variable. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.2 Using a letter as a variable

Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Solve n + 7 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 2

Problem: Solve n + 7 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 3

Problem: Solve n + 5 = 10.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 5

Worked Example 4

Problem: Solve n + 9 = 11.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 2

Worked Example 5

Problem: Solve n + 8 = 23.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 15

Worked Example 6

Problem: Solve n + 1 = 16.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 15

Worked Example 7

Problem: Solve n + 7 = 12.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 5

Worked Example 8

Problem: Solve n + 2 = 4.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 2

Worked Example 9

Problem: Solve n + 3 = 9.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 10

Problem: Solve n + 7 = 21.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 14

Practice Exercise

Create and solve one new example of Using a letter as a variable. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.3 Using a shape as a variable

Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Solve n + 7 = 19.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 12

Worked Example 2

Problem: Solve n + 4 = 18.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 14

Worked Example 3

Problem: Solve n + 1 = 12.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 11

Worked Example 4

Problem: Solve n + 2 = 11.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 9

Worked Example 5

Problem: Solve n + 3 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 10

Worked Example 6

Problem: Solve n + 4 = 9.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 5

Worked Example 7

Problem: Solve n + 3 = 15.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 12

Worked Example 8

Problem: Solve n + 8 = 10.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 2

Worked Example 9

Problem: Solve n + 6 = 21.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 15

Worked Example 10

Problem: Solve n + 8 = 15.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 7

Practice Exercise

Create and solve one new example of Using a shape as a variable. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.4 Writing a variable expression

Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Solve n + 5 = 18.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 13

Worked Example 2

Problem: Solve n + 3 = 5.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 2

Worked Example 3

Problem: Solve n + 6 = 19.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 13

Worked Example 4

Problem: Solve n + 1 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 12

Worked Example 5

Problem: Solve n + 5 = 12.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 7

Worked Example 6

Problem: Solve n + 6 = 10.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 4

Worked Example 7

Problem: Solve n + 1 = 7.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 8

Problem: Solve n + 8 = 20.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 12

Worked Example 9

Problem: Solve n + 3 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 10

Worked Example 10

Problem: Solve n + 4 = 6.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 2

Practice Exercise

Create and solve one new example of Writing a variable expression. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.5 Reading a variable expression

Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Solve n + 1 = 16.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 15

Worked Example 2

Problem: Solve n + 9 = 19.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 10

Worked Example 3

Problem: Solve n + 5 = 9.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 4

Worked Example 4

Problem: Solve n + 6 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 7

Worked Example 5

Problem: Solve n + 4 = 11.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 7

Worked Example 6

Problem: Solve n + 9 = 19.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 10

Worked Example 7

Problem: Solve n + 5 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 8

Worked Example 8

Problem: Solve n + 7 = 19.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 12

Worked Example 9

Problem: Solve n + 9 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 4

Worked Example 10

Problem: Solve n + 4 = 18.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 14

Practice Exercise

Create and solve one new example of Reading a variable expression. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.6 Writing an equation from words

Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Solve n + 2 = 5.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 3

Worked Example 2

Problem: Solve n + 3 = 10.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 7

Worked Example 3

Problem: Solve n + 7 = 19.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 12

Worked Example 4

Problem: Solve n + 5 = 16.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 11

Worked Example 5

Problem: Solve n + 1 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 12

Worked Example 6

Problem: Solve n + 2 = 14.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 12

Worked Example 7

Problem: Solve n + 9 = 23.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 14

Worked Example 8

Problem: Solve n + 9 = 15.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 9

Problem: Solve n + 8 = 22.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 14

Worked Example 10

Problem: Solve n + 7 = 20.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 13

Practice Exercise

Create and solve one new example of Writing an equation from words. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.7 Reading an equation with a variable

Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Solve n + 8 = 22.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 14

Worked Example 2

Problem: Solve n + 7 = 13.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 3

Problem: Solve n + 7 = 14.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 7

Worked Example 4

Problem: Solve n + 5 = 11.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 5

Problem: Solve n + 2 = 7.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 5

Worked Example 6

Problem: Solve n + 9 = 15.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 7

Problem: Solve n + 10 = 21.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 11

Worked Example 8

Problem: Solve n + 7 = 22.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 15

Worked Example 9

Problem: Solve n + 5 = 7.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 2

Worked Example 10

Problem: Solve n + 5 = 12.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 7

Practice Exercise

Create and solve one new example of Reading an equation with a variable. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.8 Known and unknown quantities

Known and unknown quantities is an important Grade 4 mathematics idea in Variables, Expressions, and Equations. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Known and unknown quantities using the numbers 14 and 18.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Known and unknown quantities.

Worked Example 2

Problem: Create a simple Grade 4 example about Known and unknown quantities using the numbers 7 and 8.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Known and unknown quantities.

Worked Example 3

Problem: Create a simple Grade 4 example about Known and unknown quantities using the numbers 17 and 14.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Known and unknown quantities.

Worked Example 4

Problem: Create a simple Grade 4 example about Known and unknown quantities using the numbers 19 and 8.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Known and unknown quantities.

Worked Example 5

Problem: Create a simple Grade 4 example about Known and unknown quantities using the numbers 7 and 2.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Known and unknown quantities.

Worked Example 6

Problem: Create a simple Grade 4 example about Known and unknown quantities using the numbers 15 and 4.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Known and unknown quantities.

Worked Example 7

Problem: Create a simple Grade 4 example about Known and unknown quantities using the numbers 10 and 20.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Known and unknown quantities.

Worked Example 8

Problem: Create a simple Grade 4 example about Known and unknown quantities using the numbers 16 and 18.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Known and unknown quantities.

Worked Example 9

Problem: Create a simple Grade 4 example about Known and unknown quantities using the numbers 16 and 19.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Known and unknown quantities.

Worked Example 10

Problem: Create a simple Grade 4 example about Known and unknown quantities using the numbers 4 and 17.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Known and unknown quantities.

Practice Exercise

Create and solve one new example of Known and unknown quantities. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.9 Substituting a value informally

Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Option A costs $4 for 5 items. Option B costs $2 for 5 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 2

Problem: Option A costs $9 for 3 items. Option B costs $9 for 5 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 3

Problem: Option A costs $8 for 5 items. Option B costs $5 for 3 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 4

Problem: Option A costs $5 for 4 items. Option B costs $4 for 4 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 5

Problem: Option A costs $7 for 5 items. Option B costs $2 for 5 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 6

Problem: Option A costs $10 for 4 items. Option B costs $2 for 5 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 7

Problem: Option A costs $4 for 4 items. Option B costs $8 for 2 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 8

Problem: Option A costs $5 for 1 items. Option B costs $6 for 2 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Worked Example 9

Problem: Option A costs $9 for 5 items. Option B costs $6 for 3 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option A

Worked Example 10

Problem: Option A costs $11 for 1 items. Option B costs $3 for 4 items. Which has the lower cost per item?

  1. Divide each price by its number of items.
  2. Compare the two costs per item.

Very beginner explanation: Value comparisons should compare equivalent quantities.

Answer: Option B

Practice Exercise

Create and solve one new example of Substituting a value informally. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.10 Variables in real-life situations

Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Solve n + 4 = 6.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 2

Worked Example 2

Problem: Solve n + 9 = 19.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 10

Worked Example 3

Problem: Solve n + 9 = 24.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 15

Worked Example 4

Problem: Solve n + 8 = 20.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 12

Worked Example 5

Problem: Solve n + 9 = 24.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 15

Worked Example 6

Problem: Solve n + 6 = 12.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 7

Problem: Solve n + 1 = 14.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 13

Worked Example 8

Problem: Solve n + 10 = 23.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 13

Worked Example 9

Problem: Solve n + 7 = 20.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 13

Worked Example 10

Problem: Solve n + 6 = 9.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 3

Practice Exercise

Create and solve one new example of Variables in real-life situations. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.11 Choosing a useful symbol

Choosing a useful symbol is an important Grade 4 mathematics idea in Variables, Expressions, and Equations. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Create a simple Grade 4 example about Choosing a useful symbol using the numbers 10 and 10.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing a useful symbol.

Worked Example 2

Problem: Create a simple Grade 4 example about Choosing a useful symbol using the numbers 5 and 5.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing a useful symbol.

Worked Example 3

Problem: Create a simple Grade 4 example about Choosing a useful symbol using the numbers 10 and 4.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing a useful symbol.

Worked Example 4

Problem: Create a simple Grade 4 example about Choosing a useful symbol using the numbers 2 and 16.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing a useful symbol.

Worked Example 5

Problem: Create a simple Grade 4 example about Choosing a useful symbol using the numbers 6 and 20.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing a useful symbol.

Worked Example 6

Problem: Create a simple Grade 4 example about Choosing a useful symbol using the numbers 4 and 2.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing a useful symbol.

Worked Example 7

Problem: Create a simple Grade 4 example about Choosing a useful symbol using the numbers 14 and 10.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing a useful symbol.

Worked Example 8

Problem: Create a simple Grade 4 example about Choosing a useful symbol using the numbers 18 and 11.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing a useful symbol.

Worked Example 9

Problem: Create a simple Grade 4 example about Choosing a useful symbol using the numbers 6 and 15.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing a useful symbol.

Worked Example 10

Problem: Create a simple Grade 4 example about Choosing a useful symbol using the numbers 9 and 9.

  1. Identify what the topic means.
  2. Use the numbers in a way that follows the rule.
  3. Check that the result or representation makes sense.

Very beginner explanation: Meaning comes first; the numbers should illustrate the concept clearly.

Answer: A correct example that demonstrates Choosing a useful symbol.

Practice Exercise

Create and solve one new example of Choosing a useful symbol. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

34.12 Checking that an equation matches a story

Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal. Work one step at a time, use a model or number sentence when useful, and check whether the answer is reasonable.

Beginner Explanation

First identify what is given and what must be found. Then choose a strategy, show the steps clearly, and check the final answer.

10 Worked Examples with Answers

Worked Example 1

Problem: Solve n + 3 = 18.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 15

Worked Example 2

Problem: Solve n + 4 = 11.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 7

Worked Example 3

Problem: Solve n + 7 = 18.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 11

Worked Example 4

Problem: Solve n + 7 = 9.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 2

Worked Example 5

Problem: Solve n + 3 = 10.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 7

Worked Example 6

Problem: Solve n + 5 = 16.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 11

Worked Example 7

Problem: Solve n + 4 = 8.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 4

Worked Example 8

Problem: Solve n + 7 = 21.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 14

Worked Example 9

Problem: Solve n + 10 = 16.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 6

Worked Example 10

Problem: Solve n + 8 = 20.

  1. Use the inverse operation.
  2. Subtract the same number from both sides.

Very beginner explanation: The solution makes both sides of the equation equal.

Answer: n = 12

Practice Exercise

Create and solve one new example of Checking that an equation matches a story. Show the steps and explain how you checked it.

Common Mistake

Do not rush into a calculation before understanding the question. Check place values, labels, units, and whether your answer fits the situation.

Advertisement area — AdSense / Auto Ads

30 Review Questions and Answers

Q1. What is important to understand about Meaning of a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q2. What is important to understand about Using a letter as a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q3. What is important to understand about Using a shape as a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q4. What is important to understand about Writing a variable expression?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q5. What is important to understand about Reading a variable expression?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q6. What is important to understand about Writing an equation from words?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q7. What is important to understand about Reading an equation with a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q8. What is important to understand about Known and unknown quantities?

Answer: Known and unknown quantities is an important Grade 4 mathematics idea in Variables, Expressions, and Equations. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q9. What is important to understand about Substituting a value informally?

Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.

Q10. What is important to understand about Variables in real-life situations?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q11. What is important to understand about Choosing a useful symbol?

Answer: Choosing a useful symbol is an important Grade 4 mathematics idea in Variables, Expressions, and Equations. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q12. What is important to understand about Checking that an equation matches a story?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q13. How would you explain Meaning of a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q14. How would you explain Using a letter as a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q15. How would you explain Using a shape as a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q16. How would you explain Writing a variable expression?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q17. How would you explain Reading a variable expression?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q18. How would you explain Writing an equation from words?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q19. How would you explain Reading an equation with a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q20. How would you explain Known and unknown quantities?

Answer: Known and unknown quantities is an important Grade 4 mathematics idea in Variables, Expressions, and Equations. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q21. How would you explain Substituting a value informally?

Answer: Financial literacy helps compare choices, understand payments, protect information, and judge whether a purchase gives reasonable value.

Q22. How would you explain Variables in real-life situations?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q23. How would you explain Choosing a useful symbol?

Answer: Choosing a useful symbol is an important Grade 4 mathematics idea in Variables, Expressions, and Equations. Understand the meaning first, then use a clear representation or strategy and check whether the answer makes sense.

Q24. How would you explain Checking that an equation matches a story?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q25. What should a beginner check when working with Meaning of a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q26. What should a beginner check when working with Using a letter as a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q27. What should a beginner check when working with Using a shape as a variable?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q28. What should a beginner check when working with Writing a variable expression?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q29. What should a beginner check when working with Reading a variable expression?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.

Q30. What should a beginner check when working with Writing an equation from words?

Answer: Algebra uses symbols for unknown or changing values. Equations show equal values; inequalities compare values that are not necessarily equal.