Chapter 56: Budgeting and Resource Distribution
Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Budgeting and Resource Distribution in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
Key Technical Terms
- Meaning of budget (The mean is found by adding all values and dividing by the number of values.)
- Income (Income is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Expenses (Expenses is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Fixed expenses (Fixed expenses is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Variable expenses (A variable is a symbol used to represent a number that may change or may be unknown.)
- Needs and wants in a budget (A budget is a plan for income, spending, saving, and other uses of money.)
How to Learn This Chapter
Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
56.1 Meaning of budget
The mean is found by adding all values and dividing by the number of values. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Find the mean of [4, 6, 8, 10].
- Add the values to get 28.
- Divide by 4.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 7
Worked Example 2
Problem: Find the mean of [5, 7, 7, 9, 12].
- Add the values to get 40.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 8
Worked Example 3
Problem: Find the mean of [3, 5, 8, 8, 11].
- Add the values to get 35.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 7
Worked Example 4
Problem: Find the mean of [10, 12, 14, 16].
- Add the values to get 52.
- Divide by 4.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 13
Worked Example 5
Problem: Find the mean of [2, 4, 6, 8, 10].
- Add the values to get 30.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 6
Worked Example 6
Problem: Find the mean of [1, 5, 5, 6, 13].
- Add the values to get 30.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 6
Worked Example 7
Problem: Find the mean of [20, 25, 25, 30].
- Add the values to get 100.
- Divide by 4.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 25
Worked Example 8
Problem: Find the mean of [7, 8, 9, 10, 11].
- Add the values to get 45.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 9
Worked Example 9
Problem: Find the mean of [3, 3, 4, 5, 9].
- Add the values to get 24.
- Divide by 5.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 4.8
Worked Example 10
Problem: Find the mean of [12, 15, 18, 21].
- Add the values to get 66.
- Divide by 4.
Very beginner explanation: The mean shares the total equally among all data values.
Answer: 16.5
Practice Exercise
Create one new Grade 6 problem about Meaning of budget. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is comparing only one number and ignoring fees, timing, limits, or the full context.
56.2 Income
Income is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Income is $500 and expenses are $420. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $80 surplus
Worked Example 2
Problem: Income is $550 and expenses are $455. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $95 surplus
Worked Example 3
Problem: Income is $600 and expenses are $490. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $110 surplus
Worked Example 4
Problem: Income is $650 and expenses are $525. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $125 surplus
Worked Example 5
Problem: Income is $700 and expenses are $560. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $140 surplus
Worked Example 6
Problem: Income is $750 and expenses are $595. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $155 surplus
Worked Example 7
Problem: Income is $800 and expenses are $630. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $170 surplus
Worked Example 8
Problem: Income is $850 and expenses are $665. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $185 surplus
Worked Example 9
Problem: Income is $900 and expenses are $700. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $200 surplus
Worked Example 10
Problem: Income is $950 and expenses are $735. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $215 surplus
Practice Exercise
Create one new Grade 6 problem about Income. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
56.3 Expenses
Expenses is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Income is $500 and expenses are $420. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $80 surplus
Worked Example 2
Problem: Income is $550 and expenses are $455. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $95 surplus
Worked Example 3
Problem: Income is $600 and expenses are $490. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $110 surplus
Worked Example 4
Problem: Income is $650 and expenses are $525. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $125 surplus
Worked Example 5
Problem: Income is $700 and expenses are $560. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $140 surplus
Worked Example 6
Problem: Income is $750 and expenses are $595. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $155 surplus
Worked Example 7
Problem: Income is $800 and expenses are $630. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $170 surplus
Worked Example 8
Problem: Income is $850 and expenses are $665. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $185 surplus
Worked Example 9
Problem: Income is $900 and expenses are $700. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $200 surplus
Worked Example 10
Problem: Income is $950 and expenses are $735. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $215 surplus
Practice Exercise
Create one new Grade 6 problem about Expenses. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
56.4 Fixed expenses
Fixed expenses is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Income is $500 and expenses are $420. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $80 surplus
Worked Example 2
Problem: Income is $550 and expenses are $455. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $95 surplus
Worked Example 3
Problem: Income is $600 and expenses are $490. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $110 surplus
Worked Example 4
Problem: Income is $650 and expenses are $525. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $125 surplus
Worked Example 5
Problem: Income is $700 and expenses are $560. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $140 surplus
Worked Example 6
Problem: Income is $750 and expenses are $595. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $155 surplus
Worked Example 7
Problem: Income is $800 and expenses are $630. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $170 surplus
Worked Example 8
Problem: Income is $850 and expenses are $665. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $185 surplus
Worked Example 9
Problem: Income is $900 and expenses are $700. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $200 surplus
Worked Example 10
Problem: Income is $950 and expenses are $735. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $215 surplus
Practice Exercise
Create one new Grade 6 problem about Fixed expenses. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
56.5 Variable expenses
A variable is a symbol used to represent a number that may change or may be unknown. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Evaluate 3x + 4 when x = 5.
- Replace x with 5.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 19
Worked Example 2
Problem: Evaluate 2n + 7 when n = 6.
- Replace n with 6.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 19
Worked Example 3
Problem: Evaluate 5a - 3 when a = 4.
- Replace a with 4.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 17
Worked Example 4
Problem: Evaluate 4p + 1 when p = 8.
- Replace p with 8.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 33
Worked Example 5
Problem: Evaluate 6m - 5 when m = 3.
- Replace m with 3.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 13
Worked Example 6
Problem: Evaluate 2.5x + 1 when x = 4.
- Replace x with 4.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 11
Worked Example 7
Problem: Evaluate 7q + 2 when q = 2.
- Replace q with 2.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 16
Worked Example 8
Problem: Evaluate 3r - 1 when r = 9.
- Replace r with 9.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 26
Worked Example 9
Problem: Evaluate 4y + 6 when y = 5.
- Replace y with 5.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 26
Worked Example 10
Problem: Evaluate 8k - 4 when k = 3.
- Replace k with 3.
- Follow order of operations.
- Calculate carefully.
Very beginner explanation: Substitution replaces a variable with a known value before calculating.
Answer: 20
Practice Exercise
Create one new Grade 6 problem about Variable expenses. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
56.6 Needs and wants in a budget
A budget is a plan for income, spending, saving, and other uses of money. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Income is $500 and expenses are $420. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $80 surplus
Worked Example 2
Problem: Income is $550 and expenses are $455. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $95 surplus
Worked Example 3
Problem: Income is $600 and expenses are $490. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $110 surplus
Worked Example 4
Problem: Income is $650 and expenses are $525. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $125 surplus
Worked Example 5
Problem: Income is $700 and expenses are $560. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $140 surplus
Worked Example 6
Problem: Income is $750 and expenses are $595. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $155 surplus
Worked Example 7
Problem: Income is $800 and expenses are $630. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $170 surplus
Worked Example 8
Problem: Income is $850 and expenses are $665. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $185 surplus
Worked Example 9
Problem: Income is $900 and expenses are $700. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $200 surplus
Worked Example 10
Problem: Income is $950 and expenses are $735. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $215 surplus
Practice Exercise
Create one new Grade 6 problem about Needs and wants in a budget. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is comparing only one number and ignoring fees, timing, limits, or the full context.
56.7 Budget balance
A budget is a plan for income, spending, saving, and other uses of money. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Income is $500 and expenses are $420. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $80 surplus
Worked Example 2
Problem: Income is $550 and expenses are $455. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $95 surplus
Worked Example 3
Problem: Income is $600 and expenses are $490. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $110 surplus
Worked Example 4
Problem: Income is $650 and expenses are $525. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $125 surplus
Worked Example 5
Problem: Income is $700 and expenses are $560. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $140 surplus
Worked Example 6
Problem: Income is $750 and expenses are $595. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $155 surplus
Worked Example 7
Problem: Income is $800 and expenses are $630. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $170 surplus
Worked Example 8
Problem: Income is $850 and expenses are $665. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $185 surplus
Worked Example 9
Problem: Income is $900 and expenses are $700. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $200 surplus
Worked Example 10
Problem: Income is $950 and expenses are $735. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $215 surplus
Practice Exercise
Create one new Grade 6 problem about Budget balance. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is comparing only one number and ignoring fees, timing, limits, or the full context.
56.8 Surplus
Surplus is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Income is $500 and expenses are $420. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $80 surplus
Worked Example 2
Problem: Income is $550 and expenses are $455. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $95 surplus
Worked Example 3
Problem: Income is $600 and expenses are $490. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $110 surplus
Worked Example 4
Problem: Income is $650 and expenses are $525. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $125 surplus
Worked Example 5
Problem: Income is $700 and expenses are $560. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $140 surplus
Worked Example 6
Problem: Income is $750 and expenses are $595. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $155 surplus
Worked Example 7
Problem: Income is $800 and expenses are $630. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $170 surplus
Worked Example 8
Problem: Income is $850 and expenses are $665. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $185 surplus
Worked Example 9
Problem: Income is $900 and expenses are $700. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $200 surplus
Worked Example 10
Problem: Income is $950 and expenses are $735. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $215 surplus
Practice Exercise
Create one new Grade 6 problem about Surplus. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
56.9 Deficit
Deficit is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Income is $500 and expenses are $420. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $80 surplus
Worked Example 2
Problem: Income is $550 and expenses are $455. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $95 surplus
Worked Example 3
Problem: Income is $600 and expenses are $490. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $110 surplus
Worked Example 4
Problem: Income is $650 and expenses are $525. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $125 surplus
Worked Example 5
Problem: Income is $700 and expenses are $560. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $140 surplus
Worked Example 6
Problem: Income is $750 and expenses are $595. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $155 surplus
Worked Example 7
Problem: Income is $800 and expenses are $630. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $170 surplus
Worked Example 8
Problem: Income is $850 and expenses are $665. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $185 surplus
Worked Example 9
Problem: Income is $900 and expenses are $700. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $200 surplus
Worked Example 10
Problem: Income is $950 and expenses are $735. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $215 surplus
Practice Exercise
Create one new Grade 6 problem about Deficit. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
56.10 Savings in a budget
A budget is a plan for income, spending, saving, and other uses of money. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Income is $500 and expenses are $420. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $80 surplus
Worked Example 2
Problem: Income is $550 and expenses are $455. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $95 surplus
Worked Example 3
Problem: Income is $600 and expenses are $490. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $110 surplus
Worked Example 4
Problem: Income is $650 and expenses are $525. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $125 surplus
Worked Example 5
Problem: Income is $700 and expenses are $560. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $140 surplus
Worked Example 6
Problem: Income is $750 and expenses are $595. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $155 surplus
Worked Example 7
Problem: Income is $800 and expenses are $630. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $170 surplus
Worked Example 8
Problem: Income is $850 and expenses are $665. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $185 surplus
Worked Example 9
Problem: Income is $900 and expenses are $700. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $200 surplus
Worked Example 10
Problem: Income is $950 and expenses are $735. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $215 surplus
Practice Exercise
Create one new Grade 6 problem about Savings in a budget. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is comparing only one number and ignoring fees, timing, limits, or the full context.
56.11 Distributing limited resources
Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Use Distributing limited resources to analyze the values 30 and 4. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 2
Problem: Use Distributing limited resources to analyze the values 9 and 16. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 3
Problem: Use Distributing limited resources to analyze the values 17 and 8. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 4
Problem: Use Distributing limited resources to analyze the values 14 and 19. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 5
Problem: Use Distributing limited resources to analyze the values 26 and 11. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 6
Problem: Use Distributing limited resources to analyze the values 23 and 15. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 7
Problem: Use Distributing limited resources to analyze the values 29 and 16. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 8
Problem: Use Distributing limited resources to analyze the values 28 and 17. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 9
Problem: Use Distributing limited resources to analyze the values 8 and 16. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Worked Example 10
Problem: Use Distributing limited resources to analyze the values 13 and 15. What should be checked first?
- Identify what each value represents.
- Choose the rule, representation, or comparison that matches the topic.
- Show the reasoning before accepting the result.
Very beginner explanation: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Answer: Check the meaning of the values and the rule required by the problem.
Practice Exercise
Create one new Grade 6 problem about Distributing limited resources. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is starting a calculation before identifying what is given, what must be found, and which rule fits the problem.
56.12 Comparing budget choices
A budget is a plan for income, spending, saving, and other uses of money. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Income is $500 and expenses are $420. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $80 surplus
Worked Example 2
Problem: Income is $550 and expenses are $455. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $95 surplus
Worked Example 3
Problem: Income is $600 and expenses are $490. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $110 surplus
Worked Example 4
Problem: Income is $650 and expenses are $525. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $125 surplus
Worked Example 5
Problem: Income is $700 and expenses are $560. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $140 surplus
Worked Example 6
Problem: Income is $750 and expenses are $595. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $155 surplus
Worked Example 7
Problem: Income is $800 and expenses are $630. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $170 surplus
Worked Example 8
Problem: Income is $850 and expenses are $665. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $185 surplus
Worked Example 9
Problem: Income is $900 and expenses are $700. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $200 surplus
Worked Example 10
Problem: Income is $950 and expenses are $735. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $215 surplus
Practice Exercise
Create one new Grade 6 problem about Comparing budget choices. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is comparing only one number and ignoring fees, timing, limits, or the full context.
56.13 Real-life budgeting problems
A budget is a plan for income, spending, saving, and other uses of money. In this Grade 6 lesson, focus on meaning first, then use a small example, show the steps, and check whether the result fits the question.
Beginner Note
Identify what is given, what must be found, and which rule or representation fits this topic. Work one step at a time and explain why each step is valid.
10 Worked Examples with Answers and Very-Beginner Explanations
Worked Example 1
Problem: Income is $500 and expenses are $420. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $80 surplus
Worked Example 2
Problem: Income is $550 and expenses are $455. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $95 surplus
Worked Example 3
Problem: Income is $600 and expenses are $490. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $110 surplus
Worked Example 4
Problem: Income is $650 and expenses are $525. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $125 surplus
Worked Example 5
Problem: Income is $700 and expenses are $560. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $140 surplus
Worked Example 6
Problem: Income is $750 and expenses are $595. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $155 surplus
Worked Example 7
Problem: Income is $800 and expenses are $630. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $170 surplus
Worked Example 8
Problem: Income is $850 and expenses are $665. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $185 surplus
Worked Example 9
Problem: Income is $900 and expenses are $700. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $200 surplus
Worked Example 10
Problem: Income is $950 and expenses are $735. Find the budget balance.
- Subtract total expenses from total income.
Very beginner explanation: A positive balance is a surplus; a negative balance is a deficit.
Answer: $215 surplus
Practice Exercise
Create one new Grade 6 problem about Real-life budgeting problems. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is comparing only one number and ignoring fees, timing, limits, or the full context.
30 Review Questions and Answers
Q1. What is important to understand about Meaning of budget?
Answer: The mean is found by adding all values and dividing by the number of values.
Q2. What is important to understand about Income?
Answer: Income is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q3. What is important to understand about Expenses?
Answer: Expenses is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q4. What is important to understand about Fixed expenses?
Answer: Fixed expenses is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q5. What is important to understand about Variable expenses?
Answer: A variable is a symbol used to represent a number that may change or may be unknown.
Q6. What is important to understand about Needs and wants in a budget?
Answer: A budget is a plan for income, spending, saving, and other uses of money.
Q7. What is important to understand about Budget balance?
Answer: A budget is a plan for income, spending, saving, and other uses of money.
Q8. What is important to understand about Surplus?
Answer: Surplus is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q9. What is important to understand about Deficit?
Answer: Deficit is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q10. What is important to understand about Savings in a budget?
Answer: A budget is a plan for income, spending, saving, and other uses of money.
Q11. What is important to understand about Distributing limited resources?
Answer: Distributing limited resources is a Grade 6 mathematics idea in Budgeting and Resource Distribution. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q12. What is important to understand about Comparing budget choices?
Answer: A budget is a plan for income, spending, saving, and other uses of money.
Q13. What is important to understand about Real-life budgeting problems?
Answer: A budget is a plan for income, spending, saving, and other uses of money.
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 final answer is reasonable before accepting it.
Q16. Why do units matter?
Answer: Units tell what a value measures and help 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, a table, or a second method.
Q19. What should you identify first in a word problem?
Answer: Identify what is known, what is unknown, and the 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, operations, signs, units, rules, and calculations.
Q22. Why are diagrams useful?
Answer: A labelled diagram can reveal relationships that are harder to see in words alone.
Q23. Why are tables useful?
Answer: Tables organize values so patterns, rates, comparisons, and missing information are easier to see.
Q24. Why are graphs useful?
Answer: Graphs make relationships, changes, trends, and comparisons visible.
Q25. Why should you explain your reasoning?
Answer: An explanation shows why a method works instead of only giving a final number.
Q26. Why can more than one strategy be correct?
Answer: Different correct strategies can represent the same mathematics in different but equivalent ways.
Q27. What should you do before using a formula or rule?
Answer: Check what each quantity means and whether the rule matches the situation.
Q28. How does practice help in mathematics?
Answer: Practice builds accuracy and fluency while helping you recognize which strategies fit different problems.
Q29. What is a good way to learn from a mistake?
Answer: Find the exact step where the reasoning changed from correct to incorrect, then solve a similar problem again.
Q30. Why should you compare an exact answer with an estimate?
Answer: The estimate gives a quick reasonableness check for the exact calculation.