Chapter 10: Mental Math and Percent Benchmarks
Learn Grade 6 mathematics with very-beginner explanations, original worked examples, practice, reasoning, and review.
Chapter Overview
This chapter teaches Mental Math and Percent Benchmarks in original, simple language with step-by-step reasoning, worked examples, practice exercises, common mistakes, and review questions.
Key Technical Terms
- Meaning of percent (Percent means 'per hundred' and compares a quantity with 100 equal parts.)
- Estimating discounts (Estimating discounts is a Grade 6 mathematics idea in Mental Math and Percent Benchmarks. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
- Estimating tax and tips (Estimating tax and tips is a Grade 6 mathematics idea in Mental Math and Percent Benchmarks. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.)
How to Learn This Chapter
Read the explanation first, follow each worked example slowly, cover the answer and retry the problem yourself, then use the practice and review questions to check understanding.
10.1 Meaning of percent
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Meaning of percent. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
10.2 Percent as per hundred
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Percent as per hundred. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
10.3 Finding 1 percent
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Finding 1 percent. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
10.4 Finding 10 percent
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Finding 10 percent. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
10.5 Finding 25 percent
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Finding 25 percent. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
10.6 Finding 50 percent
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Finding 50 percent. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
10.7 Finding 75 percent
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Finding 75 percent. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
10.8 Finding 5 percent
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Finding 5 percent. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
10.9 Finding 20 percent
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Finding 20 percent. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
10.10 Mental percent of a number
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Mental percent of a number. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
10.11 Estimating discounts
Estimating discounts is a Grade 6 mathematics idea in Mental Math and Percent Benchmarks. 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: Find 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Estimating discounts. 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.
10.12 Estimating tax and tips
Estimating tax and tips is a Grade 6 mathematics idea in Mental Math and Percent Benchmarks. 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: Find 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Estimating tax and tips. 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.
10.13 Percent in everyday situations
Percent means 'per hundred' and compares a quantity with 100 equal parts. 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 1% of 80.
- Think of 1% as 1/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 0.8
Worked Example 2
Problem: Find 5% of 120.
- Think of 5% as 5/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6
Worked Example 3
Problem: Find 10% of 64.
- Think of 10% as 10/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 6.4
Worked Example 4
Problem: Find 20% of 250.
- Think of 20% as 20/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 50
Worked Example 5
Problem: Find 25% of 96.
- Think of 25% as 25/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 24
Worked Example 6
Problem: Find 50% of 40.
- Think of 50% as 50/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 20
Worked Example 7
Problem: Find 75% of 200.
- Think of 75% as 75/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 150
Worked Example 8
Problem: Find 15% of 60.
- Think of 15% as 15/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 9
Worked Example 9
Problem: Find 30% of 150.
- Think of 30% as 30/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 45
Worked Example 10
Problem: Find 40% of 90.
- Think of 40% as 40/100.
- Multiply the quantity by the percent as a decimal or fraction.
Very beginner explanation: Percent means per hundred, so benchmark percents can often be found mentally.
Answer: 36
Practice Exercise
Create one new Grade 6 problem about Percent in everyday situations. Solve it step by step, label any units, and explain how you checked your answer.
Common Mistake
A common mistake is treating a percent as a whole number instead of converting it to a fraction or decimal when needed.
30 Review Questions and Answers
Q1. What is important to understand about Meaning of percent?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
Q2. What is important to understand about Percent as per hundred?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
Q3. What is important to understand about Finding 1 percent?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
Q4. What is important to understand about Finding 10 percent?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
Q5. What is important to understand about Finding 25 percent?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
Q6. What is important to understand about Finding 50 percent?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
Q7. What is important to understand about Finding 75 percent?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
Q8. What is important to understand about Finding 5 percent?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
Q9. What is important to understand about Finding 20 percent?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
Q10. What is important to understand about Mental percent of a number?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
Q11. What is important to understand about Estimating discounts?
Answer: Estimating discounts is a Grade 6 mathematics idea in Mental Math and Percent Benchmarks. 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 Estimating tax and tips?
Answer: Estimating tax and tips is a Grade 6 mathematics idea in Mental Math and Percent Benchmarks. The goal is to understand the meaning, choose a suitable strategy, show the steps clearly, and check that the result is reasonable.
Q13. What is important to understand about Percent in everyday situations?
Answer: Percent means 'per hundred' and compares a quantity with 100 equal parts.
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.