Year 6 Maths: Finding the Original Amount

Introduction

Hello Year 6! Today, we are going to learn about finding the original amount. This is an important skill in maths, especially when you are dealing with percentages, discounts, and other similar problems. Let’s break it down together!

What Does ‘Finding the Original Amount’ Mean?

When we talk about finding the original amount, we usually mean that we have a new amount and we need to figure out what the starting amount was before something happened, like a discount or an increase.

Example

Imagine you go to a shop, and a toy costs £30 after a 25% discount. To find out how much the toy originally cost before the discount, we need to do some calculations.

Key Steps to Finding the Original Amount

1. Understand the Percentage: The discount is 25%, which means you pay 75% of the original price.
2. Set Up the Equation:
   • If the original price is ( x ), then after the discount, you pay ( 0.75x ).
   • We know ( 0.75x = 30 ).
3. Solve for ( x ):
   • To find ( x ), divide both sides by 0.75:
   $$x = \frac{30}{0.75}$$
4. Calculate the Original Amount:
   • When you do the calculation, you find ( x = 40 ).
   • So, the original price of the toy was £40.

Key Rules

• Percentages: Remember that a percentage is a part out of 100.
• Decimal Conversion: Convert percentages to decimals when calculating. For example, 25% becomes 0.25 and 75% becomes 0.75.
• Equation Setup: Always set up an equation to represent the relationship between the original amount and the new amount.

Tips and Tricks

• Visual Representation: Drawing a pie chart can help you visualise percentages.
• Practice: The more problems you solve, the easier it becomes to find the original amount.
• Check Your Work: After finding the original amount, you can check by applying the percentage to see if you get back to the new amount.

Questions

Easy Level Questions

1. If 10% of a number is 5, what is the original number?
2. A shirt costs £20 after a 20% discount. What was the original price?
3. If you score 15 out of 20 in a test, what is the original score out of 100?
4. A book costs £12 after a 25% discount. What was the original cost?
5. If 50% of a number is 30, what is the original number?
6. A toy is sold for £15 after a 10% discount. What was the original price?
7. If a person has 80% of their money left and that is £40, what was the original amount?
8. A cake is cut and 30% is eaten. If 70% is left, and that is 21 pieces, how many pieces were there originally?
9. If 25% of a number is 10, what is the original number?
10. After a 15% discount, a jacket costs £51. What was the original price?

Medium Level Questions

11. If 60% of a number is 42, what is the original number?
12. A bicycle costs £240 after a 20% discount. What was the original price?
13. If 80% of a number is 64, what is the original number?
14. A computer is sold for £600 after a 25% discount. What was the original price?
15. If 30% of a number is 24, what is the original number?
16. A watch costs £85 after a 15% discount. What was the original price?
17. If a number is decreased by 10% and becomes 90, what was the original number?
18. After a 50% discount, a sofa costs £300. What was the original price?
19. A student scores 72 out of 90. What is the percentage score and what would that be out of 100?
20. After a 5% increase, a salary is £630. What was the original salary?

Hard Level Questions

21. If 45% of a number is 135, what is the original number?
22. A television is sold for £720 after a 10% discount. What was the original price?
23. If a person saved 20% on a £150 purchase, how much did they originally spend?
24. A car’s price is £12,000 after a 15% discount. What was the original price?
25. If 35% of a number is 49, what is the original number?
26. A restaurant meal costs £55 after a 20% discount. What was the original price?
27. If a number is reduced by 25% and becomes 75, what was the original number?
28. A phone is sold for £540 after a 10% discount. What was the original price?
29. If 70% of a number is £210, what is the original number?
30. A dress costs £120 after a 25% discount. What was the original price?

Answers and Explanations

Easy Level Answers

1. ( 50 )
2. £25
3. 75
4. £16
5. ( 60 )
6. £16.67
7. ( 50 )
8. 30
9. ( 40 )
10. £60

Medium Level Answers

11. ( 70 )
12. £300
13. ( 80 )
14. £800
15. ( 80 )
16. £100
17. ( 100 )
18. £600
19. 80%
20. £600

Hard Level Answers

21. ( 300 )
22. £800
23. £120
24. £14,117.65
25. ( 140 )
26. £68.75
27. ( 100 )
28. £600
29. ( 300 )
30. £160

I hope this lesson helps you understand how to find the original amount! Keep practising, and soon it will feel like a piece of cake!