Percentage-Change Aqa Foundation

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Exam code:8300

Percentage change

How do I find a percentage change?

The multiplier that was used for a percentage change can be found using the formula:
- $m equals fraction numerator Amount space after over denominator Amount space before end fraction$
The value of $m$ corresponds to the multiplier for the percentage change
- 1.05 corresponds to an increase by 5%
- 0.75 corresponds to a decrease by 25%
Alternatively you can use the formula:
- Percentage Change = $fraction numerator After space minus space Before over denominator Before end fraction cross times 100$
- A positive value is a percentage increase
  - An answer of 12 means an increase of 12%
- A negative value is a percentage decrease
  - An answer of -28 means a decrease of 28%

How do I find a percentage profit or loss?

Similar strategies to the above can be used to find the percentage profit or loss
Shops buy or produce items at a “cost price” and sell them at a “selling price”
Using a multiplier method:
- $m equals fraction numerator Selling space Price over denominator Cost space Price end fraction$
- 1.05 corresponds to a 5% profit
- 0.75 corresponds to a 25% loss
Alternatively you can use the formula:
- Percentage Profit = $fraction numerator Selling space Price space minus space Cost space Price over denominator Cost space Price end fraction cross times 100$
- A positive value is a profit
  - An answer of 12 means a 12% profit
- A negative value is a loss
  - An answer of -28 means a 28% loss

Examiner Tips and Tricks

Use “common sense” to check your answer!
- If an item is sold for more than it was bought for, you are expecting a profit, not a loss

Worked Example

The number of students in a school changes from 250 to 310. Describe the percentage change in number of students.

Method 1
Use the formula <img alt=”m equals fraction numerator Amount space after over denominator Amount space before end fraction” data-mathml='<math ><semantics><mrow><mi >m</mi><mo >=</mo><mfrac ><mrow><mi>Amount</mi><mo> </mo><mi>after</mi></mrow><mrow><mi>Amount</mi><mo> </mo><mi>before</mi></mrow></mfrac></mrow><annotation encoding=”application/vnd.wiris.mtweb-params+json”>{“language”:”en”,”fontFamily”:”Times New Roman”,”fontSize”:”18″,”autoformat”:true}</annotation></semantics></math>’ data-type=”commentary” height=”47″ role=”math” src=”data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20xmlns%3Awrs%3D%22http%3A%2F%2Fwww.wiris.com%2Fxml%2Fmathml-extension%22%20height%3D%2247%22%20width%3D%22150%22%20wrs%3Abaseline%3D%2230%22%3E%3C!–MathML%3A%20%3Cmath%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmi%20mathcolor%3D%22%23000000%22%3Em%3C%2Fmi%3E%3Cmo%20mathcolor%3D%22%23000000%22%3E%3D%3C%2Fmo%3E%3Cmfrac%20mathcolor%3D%22%23000000%22%3E%3Cmrow%3E%3Cmi%3EAmount%3C%2Fmi%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmi%3Eafter%3C%2Fmi%3E%3C%2Fmrow%3E%3Cmrow%3E%3Cmi%3EAmount%3C%2Fmi%3E%3Cmo%3E%26%23xA0%3B%3C%2Fmo%3E%3Cmi%3Ebefore%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmfrac%3E%3C%2Fmath%3E–%3E%3Cdefs%3E%3Cstyle%20type%3D%22text%2Fcss%22%3E%40font-face%7Bfont-family%3A’math17f39f8317fbdb1988ef4c628eb’%3Bsrc%3Aurl(data%3Afont%2Ftruetype%3Bcharset%3Dutf-8%3Bbase64%2CAAEAAAAMAIAAAwBAT1MvMi7iBBMAAADMAAAATmNtYXDEvmKUAAABHAAAADRjdnQgDVUNBwAAAVAAAAA6Z2x5ZoPi2VsAAAGMAAAAsmhlYWQQC2qxAAACQAAAADZoaGVhCGsXSAAAAngAAAAkaG10eE2rRkcAAAKcAAAACGxvY2EAHTwYAAACpAAAAAxtYXhwBT0FPgAAArAAAAAgbmFtZaBxlY4AAALQAAABn3Bvc3QB9wD6AAAEcAAAACBwcmVwa1uragAABJAAAAAUAAADSwGQAAUAAAQABAAAAAAABAAEAAAAAAAAAQEAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAACAgICAAAAAg1UADev96AAAD6ACWAAAAAAACAAEAAQAAABQAAwABAAAAFAAEACAAAAAEAAQAAQAAAD3%2F%2FwAAAD3%2F%2F%2F%2FEAAEAAAAAAAABVAMsAIABAABWACoCWAIeAQ4BLAIsAFoBgAKAAKAA1ACAAAAAAAAA

Maths Gcse Aqa Foundation

Percentage-Change Aqa Foundation