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Percentages: Increase and Decrease (Calculator)
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Foundational skills
Find the multiplier for a percentage increase
\[ 15\% \text{ increase} \rightarrow 1.15 \]
Determine the decimal multiplier for a percentage increase.
Find the multiplier for a percentage decrease
\[ 15\% \text{ decrease} \rightarrow 0.85 \]
Determine the decimal multiplier for a percentage decrease.
Find the multiplier for an increase greater than 100%
\[ 150\% \text{ increase} \rightarrow 2.5 \]
Determine the decimal multiplier for a percentage increase over 100%.
Percentage increase
Increase by a percentage using a multiplier
\[ \text{£}85 + 15\% = \text{£}97.75 \]
Increase an amount by a percentage using the multiplier method.
Increase by more than 100% using a multiplier
\[ \text{£}60 + 125\% = \text{£}135 \]
Increase an amount by a percentage over 100% using the multiplier method.
Percentage increase in context
\[ \text{House: £180k} + 12\% \]
Apply a percentage increase using multipliers in context.
Percentage decrease
Decrease by a percentage using a multiplier
\[ \text{£}120 – 35\% = \text{£}78 \]
Decrease an amount by a percentage using the multiplier method.
Percentage decrease in context
\[ \text{Car: £8500} – 18\% \]
Apply a percentage decrease using multipliers in context.
Profit and loss
Calculate selling price given percentage profit
\[ \text{Cost £}45 + 20\% \text{ profit} \]
Find the selling price to achieve a given percentage profit.
Calculate selling price given percentage loss
\[ \text{Cost £}80 – 15\% \text{ loss} \]
Find the selling price when selling at a given percentage loss.
Calculate selling price with markup
\[ \text{Cost £}35 + 60\% \text{ markup} \]
Find the selling price after applying a markup percentage.
Calculate VAT-inclusive price
\[ \text{£}450 + 20\% \text{ VAT} \]
Find the total price after adding VAT.
Reverse percentages
Find original price before a percentage increase
\[ \text{After } 15\% \uparrow = \text{£}92 \]
Work backwards to find the original amount before a percentage increase.
Find original price before a percentage decrease
\[ \text{After } 20\% \downarrow = \text{£}64 \]
Work backwards to find the original amount before a percentage decrease.
Find original price before VAT
\[ \text{Inc. VAT } = \text{£}84 \]
Work backwards to find the pre-VAT price from a VAT-inclusive price.
Find original price before a sale discount
\[ 30\% \text{ off} = \text{£}56 \]
Work backwards to find the original price before a sale discount.
Find cost price given selling price and profit percentage
\[ \text{Sell £}78, 30\% \text{ profit} \]
Work backwards from selling price and profit percentage to find cost price.
Find cost price given selling price and loss percentage
\[ \text{Sell £}51, 15\% \text{ loss} \]
Work backwards from selling price and loss percentage to find cost price.
Find original after increase greater than 100%
\[ \text{After } 150\% \uparrow = 450 \]
Work backwards to find the original before a percentage increase over 100%.
Special cases
Find multiplier for successive percentage changes
\[ +10\% \text{ then } -10\% \]
Find the combined multiplier for two successive percentage changes.
Calculate overall percentage change from successive changes
\[ +20\% \text{ then } +10\% = ? \]
Find the overall percentage change from two successive changes.
Reverse a percentage increase – given the increase amount
\[ 15\% \uparrow \text{ was £}12 \]
Find the original price when given the actual increase amount and percentage.
Reverse a percentage decrease – given the decrease amount
\[ 25\% \downarrow \text{ was £}18 \]
Find the original price when given the actual decrease amount and percentage.
Price after multiple changes
\[ \text{£}200 + 15\% – 10\% \]
Calculate a price after two successive percentage changes.
Timer (Optional)
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