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Percentages of an Amount (Calculator)
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Foundational skills
Convert a percentage to a decimal multiplier
\[ 35\% \rightarrow 0.35 \]
Convert a percentage less than 100% to its decimal equivalent.
Convert a percentage greater than 100% to a decimal
\[ 145\% \rightarrow 1.45 \]
Convert a percentage greater than 100% to its decimal equivalent.
Convert a decimal percentage to a decimal multiplier
\[ 3.5\% \rightarrow 0.035 \]
Convert a percentage with a decimal to its decimal equivalent.
Percentage of an amount
Find a percentage of an amount using a multiplier
\[ 35\% \text{ of } \text{£}240 \]
Calculate a percentage of an amount using the decimal multiplier method.
Find a percentage greater than 100% of an amount
\[ 135\% \text{ of } \text{£}80 \]
Calculate a percentage greater than 100% of an amount.
Find a decimal percentage of an amount
\[ 3.5\% \text{ of } \text{£}600 \]
Calculate a percentage that includes a decimal.
Find a percentage of an amount in context
\[ 15\% \text{ service charge} \]
Calculate a percentage of an amount in a real-world context.
Expressing as a percentage
Express one quantity as a percentage of another
\[ 45 \text{ as a \% of } 180 \]
Calculate what percentage one number is of another.
Express a larger quantity as a percentage of a smaller
\[ 270 \text{ as a \% of } 180 \]
Calculate what percentage one number is of another when the result exceeds 100%.
Express as a percentage with rounding
\[ 47 \text{ out of } 68 \text{ (1 d.p.)} \]
Calculate a percentage that requires rounding.
Express as a percentage in context
\[ 84 \text{ of } 120 \text{ items sold} \]
Calculate what percentage one quantity is of another in context.
Percentage change
Calculate percentage increase
\[ \text{£}40 \rightarrow \text{£}52 \]
Find the percentage increase between two values.
Calculate percentage decrease
\[ \text{£}80 \rightarrow \text{£}68 \]
Find the percentage decrease between two values.
Calculate percentage change in context
\[ \text{Population change} \]
Find a percentage change in a real-world context.
Calculate percentage profit
\[ \text{Cost £}25, \text{Sold £}32 \]
Find the percentage profit on a sale.
Calculate percentage loss
\[ \text{Cost £}8000, \text{Sold £}6800 \]
Find the percentage loss on a sale.
Calculate percentage error
\[ \text{Est: } 45, \text{ Actual: } 52 \]
Find the percentage error between an estimate and actual value.
Simple interest
Calculate simple interest for one year
\[ \text{£}500 \text{ at } 4\% \text{ for 1 yr} \]
Find the interest earned in a single year.
Calculate simple interest for multiple years
\[ \text{£}800 \text{ at } 3\% \text{ for 4 yrs} \]
Find the interest earned over several years.
Calculate total amount after simple interest
\[ \text{Principal + Interest} \]
Find the total value after simple interest is added.
Find the interest rate given simple interest earned
\[ \text{£}400, \text{ 2 yrs, £}32 \rightarrow r\% \]
Work backwards to find the interest rate.
Find the time given simple interest earned
\[ \text{£}500, 4\%, \text{£}80 \rightarrow t \]
Work backwards to find the time period.
Reverse percentages
Find the original given a percentage
\[ 35\% \text{ of } ? = 84 \]
Work backwards from a percentage to find the original amount.
Find the original given a percentage greater than 100%
\[ 140\% \text{ of } ? = 350 \]
Work backwards from a percentage over 100% to find the original.
Find the original in context
\[ 15\% \text{ commission} = \text{£}45 \]
Find the original amount when a percentage of it is given – stated in context.
Special cases
Find a fractional percentage of an amount
\[ 0.5\% \text{ of } \text{£}2400 \]
Calculate a percentage less than 1% of an amount.
Calculate VAT at 20%
\[ \text{VAT on } \text{£}350 \]
Calculate VAT (20%) on an amount.
Find the pre-VAT price from the VAT amount
\[ \text{VAT} = \text{£}18 \rightarrow \text{Price?} \]
Work backwards from VAT amount to find original price.
Compare percentages of different amounts
\[ 15\% \text{ of } 80 \text{ vs } 12\% \text{ of } 95 \]
Determine which of two percentage calculations gives the larger result.
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