# THE SUN: Quick maths puzzle divides the internet – and even calculators are getting it wrong

Press/Media: Expert comment

Release date: 1/8/2019

## Description

Speaking to The Sun, Dr GeoffEvatt, a lecturer in applied mathematics at the University of Manchester, said the way the original equation is written is what's confusing people. The question is ambiguous," he said. "Looks to me like an issue with where one should be placing brackets. It's not 100% clear what operation the (2+2) is supposed to achieving from the way it is stated, presumably hence the debate."

Dr Thomas House, a lecturer in Applied Mathematics at the University of Manchester, said it depends on how you use the equation's brackets.

"The usual way to interpret the calculation is that anything within brackets comes first," Dr House told The Sun.

"So we have 8÷2(2+2) = 8÷2(4). Then division takes place before multiplication, so we have 4(4), which is 16."

"If someone wants to give multiplication precedence over division, there’s nothing to stop them saying that 8/2(4) means 8/8 = 1," Dr House added.

So where does that leave us? The maths expert says when in doubt, trust your computer.

"Typing the ambiguous 8/2*(2+2) into my computer gives 16, the ‘standard’ interpretation."

"The lesson is that we have to be careful about definitions," Dr House said.

"When writing computer code the first interpretation would normally be written (8/2)*(2+2) and the second 8/(2*(2+2)) to avoid any ambiguity."

## Media coverage

Title Quick maths puzzle divides the internet – and even calculators are getting it wrong The Sun Web United Kingdom 1/08/19 Speaking to The Sun, Dr Geoff Evatt, a lecturer in applied mathematics at the University of Manchester, said the way the original equation is written is what's confusing people. The question is ambiguous," he said. "Looks to me like an issue with where one should be placing brackets. It's not 100% clear what operation the (2+2) is supposed to achieving from the way it is stated, presumably hence the debate."Dr Thomas House, a lecturer in Applied Mathematics at the University of Manchester, said it depends on how you use the equation's brackets."The usual way to interpret the calculation is that anything within brackets comes first," Dr House told The Sun."So we have 8÷2(2+2) = 8÷2(4). Then division takes place before multiplication, so we have 4(4), which is 16.""If someone wants to give multiplication precedence over division, there’s nothing to stop them saying that 8/2(4) means 8/8 = 1," Dr House added.So where does that leave us? The maths expert says when in doubt, trust your computer."Typing the ambiguous 8/2*(2+2) into my computer gives 16, the ‘standard’ interpretation.""The lesson is that we have to be careful about definitions," Dr House said."When writing computer code the first interpretation would normally be written (8/2)*(2+2) and the second 8/(2*(2+2)) to avoid any ambiguity. https://www.thesun.co.uk/tech/9631520/maths-puzzle-quick-confusing-two-answers/ Geoffrey Evatt, Thomas House