Video: AQA GCSE Mathematics Foundation Tier Pack 4 • Paper 1 • Question 17

Sandra says “If you divide any even number by 2, the answer is always an odd number.” Is Sandra correct? Use a calculation to support your answer.

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Video Transcript

Sandra says “If you divide any even number by two, the answer is always an odd number.” Is Sandra correct? Use a calculation to support your answer.

As Sandra is making a claim about any even number, we only need to find one counterexample to prove she is incorrect. Sandra is considering the even numbers. These are two, four, six, eight, 10, 12, and so on. She says that when we divide them by two, the answer is always odd. Let’s try and divide these even numbers by two. Two divided by two is equal to one. Four divided by two is equal to two. Six divided by two equals three. Eight divided by two is equal to four and so on.

As Sandra said the answer would always be odd, we can already see that she is incorrect as we have found three even numbers already, two, four, and six. Dividing the numbers four, eight, and 12 by two gives us an even number. We can therefore conclude that Sandra is incorrect as dividing any multiple of four, in this case, four, eight, 12, and so on, by two gives us an even number. For example, eight divided by two is equal to four. Any multiple of four would work as the counterexample.

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