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Joanna states, “five is odd and seven is odd, so the product of any multiple of five and any multiple of seven must also be an odd.“ Is she correct?
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Give an example to support your answer.
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First, let’s think about what we know about even and odd multiplication.
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An odd number times an odd number equals an odd number.
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An example of this would be three times five equals 15.
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Then, we have the odd times even case, which equals an even number.
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We see this in three times two equals six.
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The last case, even number times an even number equals an even number, an example being four times two equals eight.
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If you didn’t remember the rules, you could consider examples of each scenario to help you remember.
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Now we’ve considered the even and odd multiplication, we need to ask the question “is every multiple of five and every multiple of seven odd?“
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A multiple is what we get when we multiply a number by an integer.
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Right here, we should note that integers can be both even and odd.
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Let’s list some of the multiples of five: five times one, where one is the integer we’re multiplying five by, equals five; five times two, where two is the integer we’re multiplying five by, which equals 10; five times three equals 15; five times four equals 20.
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We’re already noticing that five has some even-numbered multiples.
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The first multiple of seven, seven times one, equals seven, seven times two equals 14, seven times three equals 21, and seven times four equals 28.
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Seven also has even-numbered multiples.
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Joanna’s claim is that multiplying any multiple of five by any multiple of seven will always be odd.
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Imagine we choose 10 as our multiple of five and seven as our multiple of seven.
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10 times seven equals 70.
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We know that 10 is a multiple of five, it’s five times two, and that seven is a multiple of seven, seven times one, that this two makes five times two makes 10 an even number multiplied by a multiple of seven, seven which is an odd number and they produce an even number.
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Although 10 and seven are both multiples of five, 70 is not odd.
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This is a counterexample.
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It’s a place where Joanna’s statement is false.
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And we only need one counterexample to make the whole statement false.
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Joanna is not correct because multiplying seven or five by an even number produces an even multiple, which will yield an even final product.
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Remember that in this question, it’s not enough just to answer is she correct.
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You also need to support your answer with an example, which we’ve done here.