How can one division expression have more than one answer?

Question

My 5th grader is in Ag Math and they are to answer questions regarding math in their journal daily. Today's question is "Explain how one division expression can have many different answers and give an example to support your answer". We are truly stumped, we maybe overthinking the question. My daughter thinks that it could have different answers if the expression ask for an estimate or exact number. Please help!!

Answer 1

I agree with Kelly. As long as you keep the top and bottom of a fraction (a division expression) proportional, each answer remains equivalent. 1/2 equals 3/6 which equals 5/10. 

Given the division expression "5 divided by 10," possible answers include 1/2, .5, and even 50%. What seems to be important in this question is that all these different looking numbers express the same quantity. 

A half a pie is still a half a pie -- any way you slice it :)

Answer 2

I think in this context the division expression referred to is any number divided by any other number. For example take the expression 30 divided by 6 which can be written as 30/6. In its simplest form it is equal to 5. However it could also be expressed as 15 divided by 3 (also written as 15/3). This result is obtained by dividing both the numerator (top number, in this case 30) and denominator (bottom number, in this case 6) by 2.  You could have your child come up with a similar example to the one given above.

Answer 3

A simple division expression is x/y.  This expression can have many different answers, depending on what the number 'x' is, and what the number 'y' is.  So one division expression can have many answers, depending on the values assigned to x and y.  The math always remains the same. Okay? 

Also, look at Bethany's answer because this may be the point of the question.  3/6 = 1/2; and 3 is 50% of 6; and 3 = .5 x 6.  Different answers only because a different mathematical expression (unit) for the same ratio is used in each case.  But when x and y have a set value, the ratio (answer) is the same no matter how it is expressed.

 

Answer 4

If you have an advanced fifth grader, perhaps you could introduce an expression with a variable like: x/2 = ?

which has a different answer for each number you choose to replace x. 

Answer 5

Your answer can be different according to the numbers you use 

Answer 6

There are many answers as you plug in any number and divide them out or put them into fractions which still does this in the LCD. Sometimes, the easiest answer is the one that we over look. Math makes one over think some times so take a deep breath it will be okay.

Answer 7

An equation that includes a radical (squareroot) would have more than one solution. 

Sqrt 4 has two solutions, 2 (e.g. 2*2=4) and -2 (e.g. -2*-2=4).

Use Sqrt in a division expression.   Sqrt 4 / 2 = ?   The answers are 1 and -1.

You could be creative and have two SQRTs.  Sqrt 4 / Sqrt 4 = ?.  The answers are still 1 and -1.