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Why can’t you divide a certain number by zero?

The complete phrasing of the question: Why can’t you divide a certain number by zero? Supposedly, the meaning of dividing by zero is that you do not divide the number (you “divide” it to 0 sets…) and so the result should be the same as the number divided?

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Does the rule of positive numbers, in which dividing 10 by an increasingly smaller number increases the product, also works when we divide 10 by a negative number? Choose the correct response.

1.

No, the more you divide 10 by an increasingly smaller negative number, the result decreases.

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2.

There is no way of knowing of certain. There are exceptions.

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3.

Yes, the more you divide 10 by an increasingly smaller negative numbers, the result increases.

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The X axis represents the denominator (the dividing number).

The Y axis represents the quotient (the product of the division).

Based on the explanation, why does 10 divided by 0 tends towards infinity? Choose the correct answer.

1.

When you divide 10 by a number that slowly tends towards zero, the product becomes very small, and therefore something that is almost zero tends towards infinity.

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2.

When you divide by 0 there is no way of knowing the product, and therefore an unknown product tends towards infinity.

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3.

It is not clear how the exercise is performed, and it is custom to mark unknown answers as infinity.

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4.

When you divide 10 by a number that slowly tends towards zero, you get an enormous product, and therefore it tends towards infinity.

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Based one the video, we can conclude that the multiplication of any number by its multiplicative inverse is? Choose the correct answer:

1.

There is no way to know

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2.

10

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3.

1

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4.

0

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Draw a line between the number at column A to its multiplicative inverse in column B

1. 0
2. 5
3. 3/4
4. 3
5. 4
6. 1
1. 1/3
2. No multiplicative inverse
3. ¼
4. 4/3
5. 0.2
6. 1
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The creation of Complex Numbers, at the early 16th century, is attributed to Girolamo Cardano that used them to solve cubic equations. These numbers were explicitly defined by Rafael Bombelli in 1527. During that time, these numbers were considered unreal. Mathematician found it hard to grasp the new concept, as evident by the name they attributed to these numbers.

In summary, in the world that we employ of normal numbers, can you divide by zero? If so, what is the product? Choose the correct answer.

1.

You can not divide by zero, this is impractical and creates problem.

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2.

Anyone can decide if you can divide by zero or not and what is the product.

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3.

You can divide by zero, and the quotient is infinity.

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4.

You can divide by zero, and the quotient is 0.

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Interactive Video

Why Is It Forbidden to Divide By Zero - An Interactive Video

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Activity Overview

In this video the pupils will be exposed to the problems that arise when dividing a number by zero. The pupils will see different angles of approaches to performing such task, using coordinate system, multiplicative inverses and tending towards infinity. All this while viewing the internal contradictions that occur when dividing by zero. The length of the video including answering the questions is 10 minutes.

Terms

Zero, Division, Infinity, Properties of numbers, Arithmetic

Skills

Knowledge building