Subtraction of natural numbers and its properties

Problems

Is the following equality true?

$$23−14=14−23$$

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Development:

On both sides of the equality there are the same numbers, but mixed up. In the subtraction we cannot use the commutative property (that is, you cannot mix them up), and therefore the equality is false.

Solution:

The equality is false.

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Which of these subtractions gives a natural number?

a) $$34−52$$

b) $$22−63$$

c) $$70−23$$

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Development:

We have to look at which cases the first number is bigger than the second:

a) $$34$$ is less than $$52$$

b) $$22$$ is less than $$63$$

c) $$70$$ is bigger than $$23$$

Solution:

a) The result is a natural number.

b) The result is not a natural number.

c) The result is a natural number.

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Is the following equality true?

$$33−(17−1)=(33−17)−1$$

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Development:

Brackets indicate that we have the subtraction terms grouped differently: on the left side we firstly do $$17−1=16$$, then do $$33−16$$. By contrast, on the right side we firstly do $$33−17=16$$ and then $$16−1$$. But with the rest we cannot apply the associative property, and therefore the equality is false.

Solution:

The equality is false.

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Say which of the following subtractions gives a natural number and compute the result:

a) $$85−62$$

b) $$62−85$$

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Development:

a) $$85$$ is bigger than $$62$$, so the result will be a natural number.

b) $$62$$ is less than $$85$$, so the result will not be a natural number.

Solution:

Only the first subtraction gives a natural number, and the result is: $$85−62=23$$.

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