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It is the same because in each scenario you are not changing the value.

An example:

Take the fraction 2/5. Let's multiply top and bottom by 3. We get 6/15.

As we have multiplied both top and bottom by the same amount we have not changed the value of the fraction (because the proportion between the two numbers is identical).

2/5 is equal to 6/15. In this case both are equal to 0.4. The same principle applies for division.

Likewise, dividing or multiplying something by 1 does not change the value. 0.4 * 1 = 0.4/1 = 0.4.

Q: Why is multiplying or dividing the numereator snd denominator by the same nonzero number the same as multiplyingor dividing the fraction by 1?

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Because multiplying or dividing them by the same NON-ZERO number does not alter their ratio.

This is because dividing by a number is the same as multiplying by its reciprocal.

Because doing so is equivalent to multiplying or dividing by x/x, which can be cancelled down to 1.

Because it is not how multiplication or division are defined.

Dividing a friction is multiplying by its reciprocal. The reciprocal of a fraction is the numerator and the denominator switched around.

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No you do not.

Because multiplying or dividing them by the same NON-ZERO number does not alter their ratio.

This is because dividing by a number is the same as multiplying by its reciprocal.

Because doing so is equivalent to multiplying or dividing by x/x, which can be cancelled down to 1.

because of mathematical equivalence: it doesn't change the result

Because it is not how multiplication or division are defined.

Dividing a friction is multiplying by its reciprocal. The reciprocal of a fraction is the numerator and the denominator switched around.

When you're dividing fractions ... or multiplying thrm ... they don't need to have the same denominator.

123.456 is changed into fraction by multiplying and dividing it by a number such that both denominator and numerator don't contain decimal. Multiplying and dividing by 100, we get 123.456 as 123456/100.

only when adding and subtracting

Yes. One method for dividing fractions is to multiply the numerator fraction by the reciprocal of the denominator fraction.

The numerator is the first nuber and the denominatoris the second.Ex. 1/2=1÷2=0.5