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This is just an example of a more general rule: dividing by a number is the same as multiplying by the reciprocal (multiplicative inverse). You might say that division can be DEFINED that way. Here is one way to make it look plausible:Take a number - say, 10 - then multiply it by 4, and then multiply it by 1/4. What do you get?

10 x 4 x 1/4 = 10 x (4 x 1/4) = 10 x 1 = 10

Since the product of a number and its multiplicative inverse, by definition, is 1.

But since multiplying by 4 and dividing by 4 are inverse operations, you also get the same result if you first multiply by 4, then divide by 4:

10 x 4 / 4 = 10 (because of the multiplicative inverse)

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Division and multiplication are inverses of one another. As a result, division by a number is equivalent to multiplication by its reciprocal (or multiplicative inverse).

Q: Why is dividing by four the same as multiplying by one fourth?

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10

No, taking ½ of a number is the same as dividing it by 2. Dividing a number by ½ is the same as multiplying it by 2.

That is the definition of reciprocal.

no, dividing a number is halving it, multiplying iy by 2 is doubling it

Dividing by any fraction is the same as multiplying by that fraction's reciprocal. To find a fraction's reciprocal on a calculator, simply raise the fraction to the power of -1. In this case, dividing by 1/3 is the same as multiplying by (1/3)-1 = 3. For example, 8 / 1/3 = 8 x 3 = 24

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no

10

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

because there the same

Dividing by a fraction is mathematically identical to multiplying by its reciprocal, so a half divided by one over four is the same as a half multiplied by four over one and the answer is 2.If you meant to multiply a half by a fourth, the answer would be one-eighth.

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

it is the same as multiplying by 0.4

No, taking ½ of a number is the same as dividing it by 2. Dividing a number by ½ is the same as multiplying it by 2.

Dividing by a non-zero rational number is the same as multiplying by its reciprocal.

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

Multiplying by -1/3

1/2