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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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JordanDivision and multiplication are inverses of one another. As a result, division by a number is equivalent to multiplication by its reciprocal (or multiplicative inverse).
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Is dividing by 100 the same as multiplying by 0.1?
10
Is taking ½ of a number is the same as dividing by ½?
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.
Why is dividing by a number the same as multiplying by its reciprocal?
That is the definition of reciprocal.
Is multiplying a number by 2 is the same as halving that number?
no, dividing a number is halving it, multiplying iy by 2 is doubling it
Dividing one third is the same as multiplying by what number?
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
