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

Updated: 4/28/2022

Sophmillmill

Lvl 1
8y ago

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)

Wiki User

8y ago

Wiki User

8y ago

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).

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Q: Why is dividing by four the same as multiplying by one fourth?
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### Why is multiplying or dividing the numerator and the denominator by the same number the same as multiplying or dividing the fraction by 1?

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

### How is multiplying by 10 and dividing by 2 the same as multiplying by 5?

because there the same

### How would you divide one half by one fourth?

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.

### Why is multiplying or dividing the numerator and denominator by the same nonzero number the same as multiplying or dividing the fraction the fraction by 1?

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

### Could you answer Dividing a number by 2.5 is the same as multiplying a number by what?

it is the same as multiplying by 0.4

### Is taking ½ of a number is the same as dividing by ½?

No, taking &frac12; of a number is the same as dividing it by 2. Dividing a number by &frac12; is the same as multiplying it by 2.

### How is multiplying and dividing rational numbers similar?

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

### Why is multiplying or dividing the numerator and denominator by the same nonzero number the same as multiplying or dividing the fraction by 1?

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

### Which is the same as dividing by -3?

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