- #1
AndersHermansson
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Multiplication is defined as repeated addition.
3x5 = 5+5+5
How do we define 10/2?
3x5 = 5+5+5
How do we define 10/2?
Originally posted by Hurkyl
Multiplication is generally defined as satisfying the particular axioms. When multiplying integers, it reduces to "repeated addition", but "repeated addition" doesn't extend to quantities like 3.7 * 4.1.
Division is generally defined as multiplication by a multiplicative inverse.
Originally posted by Doctor Luz
Repeated adition is not satisfied enven with negative integers.
Not sure here, but how can you define division when using the word INVERSE? INVERSE as in RECIPROCAL means DIVIDING into ONE.
It kind of does work.
Originally posted by Hurkyl
Definition: y is a multiplicative inverse of x iff y * x = x * y = 1
Compare with inverses of functions; a function g is a function of f if f.g = g.f = i (where i is the identity function and . means function composition)
Definition: for nonzero y, (x / y) is defined to be (x * z) where z is the unique multiplicative inverse of y.
That is how you define division using the word inverse.
Of course, from here, it's a trivial exercise from here to show that (1/x) is the multiplicative inverse of x.
And incidentally, you did not arrive at 3.7 * 4.1 with repeated addition; you added 3.7 a few times then used a distinct operation.
What about -1 * -1?
Division is a mathematical operation that involves separating a quantity or group into equal parts or groups.
Division is typically represented by the symbol "÷" or "/", and can also be expressed as a fraction or with the words "divided by". For example, 10 ÷ 2 = 5, 10/2 = 5, and 10 divided by 2 = 5.
Division is the inverse operation of multiplication. This means that dividing a number by another number is the same as multiplying that number by the reciprocal of the second number. For example, 10 ÷ 2 is the same as 10 x 1/2.
Yes, there are several rules and properties that apply to division, including the commutative property, associative property, and distributive property. These properties dictate the order in which numbers can be divided and how they can be grouped together in a division problem.
Yes, division can result in a fraction or decimal if the dividend (the number being divided) is not evenly divisible by the divisor (the number doing the dividing). In these cases, the resulting quotient will be a fraction or decimal that represents the remainder of the division.