Division defined. The result of dividing a real number a by a real number b is that real number c such that a = b · c. In other words, division is defined in terms of multiplication, which we studied in the previous section. |
Division (of a non-zero number) by zero is undefined. The reason is this. Suppose that it was possible that a / 0 (where a is non-zero) could equal some number c. Then by the definition of division this would mean that a = 0 · c. But this is impossible because zero times anything is zero. Zero divided by zero is indeterminate. (Indeterminate means that 0 / 0 could equal any number c.) The reason is that by the definition of division this means that 0 = 0 · c. But this is true for any number c whatsoever. |
Reciprocals. Two numbers whose product is 1 are called reciprocals. |
4/5 and 5/4 are reciprocals becauseJust as subtraction can be replaced by the addition of a negative so division can be replaced by multiplication by a reciprocal:
8 and 1/8 are reciprocals because
The division of a by b is equivalent to the multiplication of a by the reciprocal of b : |
replace this division by this multiplication
by the reciprocal
Algebra Coach Exercises |