Question

Multiply 6divde 13 by the reciprocal of -7 divide 16

Answer 1

Step-by-step explanation:

Show that 5/6-: 1/2 = 5/6 * 2/1 :

(1) One definition of division is multiplication by the multiplicative inverse. Thus dividing by 2 is the same as multiplying by 1/2 .

By this definition it is clear that dividing by 1/2 is the same as multiplying by the multiplicative inverse, which in this case is 2/1 .

(The multiplicative inverse for a real number a is the number b where a*b=b*a=1 . In general, this is the reciprocal of a or 1/a since a*1/a=1/a*a=1 for all real numbers except zero. This is one of the reasons that you cannot divide by zero -- it does not have a multiplicative inverse.)

(2) Write the problem as a "compound fraction":

(5/6)/(1/2) . In general we avoid compound fractions -- usually we try to eliminate the fraction in the denominator. We can accomplish this by multiplying numerator and denominator by 2/1 :

(5/6)/(1/2)=(5/6)/(1/2)*(2/1)/(2/1)=(5/6*2/1)/(1/2*2/1)=5/6*2/1

(3) We can rewrite the division problem as a multiplication problem. For example if 42-:7=6 then 42=6*7 . A closer example is to find 10-:1/2 . Then when we find an answer, say x, then we know that 10=1/2*x or x=20 . Thus if 5/6-:1/2=x then 5/6=1/2*x and x must be 10/6=5/6*2/1