Why does 5/6 divided by 1/2 equal 5/6 multiplied by 2/1?
- print Print
- list Cite
Expert Answers
calendarEducator since 2011
write3,002 answers
starTop subjects are Math, Science, and Business
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`
Related Questions
- proof by induction that n(n² + 5) can be divided by 6?
- 1 Educator Answer
- 5/8 divided by 3
- 1 Educator Answer
- How do you divide mixed fractions like 1 1/2 divided by 3 1/4?Im confused Thank You!
- 2 Educator Answers
- 5/6·1/2+2/3÷4/3 How do I solve this problem?
- 1 Educator Answer
- What is 2 1/4 divided by 3/4
- 1 Educator Answer