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  • hba

If a*b equals the remainder when a+b is divided by 12,then (11*10)*9=................

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  • hba
@sirm3d yes ?
yes it is.

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  • hba
Yes but how do i do it lol :D
(11 * 10) * 9 = (9) * 9 = 6
just perform the operation inside the parentheses first
  • hba
please dont confuse me
what is the value of 11 * 10 ?
  • hba
  • hba
or 11+10/2
that is not multiplication
its simple firstly solve the bracket 110 now divide it by 12 remainder is 2 multiply 2 by 9,its 18 divide 18 by 12 remainder is 6
a * b means you add a and b (a +b), divide by 12, and get the remainder
@nitz a * b = the remainder when (a + b) is divided by 12.
  • hba
11 * 10 means add the two numbers, divide the sum by 12, and get the remainder. so 11 * 10 = remainder in (11+10) divided by 12 or 11 * 10 = 2
Let a*b=R So that means we have \[\frac{a+b}{12}= Q+\frac{R}{12}\] Q is for Quotient I'm about to replace the remainder, R with a*b So we have \[12 \frac{a+b}{12}=12(Q+\frac{a*b}{12})\] \[a+b=12Q+a*b\] Solving for a*b gives us: \[a*b=a+b-12Q\]
\[11 * 10=11+10-12Q\] \[11*10=21-12Q\] Q=1 so we don't get a negative \[21-12(1)=21-12=9\]
don't mind the quotient. the result of the operation is the remainder only. FORGET the quotient Q
Now you try 9*9
Remainders shouldn't be negative is why I said take Q to be 1
\[\text{ \check} 10*11=9 =R\] \[\frac{10+11}{12}=\frac{21}{12}=Q+\frac{R}{12}=1+\frac{9}{12}\] 12 goes into 21 1 time
  • hba
Thanks a lot everyone.

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