hba
If a*b equals the remainder when a+b is divided by 12,then (11*10)*9=................
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hba
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@sirm3d yes ?
nitz
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IS 6 THE ANSWER
sirm3d
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yes it is.
hba
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Yes but how do i do it lol :D
sirm3d
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(11 * 10) * 9
= (9) * 9
= 6
sirm3d
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just perform the operation inside the parentheses first
hba
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please dont confuse me
sirm3d
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what is the value of 11 * 10 ?
hba
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110
hba
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or 11+10/2
sirm3d
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that is not multiplication
nitz
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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
sirm3d
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a * b means you add a and b (a +b), divide by 12, and get the remainder
sirm3d
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@nitz a * b = the remainder when (a + b) is divided by 12.
hba
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SHOW ME THE WHOLE SOLUTION 0-0
sirm3d
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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
freckles
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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:
\[a*b=a+b-12Q\]
freckles
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\[11 * 10=11+10-12Q\]
\[11*10=21-12Q\]
Q=1 so we don't get a negative
\[21-12(1)=21-12=9\]
sirm3d
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don't mind the quotient. the result of the operation is the remainder only. FORGET the quotient Q
freckles
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Now you try 9*9
freckles
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Remainders shouldn't be negative is why I said take Q to be 1
freckles
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\[\text{ \check} 10*11=9 =R\]
\[\frac{10+11}{12}=\frac{21}{12}=Q+\frac{R}{12}=1+\frac{9}{12}\]
12 goes into 21 1 time
hba
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Thanks a lot everyone.