## hba 3 years ago If a*b equals the remainder when a+b is divided by 12,then (11*10)*9=................

1. hba

@sirm3d yes ?

2. nitz

3. sirm3d

yes it is.

4. hba

Yes but how do i do it lol :D

5. sirm3d

(11 * 10) * 9 = (9) * 9 = 6

6. sirm3d

just perform the operation inside the parentheses first

7. hba

8. sirm3d

what is the value of 11 * 10 ?

9. hba

110

10. hba

or 11+10/2

11. sirm3d

that is not multiplication

12. nitz

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

13. sirm3d

a * b means you add a and b (a +b), divide by 12, and get the remainder

14. sirm3d

@nitz a * b = the remainder when (a + b) is divided by 12.

15. hba

SHOW ME THE WHOLE SOLUTION 0-0

16. sirm3d

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

17. freckles

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: $a*b=a+b-12Q$

18. freckles

$11 * 10=11+10-12Q$ $11*10=21-12Q$ Q=1 so we don't get a negative $21-12(1)=21-12=9$

19. sirm3d

don't mind the quotient. the result of the operation is the remainder only. FORGET the quotient Q

20. freckles

Now you try 9*9

21. freckles

Remainders shouldn't be negative is why I said take Q to be 1

22. freckles

$\text{ \check} 10*11=9 =R$ $\frac{10+11}{12}=\frac{21}{12}=Q+\frac{R}{12}=1+\frac{9}{12}$ 12 goes into 21 1 time

23. hba

Thanks a lot everyone.