8 3/7 + 5 5/7 = 13 8/7 = 14 1/7
6 3/5 / (7/8) = (33/5) / (7/8) = (33/5) * (8/7) = 264/35 = 7 19/35
7 * (5 + 3) - 4 = 7*8 - 4 = 56 - 4 = 527 * (5 + 3) - 4 = 7*8 - 4 = 56 - 4 = 527 * (5 + 3) - 4 = 7*8 - 4 = 56 - 4 = 527 * (5 + 3) - 4 = 7*8 - 4 = 56 - 4 = 52
The LCM is 840.
5/8 * 3/7 = 15/56
Add 5 in mod 8. (You can always subtract 3 in mod 8 as well, eg 5 + 3 = 0; 0 - 3 = 5.)
The remainder is 2. Knowing how to do modular arithmetic makes the problem much easier to solve. We say a number x has a value of k "mod" 7 if dividing x by 7 leaves a remainder of k. Multiples of 7 are equal to 0 mod 7 (they leave no remainder), and 32 is equal to 4 mod 7, because 32 / 7 = 4 remainder 4. The product of 100 5s is equal to 5 to the 100th power, or 5^100 in shorthand. Let us look at what the first few powers of 5 are equal to mod 7: 5^1 = 5 = 5 mod 7 5^2 = 25 = 4 mod 7 5^3 = 125 = 6 mod 7 5^4 = 625 = 2 mod 7 5^5 = 3125 = 3 mod 7 5^6 = 15625 = 1 mod 7 5^7 = 78125 = 5 mod 7 5^8 = 390625 = 4 mod 7 It looks as if we might have a repeating pattern, and indeed the next few powers of 5 are equal to 6, 2, and 3, confirming that 5^k = 5^(k-6) mod 7. This means that 5^100 has the same remainder after dividing by 7 as 5^94, which has the same remainder as 5^88, etc. etc. until we reach 5^4, which leaves a remainder of 2. Therefore by induction 5^100 leaves a remainder of 2. Hope this all makes sense.
3 = (3 + 5)/4 + 8 - 73 = 3*(5 - 4)*(8 - 7)
8 3/7 + 5 5/7 = 13 8/7 = 14 1/7
(7-5) * 3 + 8 2 * 3 + 8 6 + 8 ■
3
4(-5+7)+8(-8+5)4(+2)+8(-3)8+8(-3)8+-24-16
what is the median of these numbers 5 6 6 7 8 9 9 0 2 3 5 6 8 8 8 8 0 1 2 3 5 5 6 7 7 8 0 2 4 5 7 8
6 3/5 / (7/8) = (33/5) / (7/8) = (33/5) * (8/7) = 264/35 = 7 19/35
7 * (5 + 3) - 4 = 7*8 - 4 = 56 - 4 = 527 * (5 + 3) - 4 = 7*8 - 4 = 56 - 4 = 527 * (5 + 3) - 4 = 7*8 - 4 = 56 - 4 = 527 * (5 + 3) - 4 = 7*8 - 4 = 56 - 4 = 52
3 flip flops are required.
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