if a/b=c/d then a+b/c+d = a/b=c/d
For the equation A/B = C/D. Multiply both sides by B: A*B/B = C*B/D, then multiply both sides by D: A*B*D/B = C*B*D/D, then simplify (the B's cancel and the D's cancel): A*D = C*B
#include <stdio.h> #include <conio.h> int main() { int a,b,c,d; printf("Enter any 4 numbers"); scanf("%d%d%d%d",&a,&b,&c,&d); if(a>b&&a>c) { else if(a>d) printf("%d is greatest",a); } if(b>a&&b>c) { else if(b>d){ printf("%d is greatest",b); } if(c>a&&c>b) { else if(c>d) printf("%d is greatest",c); } else { printf("%d is greatest",d); } }
If: a = b+c+d Then: c = a-b-d
Suppose the two fractions are b/f and c/d.Then (b/d)/(c/d) = (b/d)*(d/c) = (b*d)/(c*d) = b/d.
If a=b and c=d then (a+c)=(b+d) ? This is proved very simply by the direct application of perhaps the most fundamental statement in all of Algebra: "If equals are added to equals, the sums are equal."
Suggested layouts . . . Just play ! ( Not sure if images will show . . . If not, here they are written out . . . Layout 01 - A, B, C, D, C, B, A D, C, A, B, A, C, D A, B, C, D, C, B, A D, C, A, B, A, C, D A, B, C, D, C, B, A D, C, A, B, A, C, D A, B, C, D, C, B, A D, C, A, B, A, C, D A, B, C, D, C, B, A Layout 02 - C, D, B, A, B, D, C D, B, A, D, A, B, D B, A, D, C, D, A, B A, D, C, B, C, D, A D, C, B, A, B, C, D A, D, C, B, C, D, A B, A, D, C, D, A, B D, B, A, D, A, B, D C, D, B, A, B, D, C Layout 03 - D, B, C, B, C, B, D A, D, B, C, B, D, A D, A, D, B, D, A, D C, D, A, D, A, D, C B, C, D, A, D, C, B C, D, A, D, A, D, C D, A, D, B, D, A, D A, D, B, C, B, D, A D, B, C, B, C, B, D Layout 04 - A, B, C, D, C, B, A B, A, B, C, B, A, B D, B, A, B, A, B, D C, D, B, A, B, D, C A, C, D, B, D, C, A C, D, B, A, B, D, C D, B, A, B, A, B, D B, A, B, C, B, A, B A, B, C, D, C, B, A
B b b d d b d d d c b a a a a d d b d d d c b a c b a g d b b b c b a g e g d b b b d d b d d d c b a c b a g e g b d d d d d c b d d d d d e b a c d c b d d d c b a c g c b c d d d d d c b c d d d d d e b a c d c b d d d c b a c g c b b c b b b b d d b d d d c b a a a d d b d d d c b a c b a g d d b b b c b a g e g b =)
The answer is 4! (4 factorial), the same as 4x3x2x1, which equals 24 combinations. The answer is 24 and this is how: A b c d A b d c A c d b A c b d A d c b A d b c B c d a B c a d B d a c B d c a B a c d B a d c C d a b C d b a C a b d C a d b C b d a C b a d D a b c D a c b D b c a D b a c D c a b D c b a
b d d b b c b b a b a c c d d b c b a d c a b c d a b c c a a d b d d b a a d b c a c d d c b b a
Nims 100 exam answers D C A B B D A C C D D A A B B C A B C D A B A Nims 200 exam answers B D B C B A D D B D C D A A B D C A B B C D A Nims 700 exam answers D A B D C D B A D B C C B B B A D B C C  Nims 800 exam answers A A C D B C C D B C A D B C D B D A C B
b d d b b c b b a b a c c d d b c b a d c a b c d a b c c a a d b d d b a a d b c a c d d c b b a
PLEASE NOTE ~ |= MEASURE SEPARATION ALL OF THE Ds ARE HIGH D AND OPEN D WILL BE WRITTEN IN ITALICS ( D )4/4 B B B B B B| B D G A B| C# C# C# C# C# B B|B A A B D|B B B B B B| B D G A B| C# C# C# C# C# B B B| D D C# A G| D B A G D | D B A G E | E C# B A F | D D C# A B| D B A G D | D B A G E | E C# B A D D D D | E-(high) D C# A G D| B B B B B B| B D G A B| C# C# C# C# C# B B|B A A B D| B B B B B B| B D G A B| C# C# C# C# C# B B B| D D C# A G|
A c b d a c c b d d a b a d a b b a c d c d c a b a b c c d a b a c
{a,b,c,d} {a,b} {a,c} {a,d} {b,c} {b,d} {c,d}
D c b , d c a , d c b b b , d c a , d c b , d c a , d c b b b , d c a
a c b d a a c d b a c d b c d d c a b c c d d d d c c b a b b a a d c d a a b b