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There are 22 ways to make change from a dollar using nickels, dimes, and quarters. 1. 4 q 2. 10 d 3. 20 n 4. 2 q , 5 d 5. 3 q , 2 d , 1 n 6. 1 q , 7 d, 1 n 7. 9 d, 2 n 8. 8 d, 4 n 9. 7 d, 6 n 10. 6 d , 8 n 11. 5 d , 10 n 12. 4 d , 12 n 13. 2 d , 16 n 14. 1 d , 18 n 15. 5 n , 3 q 16. 3 n , 1 q , 6 d 17. 7 n , 1 q , 4 d 18. 9 n , 1 q , 3 d 19. 11 n , 1 q , 2 d 20. 13 n , 1 q , 1 d 21. 14n , 3 d 22. 15n , 1 q
Suppose n/d is an improper fraction where, by definition, n > d.Divide n by d to give a quotient q and a remainder r. Then the equivalent mixed number is q r/d.
"Respective" means "in that order". So, for example, weights of 1 Newton, 2 N and 3 N at points p q and r respectively, menas a weight of 1 N at point p, 2 N at q and 3 N at r.
With a given fraction N/D, where N & D are integers [D not equal to zero]. Take any nonzero integer (p). Multiply both N and D by p:N/D = (N*p)/(D*p)Also, if N & D have any common factors {call it q}, then dividing N & D by q will give an equivalent fraction. So if the fraction is 6/16, let p = 3: the new fraction is 18/48. Since 6 and 16 have a common factor of 2, you can divide both 6 & 16 by 2 and get 3/8, which is equivalent to 6/16 and 18/48.Here are some more examples: a fraction equivalent to 1/2 would be 7/14. to reduce a fraction, find the Greatest Common Factor between the two sides. for example, if you were reducing 36/60, the greatest common factor between 36 and 60 would be 12. 36 divided by 12 is 3, and 60 divided by 12 is 5. so, a fraction equivalent to 36/60 would be 3/5. 3 and 5 cannot reduce any further.
Any polygon with 3n sides (n > 1) where every nth side is equal and every nth angle is equal: that is the sides and angles repeat in sets of n. For example a hexagon (n = 2) with sides of length x,y,x,y,x,y and angles of P,Q,P,Q,P,Q.