Activity: Algebra Class Activity B How gh-Fives? high-ies nally known as the han

Question

Activity: Algebra Class Activity B How gh-Fives? high-ies nally known as the handshake problem): There are 20 students ins t If every student 4ever other student, how many high-fives will there be?O two different expressions for the total number of high-fives among 20 students, Or Try to fin Eld involve addition, and the other esxpression should involve multiplication Explain why stands for the total number of high-fives. 10 haadsvape 2. Solve the I by evaluating one of the expressions Which expression is easiest to evaluate? 3. What if there were 50 students in the class? Write two expressions for the number of high-fives in this case; feel free to use an ellipsis (...) in one of your expressions! Explain why the expres sions stand for the number of high-fives. Then solve the high-five problem in this case. Which expression is easiest to use to solve the high-five problem?

Explanation / Answer

number of highfives = n *(n-1)/2

each person with other (n-1) person, hence n *(n-1) , but we have counted 2 times for eahc high-five
hence we have to divide by 2

= 20*19/2
= 190

in simpler way
first person will high-five 19 person , next will high five 18 and so on
19 +18+ ...=1   {sum of first 19 natural number}
= 19 * (19+1)/2
= 190

for n = 50

1+2+3+..49 = 50*49/2 = 1225

50*49/2 = 1225

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