How do you express a math formula in words?

Question

My sister has a question on her assignment where she needs to express a formula in words. It's asking how many hand shakes would take place at a party if everyone shakes hands with each other, then it has the formula "S = n(n - 1) ÷ 2. Where "S" is the number of hand shakes and "n" is the number of people at a party." There are 12 people at the party, and she knows there will be 66 handshakes total using distributive law, but she's not sure how to "express the formula in words" as it's asking. Can anyone please help us out?

Answer 1

The number of handshakes that would take place at a party, if everyone shakes hands with each other:

"S = n(n - 1) ÷ 2, where "S" is the number of hand shakes and "n" is the number of people at a party":

S = 12(11) ÷ 2 = 66 handshakes

Answer 2

S equals n over 2, all into n minus one.

Answer 3

Greyhairs says: Write a pattern and look at the answers



1 person n = 1: S =1(1 - 1)/2 = 0

2 persons n = 2: S = 2(2 -1)/2 = 1

3 persons n = 3: S = 3(3 -1)/2 = 3

4 persons n = 4: S = 4(4 -1)/2 = 6

5 persons n = 5: S = 5(5 -1)/2 = 10

etc



the answers are ALL triangular numbers meaning 3 dots will form a triangle as will 6 dots and 10 dots.

10 dots form the triangle for ten pin bowling



the formula generates triangular numbers where n is the number of people shaking hands



Let me know if this is helpful

Answer 4

The number of hand shakes that would take place at a party if everyone shakes hands with each other:

"S = n(n - 1) ÷ 2", where "S" is the number of hand shakes and "n" is the number of people at a party."

S = 12(11)/2 = 66

Answer 5

the number of handshakes is half the product of the number of people times one less than number of people.

Answer 6

The total Sum of unique handshakes in a group of 12 people is found by multiplying the Number of people [(in this case, 12)] times that Number less/minus [pick one word]1 [( i e 12 - 1 = 11)] with that quantity divided by 2 [(to eliminate duplicate handshakes)].

Answer 7

S equals n times n-1, then divided by 2

Answer 8

Any one person can shake hands with 11 others.

So that you might say that there must be 12*11 total handshakes = 132

But that needs to be divided by 2 to take into account when A shakes B it also means that B has already shaken A.

So it would be 12*11/2 = 66

∴ the general formula for n people in the room

S = n(n-1)/2

Answer 9

I think this is an exercise to show how to think of a word problem to turn it into an equation by thinking about it backward.



Here's how I would think about this problem.



Let "n" be the number of people at a party. Every person must shake hands with everyone else (you can't shake hands with yourself).



So in an example of 5 people at a party, each person shakes hands with 4 other people. So that's why n is multiplied by (n - 1).



But if I'm shaking your hand, you are also shaking mine. So this would count as two shakes even though it's really only one. So that's why you divide the expression by 2, to eliminate the duplicates.



That's why the equation is:



S = n(n - 1) / 2



So when n = 12, we get:



S = 12(12 - 1) / 2

S = 12(11) / 2

S = 121 / 2

S = 66 handshakes.