I ultimately want to find a way to, given a times table of any size, calculate whether a given number will appear, and how many times.Īlso, I'm pretty sure that for times tables 7x7 and below, more than half of the possible numbers are represented on the table, but for times tables above 7x7, less than half are represented. I'm also having trouble seeing the pattern (or patterns) in the numbers with four representatives. I'm having trouble accounting for why 16 and 36 have three representatives. 4 and 9 make sense to me, as they are squares within the basic range of the times table, so they are hit by themselves, their square root, and 1. The four with 3 are the remaining squares - 4, 9, 16, and 36. The 23 numbers with 2 instances are kind of the default I guess. This makes sense - squares don't fall into that 4x5 = 5x4 redundancy. The six numbers that have only 1 instance are all squares - those of 1, 5, 7, 8, 9, and 10.

They all have either 1, 2, 3, or 4 instances. I feel like the number 42 should be calculable from the natural log of 100 and 10, or something, but I can't really figure it out.Īlso, I counted the frequency of all the numbers represented. I couldn't figure out a satisfying reason like that for 75, 84, 96 and 98. I had to wonder, why 42? I counted the 58 non-listed numbers - most of them are either primes >10 or multiples of those primes.

There are 42 out of a possible 100 numbers represented.

The various resources listed below are aligned to the same standard. 24-25.I was looking at a 10x10 multiplication table, and I decided to count the unique products. 3 times (3x) Multiplication Table Simple and Easy to Print Related Resources The Multiplication and division resource above is aligned (wholly or partially) with standard 3OA07 taken from the Common Core Standards For Mathematics (see the extract below). And it has helped me with my kids homework. (We thank Arthur Benjamin for this method in The Magic of Math: Solving for X and Figuring out Why (2015), pp. 3 times table up to 100 - The 3 Times Table 1 3 3 2 3 6. We begin by adding the numbers in the first row. Here is a simple procedure to solve the problem. But remember when we (and Carl Friedrich Gauss (1777- 1855)) summed all the integers from one to one hundred? It was not difficult! The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with. When you first read the question, it seems intimidating. Multiplication tables from 1 to 100 In mathematics, a multiplication table is a mathematical table used to define a multiplication operation for an algebraic system. What is the sum of all 100 numbers in the multiplication table? Sum of All 100 Numbers in the Multiplication Table