Answer :
"Fact families" are a term teachers use to describe a set of three numbers where the first number and the second number add, subtract, multiply, or divide to make the third. Dividends exist only in division, so you want a set of numbers where the first divided by the second equals the third. An example of this would be
12 ÷ 4 = 3
Fact families are useful because we can reorder these numbers and realize that
3 × 4 = 12.
All of the numbers must be odd, so we're really just trying to find two odd numbers that mulitply together to make another odd number.
Looking at a multiplication table we see that two odd numbers multiplied together always make an odd number!
So now we just need to find as many pairs of odd numbers as we can that multiply to make a number less than 100.
This is actually really time consuming to work out--1 times 1, 1 times 3, all the way up to 1 times 99, makes 49 possible combinations with 1...3 times 1, 3 times 3, 3 times 5...3 times 33...16 possible combinations. 5 times 19, so 9 possible...7 times 13, so 6 possible...9 times 11, so 5 possible...11 times 9, 5 possible...you get the point. Then you end up with 310, divide by two because 3 x 4 is the same thing as 4 x 3 and we want to get rid of all the inverses...
and we get 155 as our final answer. My goodness. Working that out is so crazy time consuming that I'm almost certain there's something wrong with your question, that maybe the quotient should be less than 100. You should really just talk to your teacher if you're confused, it's their job to clear things up anyways.
P.S. I didn't actually work that out on paper, I used an algebraic calculator. ;)
12 ÷ 4 = 3
Fact families are useful because we can reorder these numbers and realize that
3 × 4 = 12.
All of the numbers must be odd, so we're really just trying to find two odd numbers that mulitply together to make another odd number.
Looking at a multiplication table we see that two odd numbers multiplied together always make an odd number!
So now we just need to find as many pairs of odd numbers as we can that multiply to make a number less than 100.
This is actually really time consuming to work out--1 times 1, 1 times 3, all the way up to 1 times 99, makes 49 possible combinations with 1...3 times 1, 3 times 3, 3 times 5...3 times 33...16 possible combinations. 5 times 19, so 9 possible...7 times 13, so 6 possible...9 times 11, so 5 possible...11 times 9, 5 possible...you get the point. Then you end up with 310, divide by two because 3 x 4 is the same thing as 4 x 3 and we want to get rid of all the inverses...
and we get 155 as our final answer. My goodness. Working that out is so crazy time consuming that I'm almost certain there's something wrong with your question, that maybe the quotient should be less than 100. You should really just talk to your teacher if you're confused, it's their job to clear things up anyways.
P.S. I didn't actually work that out on paper, I used an algebraic calculator. ;)
