Mathematical Glossary
Formal terminology
Difference
The difference between two numbers usually refers to the positive difference which is largest minus the smallest, so the difference between 4 and 7 is 7 - 4 = 3.
Product
The product of two or more numbers is the result of multiplying them both/all together, so the product of 5 and 7 is 35; the product of -8 and -2 is 16.
Quotient
The quotient of two numbers is the result of dividing one by the other. Usually it would refer to dividing the first number by the second, but in some cases the context might make it clear that it is appropriate to divide the largest by the smallest. The quotient of 18 and 6 would be 3.
Sum
The sum (or total) of two or more numbers is the result of adding both/all the numbers together, so the sum of 5 and 9 would be 14; the sum of 5, 3, 8 and 2 would be 18. Informally the word “sum” is often used to refer to any mathematical calculation.
Total
The total (or sum) of two or more numbers is the result of adding both/all the numbers together, so the total of 5 and 9 would be 14; the total of 5, 3, 8 and 2 would be 18.
Informal terms
“F.O.I.L.”
This is a common acronym used to teach the process of multiplying a pair of binomial brackets. A common example might be the expansion (or multiplying out) of (x + 3)(x + 7) as follows:
(x + 3)(x + 7)=x^2 + 7x + 3x + 21 = x^2 + 10x + 21
Whilst, properly understood, we are simply multiplying each term in the first bracket by each term in the second bracket, “F.O.I.L.” provides an aide memoire to ensure we don’t miss multiplying a particular pairing. It stands for:
First: multiply the first term in the first bracket by the first term in the second bracket.
Outer: multiply the outer terms (the first term in the first bracket and the second term in the second bracket!).
Inner: multiply the inner terms (the second term in the first bracket and the first term in the second bracket!).
Last: multiply the last term in the first bracket by the last term in the second bracket.