What is a monomial?
Permalink Submitted by Dee (not verified) on 25 March, 2024In reply to "Implicit" multiplication by Don MacQueen (not verified)
Think back to 9th grade Basic Algebra class, when your teacher covered what a "term" is (specifically a monomial) & how to divide one monomial by another monomial.

The term "4x" is a monomial because it is a coefficient and a variable. Given that "x" does not equal zero, the monomial "4x" holds a single value, which is the coefficient of "4" multiplied by whatever "x" equals.

An example of the value of the value of a monomial would be if I said I had bought 4 dozen eggs, you would understand that " 4 dozen" is a single total quantity of eggs-- 4 cartons of a dozen eggs each equals a total quantity of 48 eggs. In other words...

4 dozen = 1 dozen + 1 dozen + 1 dozen + 1 dozen

In your local diner, if 4 dozen eggs were to be split evenly amongst 2 groups of a dozen people each, how many eggs would each customer get?

4 dozen eggs divided by 2 dozen customers

4 dozen ÷ 2 dozen

4(12) ÷ 2(12)

48 ÷ 24 = 2

Now replace "(12)" with the variable "x." The statement is now:

4x ÷ 2x or 4x / 2x

...which is also correctly written as 4x over 2x.

The like variable of "x" cancels out, leaving 4/2 or 4 over 2, which equals 2.

The calculation represents that each diner customer gets 2 eggs, no matter which division symbol is used (obelus, solidus, or vinculum) and/or if the word "dozen" is used (and if x = dozen)

Your 9th grade Basic Algebra teacher explained that a monomial never needs parentheses because it is ONE TERM with a SINGLE VALUE which is the PRODUCT of the coefficient multiplied by the variable. The coefficient cannot be "peeled off" & used in some other operation in a horizontally written division statement. A monomial does not need to be encase inside of parentheses any more than the term"4 dozen" needs parentheses around it to be understood as a total quantity of 48 -- it's the same implied multiplication by juxtaposition as "4x," which is a monomial.

What is a monomial?

Permalink Submitted by Dee (not verified) on 25 March, 2024In reply to "Implicit" multiplication by Don MacQueen (not verified)

Think back to 9th grade Basic Algebra class, when your teacher covered what a "term" is (specifically a monomial) & how to divide one monomial by another monomial.

The term "4x" is a monomial because it is a coefficient and a variable. Given that "x" does not equal zero, the monomial "4x" holds a single value, which is the coefficient of "4" multiplied by whatever "x" equals.

An example of the value of the value of a monomial would be if I said I had bought 4 dozen eggs, you would understand that " 4 dozen" is a single total quantity of eggs-- 4 cartons of a dozen eggs each equals a total quantity of 48 eggs. In other words...

4 dozen = 1 dozen + 1 dozen + 1 dozen + 1 dozen

In your local diner, if 4 dozen eggs were to be split evenly amongst 2 groups of a dozen people each, how many eggs would each customer get?

4 dozen eggs divided by 2 dozen customers

4 dozen ÷ 2 dozen

4(12) ÷ 2(12)

48 ÷ 24 = 2

Now replace "(12)" with the variable "x." The statement is now:

4x ÷ 2x or 4x / 2x

...which is also correctly written as 4x over 2x.

The like variable of "x" cancels out, leaving 4/2 or 4 over 2, which equals 2.

The calculation represents that each diner customer gets 2 eggs, no matter which division symbol is used (obelus, solidus, or vinculum) and/or if the word "dozen" is used (and if x = dozen)

Your 9th grade Basic Algebra teacher explained that a monomial never needs parentheses because it is ONE TERM with a SINGLE VALUE which is the PRODUCT of the coefficient multiplied by the variable. The coefficient cannot be "peeled off" & used in some other operation in a horizontally written division statement. A monomial does not need to be encase inside of parentheses any more than the term"4 dozen" needs parentheses around it to be understood as a total quantity of 48 -- it's the same implied multiplication by juxtaposition as "4x," which is a monomial.