How to write equations &expressions

How to write equations and expressions

Very important but missed by most textbooks or teachers

Author: Mr Lam

Mathematician Vs Novelist

Novelist communicates their passion and imagination to his/her readers by alphabets.

Mathematician shows their ideas by symbols.

An English article has its standard formats or we called this “grammars”. Grammars can help the reader easier to read

Mathematical grammar

If a piece of mathematic work is written properly, readers from any country can understand it. In some sense, Mathematics has it own language for communicating ideas.

Similar to English, Mathematics also has “grammar”

Correct use of mathematical grammars can make the reader easier to understand the author.

Moreover, it can show the author’s understanding of the topics. Usually, an unintelligible mathematical work associated with unclear mathematical minds and ability

Equation and expression

These mathematical grammars are the ones commonly ignored by the students, not explicitly showed in the textbook, or not taught properly by their teachers.

This presentation is trying to address some of these common mathematical grammars in expressions and equations.

Equation Vs expression

Many students cannot tell the difference between an expression and an equation.

Equation has an equal sign e.g. Expression does not have an equal sign

e.g.

Nomination

Consider an expression: “”

and “5” are the terms of this expression “” and “” are the variables “7” is the coefficient of “2” is the coefficient of “-5” is the constant term or just simply “constant”

Consider another expression: “ “” , “” and ” are the factors of the above expression Technically 103 is also a factor, but more specifically

we call it coefficient

Coefficient

We usually write the coefficients in front of the variables, e.g. instead of

There is no need to write “1” in front of a variable, e.g. “” instead of “”, “” instead of “”

Multiplication

There are different ways to express multiplication. “”, “”, “

Note: The 1st expression is called a cross product.

The 2nd expression is called a dot product. The dot is in the middle and do not confused it with or The later is a decimal point, which is at the bottom between the numbers.

There are some differences between these symbols in advanced mathematics (vector). But in junior secondary school mathematics, they all means the same.

Quiz 1

Solve for

The correct answer is 12. If your answer is 4, then revise this power point again.

Quiz 2

Express the following expressions in fraction with denominator = 10

Answers:

More on multiplication

Because in algebra, we use “” a lot as our variable, we prefer to not use the cross product to avoid confusion.

can be just simply expressed as Some teachers may insist you need put

the variables in alphabetic order In my opinion, it is not totally necessary

as long as you are not missing any variables and putting the coefficient in the front.

Answer for equations

Bad Good

X=2 Vs 2=X

There is some very subtle difference between .

I can illustrate the difference in English as:

Crocodile is reptile but reptile is not crocodile. Therefore, it is better to express your

answer as

Instead of

Aligning equations***very important***

Working on equations, it is best to align all the equal signs on the same column

In general, no two equal signs should be occurred in one line.

Bad Good

Simplifying expressions

There are two formats for simplifying expression. Both are good as long as the equal signs are aligned in the same column

Omission

Think about this English paragraph: Tom lives with his parents. Tom has a

younger sister. Tom goes to see his friend very day. Tom loves chocolate cake. Tom’s mother is an accountant.

Do you feel the above paragraph clumsy? Can you improve it?

In mathematics, sometimes we purposely omit the terms on the left hand side if they are not changing. This is to make the workout much neater.

Example of omission

Good Better (neater)

Although the work out in the first column including the answer is absolutely correct, but it looks clumsy, especially, if the equations is a complicated one. Also note: omission can only use for left hand side of the equations. If the right hand side does not change, we still need to rewrite the right hand side. See the highlighted red text in the above example.

Hand writing

Some teachers /schools insist students to write their “x” in this form:

I myself am not too fussy about this as long as you can make a consistent difference between “x” and “” (the multiplication sign) e.g.

Confusing symbols

Not to confuse z with 2Not to confuse l with 1

Not to confuse 6 with b Not to confuse g with y

These are only a few examples. You can name more, e.g. h and b, x and y, 5 with S, K with R, q with 9 and H with 1-1