Subject: Algebra and how to balance equations
Name: Della
Who are you: Other

I'm a grandparent trying to help my grandkids with algebra. It's been awhile so I have forgotten some basics
With the following equations, how do you know whether you need to apply the multiplication or division rule of equality?

75% t = 18

120% w = 72


Hi Della

I like your use of the word balance as this is exactly the way you can think of these equations. For example consider your first equation. There are two sides and a balance point (equal sign) between them. The task is to manipulate the quantities on the two sides, all the time maintaining the balance, and conclude with the variable t alone on one side and a number on the other.

The first task is to interpret 75%. the term "percent" means per one-hundred so 75% is the fraction 75/100. Hence the first equation can be written

  75/100 t = 18

or in decimal form

0.75 t = 18.

To manipulate the equation, maintain the balance and leave t alone on the left side you can divide both sides by 0.75. Thus

0.75 t/0.7518/0.75

which is

t = 24.