How to teach equation solving

I got this question in my mailbox recently:

I am having a problem with show my son how to work out the proportion problem and solving equation by division, like 7.y=105 64=y.8 and find the missing term for the proportion of 3/4=x/16.

Can you help me out?

Always remember this problem solving strategy: when a problem is too difficult, make another, similar, but in some way easier problem, and observe for a strategy to solve that one.

If 7 ⋅ y = 105 and 64 = y ⋅ 8 are difficult, use easier examples first. Have him solve these ones:

2 ⋅ __ = 4
5 ⋅ x = 10
2 ⋅ x = 6


8 = 2 ⋅ __
12 = 3 ⋅ x
9 = 3 ⋅ x

If 'x' intimidates him, you can use an empty line.

Then ask him, HOW did he solve these ones? Well, chances are, of course, that he just 'sees' the answer, or remembers his multiplication tables and gets the answer from those.

But then SHOW him how division, in each case, gives us the answer too:

5 ⋅ x = 10. (We already know the answer is 2)
10 ÷ 5 gives the answer.

After going thru this, the initial problems should not be difficult. If they still do, then your son might have problems in understanding division concept and might need review in that area first.

Solving a proportion problem

One can solve the proportion 3/4 = x/16 in several different ways. This one is easy to solve thinking via fractions.

Essentially, you have two equivalent fractions: 3/4, and x/16. IF your son has difficulty solving this problem when it's written as fractions, then he should study again equivalent fractions.

Another way to solve this is to see it as an equation:
(number) = x/(number)
Can he solve easier equations such as 5 = x/2 or 2 = x/4 ?
Again, the opposite operation will work: x is divided by a number, so when solving, you need to multiply.

Hope this helps.
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