Essentially we need to realize that problem solving with rational numbers is the same as any other kind of problem solving. Follow the steps

Understand the problem

Find all the crutial numbers and relationships or rules in the problem

Make a plan

What approach are you going to take – what can you figure out from what you have

Carry out the plan

Try out your plan and make some guesses at what the answer might be, check to see if they work with the rules that were given in the question

Look Back

Make sure that all aspects of the problem have been satified.

HELP SECTION:

for those of you who check this blog, I will help you complete one homework question, here’s #3

The number of kilometres in the perimeter of this park is 8 greater than the number of square kilometres in its area. What is the width? Use a calculator to help.

Understand the problem

Perimeter (2 x Length + 2 Width) is 8 more than the area (Length x width)

the length is 6 km

Make a plan

Im going to look at the diagram and estimate how big the width is, then find the perimeter, and the area and find the difference between them (subtraction)

Carry out the plan

The length looks about three times the width, so if the length is 6, I’m going to try 2 as the width.

Perimeter = 2l + 2w = 2 x 6 + 2 x 2

12 + 4 = 16

Area = l x w = 6 x 2 = 12

Perimeter – Area should be 8, 16 – 12 = 4

The result is too small, so I will try again with a width of 3

Perimeter = 2l + 2w = 2 x 6 + 2 x 3

=12 + 6 = 18

Area = l x w = 6 x 3 = 18

Perimeter – area should be 8, but 18-18 =0

So lets try going the other way, width of 1

Perimeter = 2l + 2w = 2 x 6 + 2 x 1

=12 +2 = 14

Area = l x w = 6 x 1 = 6

Perimeter – Area = 14 – 6 = 8

Look Back

We look back to see that the Perimeter of the park (2l + 2w)(2×6+2×1 = 14) – area of the park (l x w) (6×6=6) = 8