Trail and Improvement

The basic idea of trail and improvement is to keep trying different values of x that are getting closer and closer to the solution. Here is the method to follow:

Step 1:   Put two values into the equation that give opposite cases ( one too big, one too small).

Step 2:   Choose the next value between the two opposite cases.

Step 3:   Repeat STEP 2 until you have two numbers:

•   both to 1 d.p.
•   differing by 1 in the last digit ( e.g. 4.3 and 4.4)

These are the two possible answers.   

Step 4:    Take the exact middle value to decide which one it is.

To reduce a ratio to a simpler form, divide all the numbers in the ratio by the same thing ( a bit like simplifying a fraction. It is in its simplest form when theres nothing left you can divide by.

Example: Write the ratio 15:18 in its simplest form.

For the ratio 15:18, both numbers have a factor three, so divide them by three.

15:18 divided by three= 5:6

You cant reduce this any further. So the simplest form of 15:18 is 5:6.

Proportional Division: Example

 Jess, Mo and Greg share £9100 in the ratio of 2:4:7. How much does Mo get?

1) 2+4+7= 13 parts

2) £9100 divided by 13= £700 (=1 part)

3) 4 parts = 4 x 700 = £ 2800