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