User:Adamfuad

456's method
6 → (2,4) ; What this mean is that the numbers in location 2 and location 4 are multiply together

5 → (1,4) and (2,3) ; 1×4 + 2×3 ; The number in locations 1 and 4 are multiplied together and locations 2 and 3 are multiplied together then both are added together

4 → (1,3) ; 1×3

Example 1

Work out

6 → (4,3) ; 4 × 3 = 12

5 → (2,3) and (4,3) ; 2×3 + 4×3 = 6 + 12 = 18 4 → (2,3) ; 2×3 = 6

Partition method
Example

634 - 149

Answer = 485

Show working out

1. 10 - 9 + 4 = 5

2. 10 - 4 + 2 = 8

3. 5 - 1     = 4

Exercise

Subtract the following questions using partition method

Subtraction with borrowing
Exercise

Subtract the following questions

Simultaneous equations
Follow these basic rules when solving simultaneous equations

Note : Rules 1 and 2 work together

Example of simultaneous equations

Example 1. 3x + 4y = 3 x - 5y = 1

2. x2 - y = 3 2x + y = 5

So any two or more equations relating to each other are known as simultaneous equations

Solving simultaneous equations

1.

Solve for x and y 3x - 5y = - 1 2x + 5y = 16

Showing out

Apply the above rules

Rule 1 → Different signs 3x [-] 5y = - 1 2x [+] 5y = 16

Rule 2 → Same numbers 3x - [5]y = - 1 2x + [5]y = 16

So if we have rules 1 and 2 together, now we can solve for x and y 3x [- 5y] = - 1 2x [+ 5y] = 16 Rule 3 → Add 3x [- 5y] = - 1 2x [+ 5y] = 16 3x + 2x - 5y + 5y = - 1 + 16 5x + 0y = 15 So we have 5x = 15 ; note, by applying the above rules we have eliminate the variable y Rule 4 → Solve for x and y

Solve for x 5x = 15 x = 15 ÷ 5 x = 3

Solve for y To find the value of y, substituete the answer we got for x into one of the original equation

3x - 5y = - 1 ; Original equation x = 3 ; Substituting x into the above equation ↓    3x - 5y = - 1 3(3) - 5y = - 1 9 - 5y = - 1 -5y = - 1 - 9 -5y = - 10 y = - 10 ÷ ( - 5 ) y = 2

Example 2. 2x + 4y = 8 3x + 4y = 10

Show working out

By looking at the equations, we can see numbers 4 are same to both equations

 Rule 2 → Same numbers

2x + [4]y = 8 3x + [4]y = 10

Rule 1 → Different signs

To get different signs, we have to multiply one of the equation by a negative sign

(2x + 4y = 8) × (-1) ; we choose the top one! 3x + 4y = 10 we gets -2x - 4y = - 8 3x + 4y = 10

-2x [-] 4y = - 8 3x [+] 4y = 10

Rule 3 → Add

-2x [- 4y] = - 8 3x [+ 4y] = 10 we gets

-2x + 3x - 4y + 4y = - 8 + 10 x + 0y = 2

Rule 4 → Solve for x and y Solve for x x + 0y = 2 x = 2 Solve for y

Now substitute the answer of x into one of the original equation to find the value for y

2x + 4y = 8 ; Original equation, we choose the top one! x = 2 ; Substituting x into the above equation ↓     2x + 4y = 8 2(2) + 4y = 8 4 + 4y = 8 4y = 8 - 4 4y = 4 y = 1