Year 10 Interactive Maths - Second Edition

## Cross-Multiplication Method

Place the linear factors one above the other as shown below.

Multiply the numbers along the arms of the cross, and then add the products.  That is,
10 + 1 = 10x+ x = 11x.  This is not the middle term.

5 + 2 = 5x+ 2x = 7x.  This is the middle term.

###### Note:
• The solution is read across.
• 10 = 1 × 10 = 2 × 5 = 1 × 10 = 2 × 5
We did not try 1 × 10 and 2 × 5 because the middle term is positive.
• The answer can be checked using the Distributive Law.  That is:

#### Example 9

##### Solution:

Multiply the numbers along the arms of the cross, and then add the products.
14 + 1 = 14x+ x = 15x.
We reject this pair as the middle term is 9x.

7 + 2 = 7x+ 2x = 9x.  We accept this pair as the middle term is 9x.

x× – 4 + –3 = – 4x – 3x = –7x.  We accept this pair as the middle term is –7x.

###### Note:

We did not try 1 × 12, 2 × 6 and 3 × 4 because the middle term is negative.  Also, we did not try
2 × 6 and 1 × 12 because we have already obtained the middle term by using 3 × 4.

x × –7 + x × 1 = –7x + x = –6x.  We accept this pair as the middle term is –6x.

###### Note:

We did not try 1 × 7 because we have already obtained the middle term by using 1 × 7.

###### Note:

We did not try 1 × 8, 2 × 4 and 2 × 4 because we have already obtained the middle term by using 1 × 8.