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To solve

a+6 4

____ = _____

12 3

Can I multiply the numerator and denominator of the right side by 4? Then do I cancel the denominators? Does this work every time? Thanks!

The number 4 only works because 12/3 = 4.

Since 3 goes into 12, multiply both sides by 12.

This gives a+6 = 12*4/3.

Now since 12/3 = 4, that is a+6 = 4*4 = 16.

Subtracting 6 from both sides gives a = 16-6 = 10.

As another result, they could be cross multiplied, as in 3(a+6) = 4*12.

That gives 3a + 18 = 48. Subtract 18 from both sides and get 3a = 30.

Dividing both sides by 3 gives a = 10, which is the same as the other way.

Algebra

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