Simple cross multiplication method
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When to cross multiply and when to multiply across.
Cross multiplication method for adding fractions
Cross Multiply
To cross multiply is to go
from this: 812 = 23
to this: 8 × 3 = 12 × 2
How Does it Work?
Multiplying the top and bottom of a fraction by the same amount doesn't change its value.
Step 1: Multiply the top and bottom of the first fraction by the bottom number of the second fraction.
8 × 312 × 3 = 23
Step 2: Multiply the top and bottom of the second fraction by the bottom number that the first fraction had.
8 × 312 × 3 = 2 × 123 × 12
And Magic!
The bottom of both fractions is now 12 × 3
Step 3: We can get rid of the 12 × 3 (as we are dividing both sides by the same amount) and the equation is still true:
8 × 3 = 12 × 2
Job Done!
In practice, though, it is easier to skip the steps and go straight to the "cross-multiplied" form.
Using Variables
The general case, using variables instead of numbers, is:
To cross multiply is to go from this:ab = cd
To this:ad = bc
To remember think cross (x) multiply:
Cross multiplication can help speed up a solution.
Like in this ex
- when is dot and cross product used
- when can i use cross multiplication