How to Calculate Faster using Cancellation Part 2
In the previous post, we have learned how to use cancellation to reduce fractions to lowest terms and fractions. In this video, we are going to use cancellation in other calculations.
Multiplying Fractions by Whole Numbers
Example 1: Calculate .
As we have learned before, we can place 1 on the denominators of whole numbers. Therefore,
can be written as
From here, we can cancel 4 and 2 by dividing both of them by 2.
This gives us
Dividing Algebraic Expressions
From the expression, we can cancel 12 and 3 by dividing both the numerator and denominator by 3. This gives us 4/1. Next, we can divide by , where one can be cancelled. This leaves in the numerator.
Now, can be written as and can be cancelled. This leaves in the numerator. Therefore, the final answer is
Multiplying everything by 12, the least common multiple of 4 and 3, we have
We can cancel out 12 and 4 in the first term by dividing by 4. This leaves us 3(3)x = 9x in the numerator. In the second term, we can cancel out 12 and 3, which leaves 4(2) = 8 in the numerator. The right hand side becomes 96. The resulting equation is
If we want to solve the equation, we have
As we can see, cancellation is very useful in simplifying calculations. First it speeds up calculations and second it lessens the probability of computational errors because the numbers get smaller.