Reducing Fractions
Short Course
This is a short course (slide show) in the basic concepts of reducing fractions..
Reducing a Fraction
One of the concepts we need to review is that two fractions can be considered to be equivalent (same) even though they have different numerators and different denominator, if a special condition exists. This condition is when an integer (the same integer) can be divided exactly (with no reminder) into both the numerator and the denominator. For example:
1/2 is equivalent (equal to) 3/6
Why is this true? Try to picture two pizzas (of the same size), next of each other. The pizza on the left is cut once down the middle giving 2 parts. If our friend eats 1 of the 2 pieces, we still have half the pizza left (the remaining piece). The pizza on the right is cut into 6 slices. If we eat 3 of the slices of this pizza, we still have 3 pieces remaining or half the pizza. The fraction 1/2 represents the remaining pizza from the pizza on the left and 3/6 represents the remaining pizza on the right. Both fractions represent half of their pizzas. The remaining portions of the two pizzas are the same (one half for the pizza on the right and one half for the pizza on the left). In this situation, we also say that both fractions are equivalent. The key point here is that fractions can be equivalent and not have same numerators and denominators.
In the world of fractions, calculating with smaller numbers is better than calculating with larger numbers. So, before we do any calculating, we need to make sure that both fractions are reduced to the smallest numbers possible. This is called reducing the fraction or simplifying the fraction to its “simplest terms”.
We reduce a fraction or simplify the fraction to it “simplest terms” by finding the fraction with the smallest numerator and denominator that is equivalent to it. How do we do this? We need to see if an integer (the same integer) can divide evenly into both the numerator and the denominator.
Using the larger fraction 3/6 from our example above, if we divide 3 into 3 (the numerator), we get 1. Also, if we divide 3 into 6 (the denominator), we have 2. So, by dividing 3 into both the numerator and the denominator, the equivalent fraction is 1/2 . Remember that same number must be used to divide both the numerator and the denominator. So 3/6 has been reduced to 1/2. The fraction is in its “simplest terms” because there isn’t another integer that can be divided into 1/2 to create a smaller equivalent fraction.
Let’s look at some more examples of finding reducing a fraction to its “simplest terms”. In these examples, when the numerator is smaller than the denominator, we don’t use an abacus to simplify the fraction in the example. However, when the numerator is larger than the denominator, we will simplify the fraction without an abacus and with by using the Double-A method.
Examples
Let’s look at some more examples of finding reducing a fraction to its “simplest terms”. In these examples, when the numerator is smaller than the denominator, we don’t use an abacus to simplify the fraction in the example. However, when the numerator is larger than the denominator, we will simplify the fraction using the Double-A method.
Example: Reduce 9 / 54
Example: Reduce 6 / 96
Example: Reduce 8 / 12
Example: Reduce 18 / 63
Example: Reduce 18 / 3
Example: Reduce 48 / 60
Example: Reduce 88 / 56