With fractions, the relationship between the numbers, not the actual numbers themselves, is most important. Understanding how to multiply and divide fractions can give you a deeper understanding of why you can increase or decrease the numbers within a fraction without changing the value of the whole fraction.
When you multiply or divide any number by 1, the answer is the same number. This rule also goes for fractions, so
When a fraction has the same number in both the numerator and the denominator, its value is 1. In other words, the fractions
are all equal to 1. Look what happens you multiply the fraction
The net effect is that you’ve increased the terms of the original fraction by 2. But all you’ve done is multiply the fraction by 1, so the value of the fraction hasn’t changed. The fraction 6/8 is equal to 3/4.
Similarly, reducing the fraction 6/9 by a factor of 3 is the same as dividing that fraction by 3/3 (which is equal to 1):
So 6/9 is equal to 2/3.
