in this tutorial we are going to talk about reducing reducing fractions um the value of fraction is not changed if numerator and denominator are multiplied by the same number for example if we have a fraction 3 over 4 and we multiplied and if we multiply numerator and denominator by the same number for example 3 then as a result we have 9 over 12. and this right side will be equal to the left side so result is unchanged another example is say one over three and if you multiply both sides by the number five the result will be 5 over 15 and this is equal to this another example is 1 over 3 and if we multiply both sides by the number 2 the result will be this 2 over 6 and again these numbers are same numbers and this is called reducing fraction to higher terms because the numbers on the right side are bigger than left side so this is reducing fraction to higher terms we also have opposite reducing to lower terms it works to the opposite side for example 9 over 12 9 over 12. the both numerator and denominator can be divided by the same number say 3 and the result will be 304 and these two numbers are equal this is uh reducing to lower terms another example is 5 over 15 both side can be divided by 5 and result will be 1 over three and one over three is equal to five over fifteen one more example and two over six both side two can be divided by two and six can be divided by two and result will be one over three and one over three is equal to two over six again this is called reducing to lower terms reducing to lower terms to the lowest terms can be performed by dividing number numerator and denominator by gcd or once again we can reduce to the not lower but lowest terms by dividing numerator and denominator by a greatest common divisor example example example uh for example we have 108 or 144 if you watched previous tutorials you know what is gcd greatest common divisor of two numbers or several numbers in this case gcd of 108 and 144 will be equal to 36 and in other words 36 is greatest common divisor of the number 108 and 144 and we can write we can divide numerator and denominator by this gcd greatest common divisor this is divisor and this is the greatest device and result will be three over four we can actually reduce to the lowest terms this term is the lowest because we cannot divide the both side numerator and denominator and this is the finishing point we cannot divide both sides anymore but we can receive lowest terms not using gcd without calculation of gcd we we have to just divide the both sides again and again when it's possible uh let's reduce to the lowest term this fraction 108 over 144 obviously the boss both numbers are can be divided by number two we also know uh divisibility criterion for number two three four and so on for number nine watch our previous tutorials and if we divide both sides by number 2 the result will be 54 over 72.
here we write we divide it by number 2. next we can divide the both side again by the number 2 and the result will be 27 by 36 here we divided by 2 again and next it's easy to see that the both sides numerator and denominator can be divided by number 3 and result will be 9 over 12.
