Algebraic Fractions

by SuperMario
Last updated 7 years ago

Algebra I

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Algebraic Fractions

Example 3Find the value of x for the equation (x+4/3x-1)=(3x+4/7x-1)Solution!Cross multiply=7x^2+27x-4=9x^2+9x-4Reduce to 0 and treat it like quadratic equation=2x^2-18x=0Factorize=(x-9)(2x)=0(x-9)=0x=92x=0x=0x is either 9 or 0

Well,let's say 5 plate of chicken rice cost $x and 4 bowls of chicken noodle cost $x. If we are to buy 1 bowl of chicken noodle and one bowl of chicken rice,it would be easy for us to now apply it in real life. We must first find the cost of 1 plate of chicken rice,which is x/5 and 1 bowl of chicken noodle which is x/4. Now,to find the cost of 1 plate of chicken rice and one bowl of chicken noodle,add them up,which gives us x/4+x/5=5x/20+4x/20=$9x/20. Here is one of your so-called"ridiculous" way to apply algebra in real life

Now,algebraic fractions may sound very ridiculous to be applied in real life,but think carefully of the maths application,it is connected in real life by some method...

Real Life SituationWhen we are having our National Physical Fitness Award test,for the 2.4km run section,we are asked to run a distance of 2.4km. We for the first 1.2 km,we would usually be faster than the second 1.2km. The passing grade is 16 minute 50 second,our average speed must be at least 8 56/101km/h to pass. In order to check our speed,we can plot out an algebraic fraction,which is 2400/x+y. Whereas x is our timing for the first 1.2km and y is the second 1.2km. We can then plan out the time we take to run

Imagine you are asked to calculate the distance of a race's track. The track is square in shape. You thought of an idea,that is to cycle around the rectangular track. You used a bicycle that has an average speed of 15km/h to cycle around it. But at the first end of the rectangle(first quarter of the track),the bicycle broke down and you used another bicycle that has an average speed of 10km/h. You calculated that you took 1hour and 6 minutes to complete one round. But because the speed change at the first quarter,it affected the results. So,in this case,we can use algebraic fractions instead of travelling another round to solve this problem.We will use x as one side of the track.So,form an equation first,that is (x/15)+(3x/10)=1 1/10. Next,solve it. We will first simplify it,which is (2x/30)+(9x/30)=1 1/10 which is 11x/30=1 1/10,which is 110x=330.x=330/110=3km. Since x is one side of the track,we must find all side,which is to multiply by 4=3X4=12km. So the race is 12km long. This is how useful algebraic fractions can be in our daily life.

Real Life Situation

Example 4Make b the subject of the formula:a=Squareroot (3b-5)/(b+7)Solution!a^2=(3b-5)/(b+7)ba^2+7a^2=3b-53b-5-ba^2=7a^23b-ba^2=7a^2+5b(3-a^2)=7a^2+5b=(7a^2+5)/(3-a^2)Ans:b=(7a^2+5)/(3-a^2)



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