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pre algebra - 4/5p=2 3/10

by Lisa
(Elgin IL USA)











































Solve the following equation for "p".

4/5 p = 2 3/10

Although not absolutely necessary, this equation will be easier to solve if the mixed fraction (2 3/10) is converted to an improper fraction.

Comments for pre algebra - 4/5p=2 3/10

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Jan 05, 2011
Pre-algebra – Solve Equations with Fractions
by: Staff

The question:

by Lisa
(Elgin, IL, USA)


4/5p=2 3/10


The answer:

4/5p=2 3/10

I presume you mean

4/(5p) = 2 3/10

I’m going to proceed on that assumption


4/(5p) =2 3/10

Although not absolutely necessary, this equation will be easier to solve if the mixed fraction (2 3/10) is converted to an improper fraction.

Convert 2 3/10 to a single fraction

2 * 10 = 20
20 + 3 = 23

2 3/10 = 23/10


Substitute the improper fraction (23/10) for the mixed fraction (2 3/10)

4/(5p) = 23/10


Our goal is to rearrange the parts of the equation so that P is on one side of the equation (by itself), and everything else on the other side of the equation.

Each of the following steps is a step toward that goal.


Step 1: multiply each side of the equation by 5p. This will move the unknown variable P to the numerator of the fraction on the right side of the equation.

(4/5p) * (5p)=(23/10) * (5p)

(4/5p) * (5p/1)=(23/10) *(5p/1)


4* [(5p/(5p * 1)]=(23*5p)/(10*1)

4*(5p/(5p)=(23*5p)/10

4*1=(23p)*(5/10)

4 = (23p)*(1/2)


Next, we must eliminate all the numbers surrounding the P (on the right side of the equation). Remember, our goal is to rearrange the equation so that P is on one side of the equation (all by itself).

Step 2: multiply each side of the equation by 2. This will eliminate the ½ on the right side of the equation.


4 = (23p)*(1/2)

4 * 2= (23p) * (1/2) * 2

8= (23p) * (1/2) * (2/1)

8= (23p) * (2/2)

8= (23p) * 1

8= 23p


Step 3: divide each side of the equation by 23. This will eliminate the 23 on the right side of the equation, leaving the unknown variable P all by itself.



8/23= 23p/23

8/23= p * (23/23)

8/23= p * 1

8/23= p

The final answer: P = 8/23


Now, check the answer. Substitute 8/23 for P in the original equation.


4/[5(8/23)] = 23/10

4/(5 * 8/23) = 23/10

4/(40/23) = 23/10

(4/1)/(40/23) = 23/10

(4/1)*(23/40) = 23/10

(4 * 23)/(1*40) = 23/10

(23/1)*(4 /40) = 23/10

(23/1)*(1 /10) = 23/10

(23 * 1)/(1 * 10) = 23/10

(23)/(10) = 23/10

23/10= 23/10

Since both sides of the equation are equal to one another, our answer (P = 8/23) is correct.




Thanks for writing.


Staff
www.solving-math-problems.com



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