# 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

 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