Solve m+p+z/frac{1{2}+2/3+3/4}=4/4

$$\frac { m + p + z } { \frac { 1 } { 2 } + \frac { 2 } { 3 } + \frac { 3 } { 4 } } = \frac { 4 } { 4 }$$

Solve for m

$$m=\frac{23}{12}-p-z$$

Steps for Solving Linear Equation

Add \frac{1}{2} and \frac{2}{3} to get \frac{7}{6}.

$$\frac{m+p+z}{\frac{7}{6}+\frac{3}{4}}=\frac{4}{4}$$

Add \frac{7}{6} and \frac{3}{4} to get \frac{23}{12}.

$$\frac{m+p+z}{\frac{23}{12}}=\frac{4}{4}$$

Divide 4 by 4 to get 1.

$$\frac{m+p+z}{\frac{23}{12}}=1$$

Divide each term of m+p+z by \frac{23}{12} to get \frac{m}{\frac{23}{12}}+\frac{p}{\frac{23}{12}}+\frac{z}{\frac{23}{12}}.

$$\frac{m}{\frac{23}{12}}+\frac{p}{\frac{23}{12}}+\frac{z}{\frac{23}{12}}=1$$

Subtract \frac{p}{\frac{23}{12}} from both sides.

$$\frac{m}{\frac{23}{12}}+\frac{z}{\frac{23}{12}}=1-\frac{p}{\frac{23}{12}}$$

Subtract \frac{z}{\frac{23}{12}} from both sides.

$$\frac{m}{\frac{23}{12}}=1-\frac{p}{\frac{23}{12}}-\frac{z}{\frac{23}{12}}$$

The equation is in standard form.

$$\frac{12}{23}m=-\frac{12p}{23}-\frac{12z}{23}+1$$

Divide both sides of the equation by \frac{12}{23}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{12}{23}m}{\frac{12}{23}}=\frac{-\frac{12p}{23}-\frac{12z}{23}+1}{\frac{12}{23}}$$

Dividing by \frac{12}{23} undoes the multiplication by \frac{12}{23}.

$$m=\frac{-\frac{12p}{23}-\frac{12z}{23}+1}{\frac{12}{23}}$$

Divide 1-\frac{12p}{23}-\frac{12z}{23} by \frac{12}{23} by multiplying 1-\frac{12p}{23}-\frac{12z}{23} by the reciprocal of \frac{12}{23}.

$$m=\frac{23}{12}-p-z$$

Solve for p

$$p=\frac{23}{12}-m-z$$

Steps for Solving Linear Equation

Add \frac{1}{2} and \frac{2}{3} to get \frac{7}{6}.

$$\frac{m+p+z}{\frac{7}{6}+\frac{3}{4}}=\frac{4}{4}$$

Add \frac{7}{6} and \frac{3}{4} to get \frac{23}{12}.

$$\frac{m+p+z}{\frac{23}{12}}=\frac{4}{4}$$

Divide 4 by 4 to get 1.

$$\frac{m+p+z}{\frac{23}{12}}=1$$

Divide each term of m+p+z by \frac{23}{12} to get \frac{m}{\frac{23}{12}}+\frac{p}{\frac{23}{12}}+\frac{z}{\frac{23}{12}}.

$$\frac{m}{\frac{23}{12}}+\frac{p}{\frac{23}{12}}+\frac{z}{\frac{23}{12}}=1$$

Subtract \frac{m}{\frac{23}{12}} from both sides.

$$\frac{p}{\frac{23}{12}}+\frac{z}{\frac{23}{12}}=1-\frac{m}{\frac{23}{12}}$$

Subtract \frac{z}{\frac{23}{12}} from both sides.

$$\frac{p}{\frac{23}{12}}=1-\frac{m}{\frac{23}{12}}-\frac{z}{\frac{23}{12}}$$

The equation is in standard form.

$$\frac{12}{23}p=-\frac{12m}{23}-\frac{12z}{23}+1$$

Divide both sides of the equation by \frac{12}{23}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{12}{23}p}{\frac{12}{23}}=\frac{-\frac{12m}{23}-\frac{12z}{23}+1}{\frac{12}{23}}$$

Dividing by \frac{12}{23} undoes the multiplication by \frac{12}{23}.

$$p=\frac{-\frac{12m}{23}-\frac{12z}{23}+1}{\frac{12}{23}}$$

Divide 1-\frac{12m}{23}-\frac{12z}{23} by \frac{12}{23} by multiplying 1-\frac{12m}{23}-\frac{12z}{23} by the reciprocal of \frac{12}{23}.

$$p=\frac{23}{12}-m-z$$