Solve 1/a*1/b=2/5*3/4

$$\frac { 1 } { a } \cdot \frac { 1 } { b } = \frac { 2 } { 5 } \cdot \frac { 3 } { 4 }$$

Solve for a

$$a=\frac{10}{3b}$$

$$b\neq 0$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 20ab, the least common multiple of a,b,5,4.

$$20b\times 1\times \frac{1}{b}=\frac{2}{5}\times \frac{3}{4}\times 20ab$$

Multiply 20 and 1 to get 20.

$$20b\times \frac{1}{b}=\frac{2}{5}\times \frac{3}{4}\times 20ab$$

Express 20\times \frac{1}{b} as a single fraction.

$$\frac{20}{b}b=\frac{2}{5}\times \frac{3}{4}\times 20ab$$

Multiply \frac{2}{5} and \frac{3}{4} to get \frac{3}{10}.

$$\frac{20}{b}b=\frac{3}{10}\times 20ab$$

Multiply \frac{3}{10} and 20 to get 6.

$$\frac{20}{b}b=6ab$$

Express \frac{20}{b}b as a single fraction.

$$\frac{20b}{b}=6ab$$

Cancel out b in both numerator and denominator.

$$20=6ab$$

Swap sides so that all variable terms are on the left hand side.

$$6ab=20$$

The equation is in standard form.

$$6ba=20$$

Divide both sides by 6b.

$$\frac{6ba}{6b}=\frac{20}{6b}$$

Dividing by 6b undoes the multiplication by 6b.

$$a=\frac{20}{6b}$$

Divide 20 by 6b.

$$a=\frac{10}{3b}$$

Variable a cannot be equal to 0.

$$a=\frac{10}{3b}\text{, }a\neq 0$$

Solve for b

$$b=\frac{10}{3a}$$

$$a\neq 0$$