Question

Solve:

$\frac{2}{5}\times -\frac{3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}$

Answer 1

Step 1: Use ODMAS and simplify the given expression

The given equation is:

$\frac{2}{5}\times -\frac{3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}$

We, solve it using ODMAS, so the given equation can be represented as:

$\frac{2}{5}\times -\frac{3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}=-\frac{6}{35}-\frac{1}{14}-\frac{9}{35}$

Step 2: Finding the L.C.M of the denominator terms

Now, to simplify the fractions, we take the L.C.M of the denominators $35,14$ as shown below:

$$\begin{gathered} 14=2\times 7 \\ 35=5\times 7 \end{gathered}$$

So, L.C.M is $70$. Thus, we get:

$\begin{array}{rcl}-\frac{6}{35}-\frac{1}{14}-\frac{9}{35}& =& -\frac{12}{70}-\frac{5}{70}-\frac{18}{70}\\ & =& \frac{-12-5-18}{70}\\ & =& -\frac{35}{70}\\ & =& -\frac{1}{2}\end{array}$

$\therefore \frac{2}{5}\times -\frac{3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}=-\frac{1}{2}$

Hence, the value of given expression is $-\frac{1}{2}$