Question

Evaluate:
$\left( {\dfrac{7}{8} \times \dfrac{{24}}{{21}}} \right) + \left( {\dfrac{{ - 5}}{9} \times \dfrac{6}{{ - 25}}} \right)$

Answer 1

Hint: Here, we are asked to find the value of $\left( {\dfrac{7}{8} \times \dfrac{{24}}{{21}}} \right) + \left( {\dfrac{{ - 5}}{9} \times \dfrac{6}{{ - 25}}} \right)$. For that first of all, try to bring the given fraction in simplest form. Then we will be using the BODMAS rule for solving this expression. According to the BODMAS rule, we first need to solve the brackets and then perform multiplication and addition.

Complete step-by-step answer:
In this question, we are given an expression and we have to evaluate its value.
The given expression is: $\left( {\dfrac{7}{8} \times \dfrac{{24}}{{21}}} \right) + \left( {\dfrac{{ - 5}}{9} \times \dfrac{6}{{ - 25}}} \right)$
So, here we have to add the multiplication of two fractions to the other multiplication of two fractions.
Let us solve this expression step by step.
When in an expression, more than one operation is given, we use the BODMAS rule.
B – Brackets
O – Order
D – Division
M – Multiplication
A – Addition
S – Subtraction
According to this rule, one must first carry out bracket operations, then order, then division, then multiplication, then addition and lastly subtraction.
So, here we have three operations – Multiplication, addition and brackets.
So, first we will solve brackets then carry out multiplication and then addition. Therefore,
 $ \Rightarrow \left( {\dfrac{7}{8} \times \dfrac{{24}}{{21}}} \right) + \left( {\dfrac{{ - 5}}{9} \times \dfrac{6}{{ - 25}}} \right)$
Now, first of all let us try to bring these fractions in simplest form.
$ \Rightarrow \left( {\dfrac{7}{8} \times \dfrac{{24}}{{21}}} \right) + \left( {\dfrac{{ - 5}}{9} \times \dfrac{6}{{ - 25}}} \right) = \left( {\dfrac{1}{1} \times \dfrac{3}{3}} \right) + \left( {\dfrac{1}{3} \times \dfrac{2}{5}} \right)$
Now carry out multiplication inside brackets first.
$ \Rightarrow \left( {\dfrac{7}{8} \times \dfrac{{24}}{{21}}} \right) + \left( {\dfrac{{ - 5}}{9} \times \dfrac{6}{{ - 25}}} \right) = \dfrac{3}{3} + \dfrac{2}{{15}} = 1 + \dfrac{2}{{15}}$
Now, we for the last operation, that is addition, take LCM
$ \Rightarrow \left( {\dfrac{7}{8} \times \dfrac{{24}}{{21}}} \right) + \left( {\dfrac{{ - 5}}{9} \times \dfrac{6}{{ - 25}}} \right) = \dfrac{{15 + 2}}{{15}} = \dfrac{{17}}{{15}}$
Hence, we have evaluated the value of $\left( {\dfrac{7}{8} \times \dfrac{{24}}{{21}}} \right) + \left( {\dfrac{{ - 5}}{9} \times \dfrac{6}{{ - 25}}} \right) = \dfrac{{17}}{{15}}$.

Note: Here, note that when a negative number is divided by a negative number, the answer will be positive. Let us see the sign convention for all the operations.
$ \Rightarrow $If both numbers are negative, then the division will be positive, if one negative and one positive then the division will be negative.
$ \Rightarrow $If both the numbers are negative, then the product will be positive, if one negative and one positive then the product will be negative.
$ \Rightarrow $For addition and subtraction, we consider the sign of the greatest integer between the two. For example: $5 - 7 = - 2$. Here, 7 is greater than 2, so we have taken the sign of 7 that is – for our answer.