Question

For the following options fill in the blank with appropriate sign < , > or = .
$\begin{align}
  & a)(-8)+(-4)\_\_(-8)-(-4) \\
 & b)(-3)+7-(19)\_\_15-8+(-9) \\
 & c)23-41+11\_\_23-41-1 \\
 & d)39+(-24)-15\_\_36+(-52)-(-36) \\
 & e)-231+79+51\_\_-399+159+81 \\
\end{align}$

Answer 1

Hint: Now to fill the proper sign we will solve LHS and RHS of each expression. To solve the expression we will use two properties $\left( - \right)\times \left( - \right)=\left( + \right)$ and $\left( + \right)\times \left( - \right)=\left( - \right)$ . Now once we have the values we will compare them and place the correct sign.

Complete step by step answer:
Now consider the first expression.
\[(-8)+(-4)\_\_(-8)-(-4)\]
First consider the LHS of the expression
We have $\left( -8 \right)+\left( -4 \right)$
Now we know that $\left( + \right)\times \left( - \right)=\left( - \right)$ . Hence opening the bracket we get
LHS = $-8-4=-12$
Hence we have LHS = - 12
Now consider RHS
$\left( -8 \right)-\left( -4 \right)$
Now we know that $\left( - \right)\times \left( - \right)=\left( + \right)$ . Hence opening the bracket we get
RHS = $-8+4=-4$
Now we know that 4 < 12 hence we have$-4>-12$
Hence $(-8)+(-4)<(-8)-(-4)$

Now consider the second expression.
$(-3)+7-(19)\_\_15-8+(-9)$
First consider the LHS of the expression
We have $(-3)+7-(19)$
LHS = $(-3)+7-(19)=(-3-19)+7=-22+7=-15$
Hence we have LHS = - 15
Now consider RHS
$15-8+(-9)$
Now we know that $\left( + \right)\times \left( - \right)=\left( - \right)$ Hence opening the bracket we get
RHS = $15-8-9=15-17=-2$
Now we know that 2 < 15 hence we have$-2>-15$
Hence $(-3)+7-(19)<15-8+(-9)$

Now consider the third expression.
$23-41+11\_\_23-41-1$
First consider the LHS of the expression
We have $23-41+11$
LHS = $23+11-41=34-41=-7$
Hence we have LHS = - 7
Now consider RHS
$23-41-1$
RHS = $23-41-1=23-42=-19$
Now we know that 7 < 19 hence we have$-7>-19$
Hence $23-41+11>23-41-1$

Now consider the fourth expression.
$39+(-24)-15\_\_36+(-52)-(-36)$
First consider the LHS of the expression
We have $39+(-24)-15$
Now we know that $\left( + \right)\times \left( - \right)=\left( - \right)$ . Hence opening the bracket we get
LHS = $39-24-15=39-39=0$
Hence we have LHS = 0
Now consider RHS
$36+(-52)-(-36)$
Now we know that $\left( - \right)\times \left( - \right)=\left( + \right)$ Hence opening the bracket we get
RHS = $36-52+36=36+36-52=20$
Now we know that 0 < 22
Hence $39+(-24)-15 < 36+(-52)-(-36)$

Now consider the fifth expression.
$-231+79+51\_\_-399+159+81$
First consider the RHS of the expression
We have $-231+79+51$
LHS = $-231+130=-101$
Hence we have LHS = - 101
Now consider RHS
$-399+159+81$
RHS = $-399+240=-159$
Now we know that 101 < 159 hence we have$-101>-159$
Hence $-231+79+51>-399+159+81$

Note:
Note that if the signs change when we compare negative numbers that is if 4 > 2 then -2 > - 4 . Also keep a note of the sign while adding and subtracting if a bigger number is subtracted then we get a negative sign if a smaller number is subtracted then we get a positive sign.
For example we have 6 < 12 then 12 – 6 = 6 but 6 – 12 = - 6.