Question

Fill in the blank with $<$, $>$or $=$:

$45-(-11)\_\_\_\_\_57+(-4)$

Answer 1

Step 1: Evaluate the expression on the left-hand side (L.H.S)

L.H.S $=45-(-11)$

To subtract an integer $b$ from another integer $a$, we add the additive inverse of $b$ to $a$. So, $a-b=a+(-b)$

$\Rightarrow$L.H.S $=45+11$ ( as the additive inverse of $-11$ is $11$)

$\Rightarrow$L.H.S $=56$

Step 2: Evaluate the expression on the right-hand side (R.H.S)

R.H.S $=57+(-4)$

To find the sum of a positive and a negative integer, we subtract the absolute value of the smaller integer from the greater integer. Then, take the sign of the number which is greater in absolute value and put it with the result.

$\Rightarrow$R.H.S $=53$

Step 3: Compare L.H.S and R.H.S

L.H.S $=56$

R.H.S $=53$

L.H.S $>$R.H.S.

Hence, $45-(-11)>57+(-4)$.