Question

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

$(-21)-(-10)$ ______ $(-31)+(-11)$

Answer 1

Step-1: Evaluate the left-hand side of the blank:

We have to find the value of $[(-21)-(-10)]$

The difference between two integers is calculated by adding the opposite of the integer that is being subtracted to another integer.

The opposite of $-10$ is $10$.

Adding $10$ to another integer, we get $(-21+10)$

The sum of a positive and a negative integer is calculated by subtracting the absolute value of the smaller number from the absolute value of the greater number and the result takes the sign of the number which has a greater absolute value.

So, $(-21+10)=-11$

Step-2: Evaluate the right-hand side of the blank:

We have to find the value of $[(-31)+(-11)]$

The sum of two negative integers is calculated by adding the integers absolute values and putting a minus sign in the result.

Absolute value of $-31$ $=31$

Absolute value of $-11$$=11$

Sum of absolute values: $31+11=42$

So, $[(-31)+(-11)]$$=-42$

Step-3: Compare the result of the evaluation of both the sides:

$-11>-42$

Hence, $(-21)-(-10)$ $>$ $(-31)+(-11)$.