Question

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

$(-4)+(-9)$ ______ $(-6)-(-8)$

Answer 1

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

We have to find the value of $[(-4)+(-9)]$

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

The absolute value of $-4$ is $4$.

The absolute value of $-9$ is $9$

Sum of absolute values: $(4+9=13)$

$[(-4)+(-9)]$$=-13$

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

We have to find the value of $[(-6)-(-8)]$

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

The opposite of $-8$ is $8$.

Adding $8$ to another integer, we get; $(-6+8)$

$=8-6$ ( Commutative property of addition: Two integers can be added in any order)

$=2$

So, $[(-6)-(-8)]$$=2$

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

$-13<2$

Hence, $(-4)+(-9)$ $<$ $(-6)-(-8)$