Find the sum.

$52+(-30)+(-46)$

To add two numbers with similar signs, add their absolute values and keep the similar sign with the resulting number.

To add two numbers with opposite signs, subtract the absolute value of smaller number from absolute value of larger number and keep the sign of larger number with the resulting number.

If two positive numbers 2 and 3 are added, then the resulting sum will be$2+3=5$ , which is positive as well.

And if two negative numbers$-2$ and$-3$ are added, then the resulting sum will be $(-2)+(-3)=-5$, which is negative as well.

The sum of the numbers$7-3=4$ is positive because the larger number is positive as well.

And the sum of the numbers$3-7=-4$ is negative because the larger number is negative as well.

To evaluate the sum$52+(-30)+(-46)$, add the first two numbers and then add the resulting number with the last number.

Observe that first two numbers have different signs so they will get subtracted.

So, subtract the smaller number from the larger number and put the sign of larger number with the resulting number as shown below

$52+(-30)+(-46)=22+(-46)$

Again, observe that the resulting numbers have different signs so they will get subtracted.

So, subtract the smaller number from the larger number and put the sign of larger number with the resulting number as shown below

$\begin{array}{c}52+(-30)+(-46)=22+(-46)\\ =-24\end{array}$

Thus, the value of the given sum is$-24$ .