Question

which number line models $-5 + (-8)$?

add.

$-5 + (-8) = \square$

Explanation:

Step1: Recall the rule for adding negative numbers

When adding two negative numbers, we add their absolute values and keep the negative sign. So, for \(-5 + (-8)\), we first find the absolute values of \(-5\) and \(-8\), which are \(5\) and \(8\) respectively.

Step2: Add the absolute values

Add the absolute values: \(5 + 8 = 13\).

Step3: Apply the negative sign

Since both numbers are negative, the result will be negative. So, \(-5 + (-8)=-(5 + 8)=-13\).

For the number line model: We start at \(-5\) (the initial point). Adding a negative number means moving to the left (in the negative direction) on the number line. The distance we move is the absolute value of the number being added, which is \(8\) units. Starting at \(-5\) and moving \(8\) units to the left: \(-5 - 8=-13\). So the first number line (the top one) models \(-5 + (-8)\) because it starts at \(-5\) and moves \(8\) units to the left to reach \(-13\), while the second number line moves only \(3\) units to the left (from \(-5\) to \(-8\), which is a move of \(3\) units, not \(8\)).

Answer:

The number line that models \(-5 + (-8)\) is the first one (the top number line). And \(-5 + (-8)=\boxed{-13}\)