Question

Add the following numbers using a number line.
a) \[ - 7 + 2\]
b) \[1 + ( - 5)\]
c) \[ - 9 + 5\]
d) \[8 + ( - 3)\]
e) \[9 + ( - 9)\]
f) \[ - 8 + ( - 5)\]
g) \[ - 3 + ( - 1)\]
h) \[4 + ( - 9)\]

Answer 1

- Hint: In the number line the midpoint is 0 and the left side contains negative values and right side contains positive values. While addition the number moves towards right and while subtraction the number moves towards left.
Also this\[ + \left( - \right)\] represents subtraction.

Complete step-by-step solution -
a) We have \[ - 7 + 2\]
Let us mark -7 on the number line since it is an addition of 2 we move it right two steps there we have -5.
Start at -7 and move 2 places to the right:

From number line we get,\[ - 7 + 2 = - 5\]

b) We have \[1 + ( - 5)\]
Let us mark 1 on the number line since it is given the representation\[ + \left( - \right)\]therefore we have to subtract 5 to it so we move it left five steps where we have -4.
Start at 1 and move 5 places to the left:

From the number line we have,\[1 + ( - 5) = - 4\]

c) We have \[ - 9 + 5\]
Let us mark -9 on the number line since it is an addition of 5 we move it right five steps where we have -4.
Start at -9 and move 5 places to the right:

From number line we have, \[ - 9 + 5 = - 4\]

d) We have \[8 + ( - 3)\]
Let us mark 8 on the number line since it is given the representation\[ + \left( - \right)\]therefore we have to subtract 3 to it so we move it left five steps there we have 5.
Start at 8 and move -3 places to the left:

From number line we have,\[8 + ( - 3) = 5\]

e) We have \[9 + ( - 9)\]
Let us mark 9 on the number line since it is given the representation\[ + \left( - \right)\]therefore we have to subtract 9 to it so we move it left nine steps where we have 0.
Start at 9 and move -9 places to the left:

From number line we have, \[9 + ( - 9) = 0\]

f) We have \[ - 8 + ( - 5)\]
Let us mark -8 on the number line since it is given the representation\[ + \left( - \right)\]therefore we have to subtract 5 to it so we move it left five steps there we have -13.

From number line we have\[ - 8 + ( - 5) = 13\]

g) We have \[ - 3 + ( - 1)\]
Let us mark -3 on the number line since it is given the representation\[ + \left( - \right)\]therefore we have to subtract 1 to it so we move it left one step where we have -4.
Start at -3 and move 1 places to the left:

From number line we have, \[ - 3 + ( - 1) = - 4\]

h) We have \[4 + ( - 9)\]
Let us mark 4 on the number line since it is given the representation\[ + \left( - \right)\]therefore we have to subtract 1 to it so we move it left nine steps where we have -5.
Start at 4 and move 9 places to the left:

From number line we have, \[4 + ( - 9) = - 5\]

Note:
Here \[ + \left( - \right)\] represents subtraction because we know that product of positive and negative numbers is negative here\[ + \left( - \right)\]is nothing but \[( + 1) \times \left( { - 1} \right)\]which is nothing but \[ - 1\]that is \[\left( - \right)\]hence we do subtraction throughout the problem.