Question

Find the difference.

$-15-(-17)$

Short answer

The difference of the expression is 2.

Step-by-step solution

Apply the concept of adding or subtracting integers 

Rule: The sum of any integer and its opposite is equal to zero.

Rule: Adding two positive integers always gives a positive integer; adding two negative integers always gives a negative integer.

Rule: To find the sum of a positive and a negative integer, take the absolute value of each integer and then subtract these values.

Explanation: How to add or subtract the integers.

To add two numbers with the same sign, first add the two numbers then put their common sign before the answer.

To add two numbers with the opposite sign, subtract the smaller number from the bigger number. Then put the sign of the bigger number before the answer.

Example of addition and subtraction.

An example of addition is: 5 + 11 + 3 = 19.

Example: If a = 7 and b = 8, find the value of a + b and a – b

To evaluate the expressiona + b, substitute the value of a as 7 and the value of b as 8 and add the numbers as shown below,$a+b=7+8=15$

and$a-b=7-8=-1$

Find the difference:  – 15 – (– 17) 

To add two integers, we need to check the signs of those two integers.

Rule:To add two numbers with the opposite sign, ignore their signs and subtract the smaller number from the bigger number. Then put the sign of the bigger number before the answer.

Consider the provided expression:$-15-\text{\hspace{0.17em}\hspace{0.17em}(\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}17\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}}$

Double negative is positive. We can write:$-\text{\hspace{0.17em}\hspace{0.17em}(\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}17\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}}+17$

The difference of the expression is obtained as:$-15-\text{\hspace{0.17em}\hspace{0.17em}(\hspace{0.17em}\hspace{0.17em}}-\text{\hspace{0.17em}\hspace{0.17em}17\hspace{0.17em}\hspace{0.17em})\hspace{0.17em}\hspace{0.17em}=\hspace{0.17em}\hspace{0.17em}}-15+17=2.$

The required difference is2.