Find the difference: -8.4 - (-2.65).

Step-by-step solution

1. 1

   Name the two operations before touching the digits. There are two different minus signs here: the one in front of $8.4$ is a sign (it tells you the number is negative) and the one before the bracket is an operation (subtract). Mixing them up is the reason this problem is asked at all, so keep them separate.

2. 2

   Rewrite subtraction of a negative as addition. For any numbers, $a-(-b)=a+b$. Removing a debt of $2.65$ leaves you $2.65$ better off, so

   $-8.4-(-2.65)=-8.4+2.65$

3. 3

   Compare absolute values to fix the sign of the answer. Now you are adding numbers with opposite signs. Write $-8.4$ as $-8.40$ so both have two decimal places. Since $|-8.40|=8.40$ is larger than $|2.65|=2.65$, the sum keeps the sign of $-8.40$, i.e. the answer is negative.

4. 4

   Subtract the smaller absolute value from the larger.

   $8.40-2.65=5.75$

   Attaching the negative sign found in the previous step:

   $-8.40+2.65=-5.75$

5. 5

   Check with fractions to rule out a decimal slip. In exact form $-8.4=-\dfrac{42}{5}$ and $2.65=\dfrac{53}{20}$, so

   $-\frac{168}{20}+\frac{53}{20}=-\frac{115}{20}=-\frac{23}{4}=-5.75$

   The fraction route gives the same value, confirming $-5.75$.