reverse three digit subtraction

Question

I cannot get this. How does it work? Like what is the concept in this?

Imagine $895 - 598$:

• Step 1. $8 - 5 = 3$ (I got $8$ and $5$ from the hundreths place in the numbers I am subtracting)
• Step 2. $3 × 100 = 300$ ($100$ is because $8$ and $5$ were originally from the hundreths)
• Step 3. $300 - 3 = 297$ (Subtract the answer from step 2 from the answer from step 1.)
• Final result. $297$ is the answer to $895 - 598$.

Answer 1

Let the number be $a \cdot 10^2 + b \cdot 10 + c$, the reverse is $c \cdot 10^2 + b \cdot 10 + a$

Hence subtracting them gives us $$(a-c)\cdot 10^2-(a-c)$$

In the first step, you computed $a-c$.

In the second step, you computed $(a-c)\cdot 10^2$

In the third step, you computed $(a-c) \cdot 10^2-(a-c)$.

Answer 2

Simply, $$895-598=\left(8\times10^2+9\times10^1+5\times10^0\right)-\left(5\times10^2+9\times10^1+8\times10^0\right)=\left(8\times10^2-5\times10^2\right)+\left(9\times10^1-9\times10^1\right)+\left(5\times10^0-8\times10^0\right)=3\times10^2+0\times10^1+\left(-3\times10^0\right)=300-3=297$$