Left to Right Addition

To do math in your head (even faster than you can on paper), thinking in terms of left to right is easier for English speaker / writing as we do everything else the same way so why do when calculating do we go right to left?

The easiest two digit addition problems are those that do not require you to carry any number e.g. all like units sum to 9 or below

For example:

$$\begin{array}{r} 67 \\ + 12\ (10+2) \\ \hline \end{array}$$

Adding from left to right, you can simplify the problem by adding $67 + 10 = 77$; then add $77 + 2 = 79$

We can illustrate this as follows:

$$\underbrace{67+12}_{\text{(first add 10)}} \;=\; \underbrace{77+\,2}_{\text{(then add 2)}} \;=\; 79$$

The above diagram is a way of representing the mental process involved in calculating the answer using this method, this method does not require you to write anything done

Lets try a calculation that require you to carry a number

$$\begin{array}{r} 67 \\ + 28\ (20+8) \\ \hline \end{array}$$

Adding from left to right, you can simplify the problem by adding $67 + 20 = 87$; then add $87 + 8 = 95$

We can illustrate this as follows:

$$\underbrace{67+28}_{\text{(first add 20)}} \;=\; \underbrace{87+\,8}_{\text{(then add 8)}} \;=\; 95$$

for any three digit addition for that matter any addition this method can be used.