A Faster Way: Adding and Subtracting Without Expanded Form!

I’m going to let you in on a little secret—while our meowntains have been adorable and everything, there’s a faster way to add and subtract….

THREE WAYS TO ADD + SUBTRACT

You know what’s better than having to draw pictures for everything? Writing stuff in expanded form. You know what’s better than writing stuff out in expanded form? Just writing the answer! Here’s a comparison of the three different ways we can do this problem:

361 + 124 = 485

With pictures:

Wow, that’s a lot of drawing! Here’s that same problem, but using our stretching-kitty expanded form instead of drawing pictures:

And here’s that same problem again, the shortest way (shortcut!):

All we do is add directly down in each column, and we always start with the ones place. So we’ll do: 1 + 4 = 5 in the ones place, 6 + 2 = 8 in the tens place, and 3 + 1 = 4 in the hundreds place. We can circle them, but we don’t have to!

And here’s how the shortcut looks for the subtraction problem we did in #1 on page 112:

We just subtract down in each column: 5 − 5 = 0 in the ones place, 2 − 0 = 2 in the tens place, and 7 − 2 = 5 in the hundreds place. So much faster, right?

This last method is the fastest, but everybody is different, so see which method you like the most and use that one.

Can you feel your brain getting stronger?

When we see a problem like 732 + 61 with different numbers of digits, it can be tricky to line everything up correctly, and if we don’t, we might get the wrong answer!

So we should always ask, “Which digits are in the ones place?” Here, it’s the 2 and 1, so we’d make sure they are stacked up, kitty-style. “Which digits are in the tens place?” Here, it’s the 3 and 6, so we should make sure they’re lined up, too. Then we can add directly down in each column and we get the right answer! See what I mean? Also, notice that since we had 7 hundreds to start off with, and we didn’t add any hundreds, we still have 7 hundreds in the answer.