How To Add Quickly, Part 2
Learn one more quick and dirty tip to help you kick your calculator dependency and make even faster calculations in your head.
Continuing our quest towards turning you into a quick-calculating machine, today we’re building upon with one additional very important tip that will help you to perform lightning-quick mental-addition.
The Traditional Adding Method: Working From Right-to-Left
Let’s kick things off by looking at the problem $132 + $8 + $58 + $29. Perhaps you’re doing some shopping and want to get a quick total before heading to the register to make your purchases. Let's first do the problem using the method everybody learns in school: that is, right-to-left style. Start by writing the problem down with the ones column lined up vertically:
I’m actually going to ignore the dollar signs for now to save some writing. Just remember, the addition problem works the same whether we’re talking about adding dollars, euros, potatoes, hiccups, or anything else. In other words, the problem is the same as:
Continuing to solve the problem via the traditional right-to-left method, let’s add the numbers in the ones column:
2 + 8 = 10, then
10 + 8 = 18, and finally
18 + 9 = 27.
Now, write the 7 below the ones column, then carry the 2 and write it above the tens column. In other words, take the total of 27 from the ones column and break it into 20 + 7, leaving the 7 in the ones column, and putting the 2 above the tens column where it represents 20.
Next add the numbers in the tens column:
2 + 3 = 5, then
5 + 5 = 10, and finally
10 + 2 = 12.
Of course, since this was the tens column, the sum of 12 actually represents 12 tens, which is 120. So, break this 120 into 100 + 20, write the two—which represents 20—below the tens column, then carry the one—which represents 100—and write it above the hundreds column.
Finally, add the numbers in the hundreds column—that’s the 100 that we carried plus the 100 from 132—to get the final answer: 227, or $227, in this case.
The Quicker Adding Method: Working From Left-to-Right
Okay, that worked great, right? So, what's wrong with adding from right-to-left? Well, nothing is wrong with it. It does work; but it's slow. So here's a quick and dirty tip to speed things up: It's much faster to add large numbers from left-to-right than from right-to-left. Here's what I mean.
Instead of starting at the ones column on the right, start at the hundreds column on the left. So first: How many hundreds are there in this problem?
There’s just one from $132. So we've got one 100 (think of it as a single $100 bill), and the total to keep in your head is $100.
Now, move from left-to-right to the tens column. How many tens do we have? There are 3 from $132, 5 from $58, and 2 from $29. So there are 3 + 5 + 2 = 10 tens (think of this as ten $10 bills), for a total of 10 times 10 or $100. The running total in your head is now $100 + $100 = $200.
Finally, move further from left-to-right to the ones column. What's the total there? Well, the ones column contains 2 from $132, 8 from...well...$8, another 8 from $58, and 9 from $29. So the total is 2 + 8 + 8 + 9 = 27. And the grand total for the whole problem is therefore $200 + $27 = $227.
Of course, this is the same answer we got before when we worked from right-to-left. But the beauty of working left-to-right is that it’s much easier to do the work in your head without needing to carry digits and do lots of bookkeeping. Give it a bit of time and practice, and I bet you'll find it’s much faster.
And on that note, you’ll find several practice problems below to help you sharpen your skills. Remember, try to work them out in your head if you can. Check out the “videos” section of the Math Dude’s Facebook page or YouTube to see a video walkthrough demonstrating how to solve the practice problems. Okay, that’s all the math we have time for today, but start getting excited because next week we’re going to begin tackling the wonderful world of fractions, decimals, and percentages!
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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
Add the following from left-to-right. For example, in the problem
the mental addition process could be: (1) Start with 300+100=400; (2) Next, in your head, think through the sequence obtained by adding 400 to the various numbers of 10 in the tens column. So, 400, (+70 is) 470, (+20 is) 490, (+10 is) 500, (+10 is) 510; (3) Then, in your head, think through the sequence 510, 520, 529 obtained by first combining the pair of numbers in the ones column that add to 10, and then adding the rest. The particular sequence you use to arrive at the result might be a bit different, but it should definitely give the same answer!
Here are some problems for you to practice with: