数学英语 05 How To Add Quickly, Part 2
by Jason Marshall
Continuing our quest towards turning you into a quick-calculating machine, today we’re building upon last week’s tips 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:(见图一)
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:(见图二)
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:(见图三)
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:(见图四)
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.(见图五)
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?.(见图六)
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.(见图七)
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.(见图八)
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.(见图九)
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.
Wrap Up
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!
And, throughout the month of March, we’re giving away one free book each week to lucky Math Dude Twitter followers and Facebook fans. So please join our growing community of social networking math fans, ask questions, and chat with other math enthusiasts. Check it out and see how you can win a free book!
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!
Continuing our quest towards turning you into a quick-calculating machine, today we’re building upon last week’s tips 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:(见图一)
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:(见图二)
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:(见图三)
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:(见图四)
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.(见图五)
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?.(见图六)
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.(见图七)
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.(见图八)
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.(见图九)
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.
Wrap Up
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!
And, throughout the month of March, we’re giving away one free book each week to lucky Math Dude Twitter followers and Facebook fans. So please join our growing community of social networking math fans, ask questions, and chat with other math enthusiasts. Check it out and see how you can win a free book!
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!
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