Читать книгу All the Math You'll Ever Need - Steve Slavin - Страница 14

Our number system is a place value system, meaning that the value of a numeral depends on the place it sits in. In the number 444 each 4 has a different meaning. The 4 on the right is in the ones place so it represents 4 ones or simply 4. The 4 on the left is in the hundreds place and represents 4 hundreds or 400. The middle 4 is in the tens place so it represents 4 tens or 40. The number 444 is a shorthand for 400 + 40 + 4.

That expanded form, 400 + 40 + 4, helps to explain how we add large numbers. We add the ones to the ones, the tens to the tens, the hundreds to the hundreds and on up in the place value system. If you need to add 444 + 312, think:

Add the 4 ones and the 2 ones to get 6 ones, the 4 tens with 1 ten to get 5 tens and the 4 hundreds with 3 hundreds to get 7 hundreds. Now that would look like this:

You're probably thinking that you could just write the numbers underneath one another in standard form and add down the columns, and you'd be absolutely correct.

The reason to think about it in expanded form, at least for a few minutes, comes up when you have to add something like 756 + 968. The basic rule is the same.

But you can't squeeze 16 (or 11 or 14) into one place. 756 + 968 does not equal 161114. You've got to do some regrouping, or what's commonly called carrying. Those 14 ones equal 1 ten and 4 ones. You're going to keep the 4 ones in the ones place and move the ten over to the middle place with the rest of the tens. That will turn

You'll do the same sort of regrouping with the 12 tens. Ten of those tens make 1 hundred, leaving 2 tens in the tens place. You can do this without using the expanded form. Add 6 + 8 to get 14. Put down the 4 and carry the one ten.

Add 1 + 5 + 6 to get 12. Put down the 2 (tens) and carry the 1 (hundred).

Add 1 + 7 + 9 to get 17. The 7 goes in the hundreds place and the 1 (thousand) slides into the thousands place.