We group numbers to make them easier to work with. Because we use a base-10 number system, we group numbers in multiples of 10. Ten 1’s are the same as one group of 10. One hundred 1’s are the same as one group of 100. Most of the time, one group of 10 or one group of 100 is easier to work with than ten 1’s or one hundred 1’s.
Sometimes, however, numbers are easier to work with if we “regroup them -- arrange them into different groups. Let’s say, for example, you have to subtract 59 from 87. You line up the tens’ place and the ones’ place and get ready to subtract the ones. But you can’t subtract 9 from 7 because 9 is bigger than 7. So you have to take one group of 10 (ten 1’s) from the tens’ place. Now you have 7 groups of ten and seventeen 1’s. You’ve regrouped the 87 into different sized groups. You can subtract 9 from 17; the answer is 8. Then you subtract the digits in the tens’ place. (Remember you now have only 7 groups of 10.) 7 - 5 = 2. So 87-59=28.
You regroup in some addition problems too. Let’s say you want to add 55 and 27. Start with the ones’ place: 5+7=12. Regroup the 12 as one 10 and two 1’s. Put the 2 ones in the ones place, and put the 1 group of 10 in the tens place. Then add the digits in the tens place: 5’+’2’+’1’=’7. So 55’+’27’= 82.
Explain…
