2.1: Adding and subtracting with positive integers

Adding a positive integer to a positive integer

To add a positive integer to a positive integer, first add the digits in the “ones” place (regrouping or carrying if the sum is more than 9), then add the digits in the “tens” place (regrouping if necessary), and so on. For example,

• 46 + 27.
• To add 46 and 27, first add 6 ones and 7 ones to get 13 ones.
• Regroup the 13 ones into 1 ten and 3 ones (carry the 1 ten into the tens column).
• Next, add 4 tens and 2 tens and the carried 1 ten to get 7 tens.
• The answer is 7 tens and 3 ones, i.e., 73.

  4 6
+ 2 7
 1 
  7 3

For another example,

• 83 + 47.
• To add 83 and 47, first add 3 ones and 7 ones to get 10 ones.
• Regroup the 10 ones into 1 ten and 0 ones (carry the 1 ten into the tens column).
• Next, add 8 tens and 4 tens and the carried 1 ten to get 13 tens.
• Regroup the 13 tens into 1 hundred and 3 tens (carry the 1 hundred into the hundreds column).
• Next, add 0 hundreds and the carried 1 hundred to get 1 hundred.
• The answer is 1 hundred, 3 tens, and 0 ones, i.e., 130.

   8 3
+  4 7
1 1 
 1 3 0

Subtracting a positive integer from a larger positive integer

To subtract a positive integer from a larger positive integer, first subtract the digits in the “ones” place (regrouping or borrowing if the digit being subtracted is greater than the digit being subtracted from), then subtract the digits in the “tens” place (regrouping if necessary), and so on. Here we’re assuming the number we’re subtracting is less than the number we’re subtracting from. For example,

• 46 – 27
• To subtract 27 from 46, first note that 7 is greater than 6 so we need to regroup the 4 tens in 46 into 3 tens and 10 ones (borrow the 10 ones to make 16 ones).
• Now we can subtract 7 ones from 16 ones to get 9 ones.
• Next, subtract 2 tens from 3 tens to get 1 ten.
• The answer is 1 ten and 9 ones, i.e., 19.

   3 16 
  4  6
- 2  7
  1  9

For another example,

• 83 – 47.
• To subtract 47 from 83, first note that 7 is greater than 3 so we need to regroup the 8 tens in 83 into 7 tens and 10 ones (borrow the 10 ones to make 13 ones).
• Now we can subtract 7 ones from 13 ones to get 6 ones.
• Next, subtract 4 tens from 7 tens to get 3 tens.
• The answer is 3 tens and 6 ones, i.e., 36.

   7 13 
  8  3
- 4  7
  3  6

The video below works through some examples of adding and subtracting with positive integers.