Adding Two 2-Digit Numbers (No Regrouping) - First Grade Mathematics

Now you are ready to combine everything you have learned about place value to add two full two-digit numbers together, such as 34 + 25! At first glance, adding two big numbers looks like a serious challenge. But when you break both numbers apart into tens and ones, the problem magically turns into two easy kindergarten and first-grade facts! You add the tens to the tens, add the ones to the ones, and combine the results. In this chapter, you will master adding two two-digit numbers without regrouping using decomposition and vertical addition.

The Decomposing Method: Split into Tens and Ones

Every two-digit number can be split into its tens part and its ones part.

Solving 34 + 25 by Decomposing:

Decompose 34:    30   +   4
Decompose 25:    20   +   5
-----------------------------
Add the Tens:    30 + 20 = 50
Add the Ones:     4 +  5 =  9
Combine Parts:   50 +  9 = 59!

The Three Steps:

Step 1: Add the tens: 30 + 20 = 50. Step 2: Add the ones: 4 + 5 = 9. Step 3: Put the tens and ones back together: 50 + 9 = 59! It is as simple as adding two small problems!

The Vertical Addition Format

Mathematicians often stack numbers vertically so that the place-value columns line up like towers.

Vertical Addition of 52 + 36:

       Tens    Ones
         5       2
     +   3       6
     -----------------
         8       8

Step 1: Add the ONES column first: 2 + 6 = 8.
Step 2: Add the TENS column next:  5 + 3 = 8.
Result: 88!

Always Add the Ones Column First!

While you can add tens first when doing mental math, it is an essential habit in written math to ALWAYS ADD THE ONES COLUMN FIRST. Why? Because in the very next chapter, you will learn what to do when the ones add up to ten or more, and starting with the ones will make that easy!

Modeling with Base-Ten Blocks

Let us build 41 + 37 with rods and units.

Building 41 + 37:
41:  [===] [===] [===] [===]       +  [#]
37:  [===] [===] [===]             +  [#][#][#][#][#][#][#]
------------------------------------------------------------------
Combine Rods:  4 + 3 = 7 Rods (70)
Combine Units: 1 + 7 = 8 Units (8)
Total: 78!

Practice Exercises

Exercise 1: Solve 43 + 32 by decomposing both numbers into tens and ones. Show Step 1 (tens), Step 2 (ones), and Step 3 (combine).

Exercise 2: Solve these vertical addition problems: 24 63 51 72 + 35 + 26 + 44 + 17 ---- ---- ---- ----

Exercise 3: In an orchard, workers picked 45 baskets of green apples and 34 baskets of red apples. How many baskets of apples did they pick altogether?

Exercise 4: Explain why it is important to line up the digits in straight columns when adding vertically.

Solutions and Explanations

Solution to Exercise 1: Step 1 (Add Tens): 40 + 30 = 70. Step 2 (Add Ones): 3 + 2 = 5. Step 3 (Combine): 70 + 5 = 75. Total sum is 75.

Solution to Exercise 2: 24 + 35 = 59 (4+5=9 ones, 2+3=5 tens) 63 + 26 = 89 (3+6=9 ones, 6+2=8 tens) 51 + 44 = 95 (1+4=5 ones, 5+4=9 tens) 72 + 17 = 89 (2+7=9 ones, 7+1=8 tens)

Solution to Exercise 3: 45 + 34 = 79 baskets. They picked 79 baskets of apples altogether.

Solution to Exercise 4: It is important to line up digits in straight columns so you do not accidentally add a tens digit to a ones digit. Keeping tens over tens and ones over ones ensures that only like units are combined.