Adding 2-Digit Numbers and Multiples of 10 - First Grade Mathematics

In the previous chapter, you learned that when you add single ones to a two-digit number, only the ones place changes. Now, get ready for the exact opposite adventure: adding multiples of ten to a two-digit number! When you solve a problem like 35 + 40, the tens do all the work, while the ones get to relax! Because a multiple of ten has zero in the ones place, your ones digit will not change at all. In this chapter, you will master adding multiples of ten to any two-digit number and see how it feels like taking big vertical hops on the hundreds chart.

The Rule of Tens: Add Tens to Tens!

When you add a multiple of ten (like 20, 30, or 40) to a two-digit number, align your tens and ones.

Adding 35 + 40:

           Tens    Ones
             3       5
         +   4       0
         -----------------
             7       5   (3 tens + 4 tens = 7 tens; 5 ones + 0 ones = 5 ones!)

Result: 75!

Notice the Ones Digit!

Look at the ones place: 5 + 0 = 5. Because you are adding 0 ones, the ones digit remains completely identical! All your mental energy goes into adding the tens: 3 + 4 = 7 tens. Put 7 tens with 5 ones to get 75.

Hopping on the 100 Chart

Adding a multiple of ten is identical to hopping straight down the columns of a 100 chart.

Solving 26 + 30 on the 100 Chart:
Start at 26.
Adding 30 means hopping DOWN 3 rows (+10, +10, +10):
Hop 1 down: lands on 36.
Hop 2 down: lands on 46.
Hop 3 down: lands on 56!

26 + 30 = 56!

Watch the Path Down

In column 6, you stepped: 26 -> 36 -> 46 -> 56. The ones digit (6) never flinched! Each step simply increased the tens digit by one.

Modeling with Base-Ten Blocks

Let us build 47 + 20 with blocks.

Modeling 47 + 20:
Start with 47:  4 Rods and 7 Units
Add 20:         2 Rods and 0 Units
------------------------------------
Combine Rods:   4 Rods + 2 Rods = 6 Rods (60)
Combine Units:  7 Units + 0 Units = 7 Units (7)
Total Value:    67!

Practice Exercises

Exercise 1: Solve 52 + 30. Which digits do you add together, and why does the ones digit stay 2?

Exercise 2: Solve each equation mentally: 24 + 50 = __ 61 + 20 = __ 18 + 70 = __ 45 + 40 = __

Exercise 3: Start at 38 on a 100 chart. Take two steps straight down. What number do you land on, and what addition equation does this represent?

Exercise 4: A library had 33 mystery books. The librarian ordered 40 more mystery books. How many mystery books are in the library now? Write the addition equation.

Solutions and Explanations

Solution to Exercise 1: 52 + 30 = 82. You add the tens digits 5 and 3 (5 tens + 3 tens = 8 tens = 80). The ones digit stays 2 because 30 has 0 ones, and 2 + 0 = 2.

Solution to Exercise 2: 24 + 50 = 74 (2 tens + 5 tens = 7 tens, ones stay 4) 61 + 20 = 81 (6 tens + 2 tens = 8 tens, ones stay 1) 18 + 70 = 88 (1 ten + 7 tens = 8 tens, ones stay 8) 45 + 40 = 85 (4 tens + 4 tens = 8 tens, ones stay 5)

Solution to Exercise 3: Taking two steps straight down from 38: step 1 lands on 48, step 2 lands on 58. You land on 58. This represents the equation 38 + 20 = 58.

Solution to Exercise 4: 33 + 40 = 73. There are 73 mystery books in the library now.