Subtracting Single Digits from Two-Digit Numbers - First Grade Mathematics

What happens when you have a two-digit number and need to take away a small single-digit number, like 58 - 5? Just like in addition without regrouping, the tens get to stay completely calm, while the ones handle the subtraction! Because you have enough loose ones to take away what is needed, the tens digit will not change at all. In this chapter, you will master subtracting single digits from two-digit numbers without regrouping, practice counting back, and use base-ten drawings to check your thinking.

Subtracting Ones from Ones

When subtracting a single-digit number from a two-digit number, align the ones and subtract them directly.

The Place-Value Alignment of 58 - 5:

           Tens    Ones
             5       8
         -           5
         -----------------
             5       3   (8 ones - 5 ones = 3 ones!)

Result: 53!

Why the Tens Digit Stays 5

In 58 - 5, you have 5 tens and 8 ones. You are taking away 5 ones and ZERO tens. 5 tens minus 0 tens leaves 5 tens. Only the ones digit changes from 8 to 3.

Modeling with Base-Ten Sketches

Let us visualize 47 - 3 using a quick sketch.

Modeling 47 - 3:
Draw 47 (4 Rods and 7 Units):
Rods:   |  |  |  |           (4 Tens)
Units:  .  .  .  .  .  .  .  (7 Ones)

Action: Cross out 3 units:
Rods:   |  |  |  |           (Still 4 Tens!)
Units:  .  .  .  .  x  x  x  (4 Ones remaining!)

Result: 4 Tens + 4 Ones = 44!

You Never Had to Touch the Rods!

Because 7 was bigger than 3, you had plenty of loose units to cross out. The 4 rods of ten were never cut open or disturbed!

Mental Math: The Count-Back Shortcut

When the single digit being subtracted is 1, 2, or 3, you can use the count-back strategy in your head!

Solving 76 - 2 Mentally:
Lock 76 in your head: "76..."
Take 2 backward hops: "75, 74!"
Answer: 74!

Keeping the Tens In Mind

Notice that during the countdown (76 -> 75 -> 74), the tens family remained in the seventies. You only stepped down the ones!

Practice Exercises

Exercise 1: Solve 69 - 4. Explain which digits you subtract and why the tens digit stays 6.

Exercise 2: Solve each equation mentally: 48 - 6 = __ 87 - 5 = __ 39 - 7 = __ 95 - 3 = __

Exercise 3: A farmer had 38 eggs in a carton. He used 6 eggs to make an omelet breakfast. How many eggs are left? Write the subtraction equation.

Exercise 4: Use the count-back strategy to solve 54 - 3 in your head. Describe each backward step you take.

Solutions and Explanations

Solution to Exercise 1: 69 - 4 = 65. You subtract the ones: 9 - 4 = 5. The tens digit stays 6 because you subtracted zero tens from the 6 tens.

Solution to Exercise 2: 48 - 6 = 42 (8 - 6 = 2) 87 - 5 = 82 (7 - 5 = 2) 39 - 7 = 32 (9 - 7 = 2) 95 - 3 = 92 (5 - 3 = 2)

Solution to Exercise 3: The farmer started with 38 eggs and used 6: 38 - 6 = 32. There are 32 eggs left.

Solution to Exercise 4: Start at 54 and say: "54..." Take 3 backward hops: hop 1 is 53, hop 2 is 52, and hop 3 is 51. The answer is 51 (54 - 3 = 51).