Subtracting Multiples of 10 - Second Grade Mathematics

Just as adding multiples of ten moves you forward across decades without touching the ones digit, subtracting multiples of ten moves you backward across decades with that exact same elegance. Multiples of ten—such as 10, 20, 30, 40, and 50—have a zero in the ones place, meaning you are taking away zero loose ones. All the subtraction happens purely in the tens column! In this chapter, you will master subtracting multiples of ten mentally, navigate upward on hundred charts, and model backward leaps on open number lines.

The Rule of the Untouched Ones Place

When you subtract a multiple of ten from any two-digit number, the ones digit remains completely identical from start to finish.

Subtracting Multiples of Ten:
    74 - 30 = 44
    ^^   ^^   ^^
Tens: 7 tens - 3 tens = 4 tens (40)
Ones: 4 ones - 0 ones = 4 ones (4)
Difference: 40 + 4 = 44

Thinking Purely in Tens

Because 30 contains 0 ones, you do not have to subtract anything from the 4 ones. You only look at the tens: 7 tens minus 3 tens equals 4 tens. Combine 4 tens with the original 4 ones, and the difference is 44! More examples: 86 - 20: 8 tens - 2 tens = 6 tens. Attach 6 ones = 66. 59 - 40: 5 tens - 4 tens = 1 ten. Attach 9 ones = 19. 92 - 50: 9 tens - 5 tens = 4 tens. Attach 2 ones = 42.

Connecting to Single-Digit Subtraction

Subtracting multiples of ten is simply your basic subtraction facts disguised in tens: 7 - 3 = 4 =====> 70 - 30 = 40 =====> 74 - 30 = 44 9 - 5 = 4 =====> 90 - 50 = 40 =====> 98 - 50 = 48

Navigating Upward on the Hundred Chart

On a standard hundred chart, subtracting multiples of ten corresponds to moving straight up a column.

Hundred Chart Excerpt:
+----+----+----+----+----+
| 27 | 28 | 29 | 30 | 31 |   <--- 3 steps up = -30 (lands on 28)
+----+----+----+----+----+
| 37 | 38 | 39 | 40 | 41 |   <--- 2 steps up = -20
+----+----+----+----+----+
| 47 | 48 | 49 | 50 | 51 |   <--- 1 step up = -10
+----+----+----+----+----+
| 57 | 58 | 59 | 60 | 61 |   <--- Starting Number: 58
+----+----+----+----+----+

Stepping Up Decreases by 10

Every time you move up one row in the exact same column, the value decreases by 10. To subtract 10: move 1 step up. To subtract 20: move 2 steps up. To subtract 30: move 3 steps up. Starting at 58 and subtracting 30: place your finger on 58, move straight up 3 squares (48, 38, 28), and you land directly on 28. Your finger stays in the column ending in 8 the entire time!

Number Line Hops Backward

On an open number line, subtracting multiples of ten is represented by drawing backward hops to the left, labeled -10.

Solving 65 - 30 on an Open Number Line:
          -10             -10             -10
    <------------+  <------------+  <------------+
----+------------+---------------+---------------+--->
   35           45              55              65

Tracking the Tens Downward

The number 30 is three tens. Starting on the right at 65, make three backward hops of 10: First hop back: 65 - 10 = 55 Second hop back: 55 - 10 = 45 Third hop back: 45 - 10 = 35 Final answer: 35.

Mental Leaps

Once you are confident, you can make one single large backward leap of 30: start at 65, think 6 tens - 3 tens = 3 tens, and land directly on 35.

Practice Exercises

Exercise 1: Calculate the difference of 83 - 40 mentally. State what happened to the tens digit and what happened to the ones digit.

Exercise 2: If your finger is on 76 on a hundred chart and you move straight up 5 rows, what number will you land on? Write the subtraction equation that models this move.

Exercise 3: Draw or describe the backward jumps you would make on an open number line to solve 91 - 30.

Exercise 4: A school warehouse had 78 basketballs in stock. The physical education department distributed 30 basketballs to classrooms. How many basketballs remained in the warehouse?

Solutions and Explanations

Solution to Exercise 1: To calculate 83 - 40, subtract the tens: 8 tens - 4 tens = 4 tens (40). Combine with the 3 ones to get 43. The tens digit decreased from 8 to 4, while the ones digit remained 3 because 40 has 0 ones.

Solution to Exercise 2: Moving straight up 5 rows on a hundred chart means subtracting 5 tens, or 50. Starting at 76 and moving up 5 rows (66, 56, 46, 36, 26) lands on 26. The subtraction equation is 76 - 50 = 26.

Solution to Exercise 3: On an open number line, place 91 on the right. Since 30 is three tens, make three backward jumps of 10 to the left: from 91 jump back 10 to 81, jump back 10 to 71, and jump back 10 to 61. The final difference is 61.

Solution to Exercise 4: To find the remaining basketballs, calculate 78 - 30. Subtract the tens: 7 tens - 3 tens = 4 tens (40). Combine with the 8 ones: 40 + 8 = 48. There were 48 basketballs remaining in the warehouse.