Subtracting Multiples of Ten (e.g., 70 - 20) - First Grade Mathematics

Just as adding multiples of ten is as simple as adding single digits, subtracting multiples of ten is just as straightforward! When you subtract 20 from 70, you are not subtracting seventy individual little cubes one at a time. You are simply starting with 7 rods of ten and taking away 2 rods of ten. Because 7 - 2 = 5, taking 2 tens from 7 tens leaves 5 tens, which is 50! In this chapter, you will master subtracting multiples of ten within 100, use quick sketches to model your work, and build rapid mental math confidence.

The Logic of Subtracting Tens

Subtraction means taking a part away from a whole. When both the whole and the part are multiples of ten, only the tens place is affected.

The Single-Digit Connection for Subtraction:

Basic Fact:               7     -     2     =     5   (7 ones - 2 ones = 5 ones)
                          |           |           |
Tens Fact:             7 Tens   -  2 Tens   =  5 Tens
                          |           |           |
Multiples of Ten:        70     -    20     =    50!

The Ones Place Never Changes!

Look at the ones digits: 0 minus 0 is always 0. Since there were zero loose ones to start with and zero loose ones were removed, the ones digit in your difference will always be 0.

Modeling with Base-Ten Rods

Let us visualize 80 - 30 using base-ten rods.

Modeling 80 - 30:
Step 1: Start with 8 Rods (80):
  [===] [===] [===] [===] [===] [===] [===] [===]

Step 2: Cross out 3 Rods (Take away 30):
  [===] [===] [===] [===] [===]   [X]   [X]   [X]

Step 3: Count the remaining rods:
  5 Rods remain!
  Value = 50!
  Equation: 80 - 30 = 50

Using a Quick Line Sketch

Draw 8 vertical sticks: | | | | | | | |. Cross out 3 sticks: | | | | | \ \ \. Count the surviving sticks: 5 sticks! 5 tens equals 50. It takes five seconds!

Hopping Backward on the Hundreds Chart

You can also subtract multiples of ten by hopping upward on a 100 chart!

Solving 70 - 30 on a 100 Chart:
Start at 70.
Subtracting 30 means hopping UP 3 rows (-10, -10, -10):
Hop 1 up: lands on 60.
Hop 2 up: lands on 50.
Hop 3 up: lands on 40!
70 - 30 = 40!

Each Hop Up Is Minus Ten

Every time you take one step straight up on a 100 chart, you subtract 10. To subtract 30, simply hop up 3 rows!

Practice Exercises

Exercise 1: Solve 90 - 40. What basic single-digit subtraction fact helps you find the answer?

Exercise 2: Solve each equation mentally: 60 - 20 = __ 80 - 50 = __ 50 - 10 = __ 100 - 40 = __

Exercise 3: A farmer had 70 ears of corn in a wooden crate. He sold 30 ears of corn at the morning market. How many ears of corn does he have left? Write the equation.

Exercise 4: Draw or describe the quick stick sketch you would use to solve 60 - 40.

Solutions and Explanations

Solution to Exercise 1: 90 - 40 = 50. The basic single-digit fact is 9 - 4 = 5 (9 tens - 4 tens = 5 tens = 50).

Solution to Exercise 2: 60 - 20 = 40 80 - 50 = 30 50 - 10 = 40 100 - 40 = 60 (10 tens - 4 tens = 6 tens = 60)

Solution to Exercise 3: The farmer started with 70 and sold 30: 70 - 30 = 40. The farmer has 40 ears of corn left.

Solution to Exercise 4: Draw 6 vertical sticks to represent 60: | | | | | |. Draw a slash mark through 4 of the sticks: | | \ \ \ \. Count the remaining 2 uncrossed sticks, which represent 2 tens: 20. The answer is 20.