Subtraction patterns over increasing place values

key notes :

Understanding Place Value

  • Place Value Basics: Know the place values (ones, tens, hundreds, etc.) and how they affect the value of digits in a number.
  • Example: In the number 453, the digit 4 represents 400 (four hundreds), 5 represents 50 (five tens), and 3 represents 3 (three ones).

Subtraction Across Place Values

  • Simple Subtraction: Start with basic subtraction where the numbers are within the same place value.
  • Example: Subtracting 23 from 45. Both numbers are in the tens and ones place.

Subtraction Across Tens and Hundreds

  • Subtraction Across Tens: When subtracting numbers where borrowing is needed between tens and ones.
  • Example: Subtracting 27 from 53 involves borrowing from the tens place.
    • Step 1: 3 (ones) is less than 7 (ones), so we borrow 1 ten.
    • Step 2: 13 (ones) – 7 (ones) = 6 (ones).
    • Step 3: 4 (tens, after borrowing) – 2 (tens) = 2 (tens).
    • Result: 26.
  • Subtraction Across Hundreds: Subtracting numbers where borrowing may be needed from the hundreds place.
  • Example: Subtracting 245 from 500.
    • Step 1: 500 – 200 = 300.
    • Step 2: 300 – 45 = 255.

Patterns in Subtraction

  • Regular Patterns: Observe that as the place values increase (from ones to tens to hundreds), the patterns of borrowing and regrouping also change.
  • Example: Subtracting in the hundreds place may involve borrowing from thousands, and so on.

Learn with an example

Complete the pattern:

9 −____= 5
90 −____= 50
900 −____= 500
9,000 −____= 5,000

Find the first missing number:

9 ones − 4 ones = 5 ones
9 − 4 = 5

Now complete the pattern:

9 tens − 4 tens = 5 tens
90 − 40 = 50

9 hundreds − 4 hundreds = 5 hundreds
900 − 400 = 500

9 thousands − 4 thousands = 5 thousands
9,000 − 4,000 = 5,000

Complete the pattern:

____− 5 = 4
____− 50 = 40
____− 500 = 400
____− 5,000 = 4,000

Find the first missing number:

9 ones − 5 ones = 4 ones
9 − 5 = 4

Now complete the pattern:

9 tens − 5 tens = 4 tens
90 − 50 = 40

9 hundreds − 5 hundreds = 4 hundreds
900 − 500 = 400

9 thousands − 5 thousands = 4 thousands
9,000 − 5,000 = 4,000

Complete the pattern:

 ______− 6 = 1

 ______ − 60 = 10

 ______− 600 = 100

Find the first missing number:

7 ones − 6 ones = 1 one
7 − 6 = 1

Now complete the pattern:

7 tens − 6 tens = 1 ten
70 − 60 = 10

7 hundreds − 6 hundreds = 1 hundred
700 − 600 = 100

Let’s practice!