Addition and Subtraction within 10,000
๐ Addition and Subtraction within 10,000
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Addition and Subtraction within 10,000
In these notes, we will explore how to add and subtract numbers up to 10,000. This includes simple operations without regrouping, operations requiring regrouping, mental strategies, and solving word problems using these skills.
1. Simple Addition within 10,000
Simple addition involves adding numbers where the sum of digits in each place value (ones, tens, hundreds, thousands) is less than 10, so no regrouping is needed.
Example 1: Add 53 and 42.
53 + 42 = 95
Steps:
- Add the ones: 3 + 2 = 5
- Add the tens: 5 + 4 = 9
So, the sum is 95.
Example 2: Add 1243 and 506.
1243 + 506 = 1749
Steps:
- Add the ones: 3 + 6 = 9
- Add the tens: 4 + 0 = 4
- Add the hundreds: 2 + 5 = 7
- Add the thousands: 1 + 0 = 1
So, the sum is 1749.
2. Addition with Regrouping
When the sum of digits in any place value is 10 or more, regrouping is required by carrying over to the next higher place value.
Example: Add 1253 and 4968.
Steps:
- Ones: 3 + 8 = 11 (write 1, carry over 1)
- Tens: 5 + 6 + 1 = 12 (write 2, carry over 1)
- Hundreds: 2 + 9 + 1 = 12 (write 2, carry over 1)
- Thousands: 1 + 4 + 1 = 6
So, 1253 + 4968 = 6221.
3. Simple Subtraction within 10,000
Simple subtraction involves subtracting numbers without borrowing, where each digit in the minuend is greater than or equal to the corresponding digit in the subtrahend.
Example: Subtract 57 from 98.
98 - 57 = 41
Steps:
- Subtract the ones: 8 - 7 = 1
- Subtract the tens: 9 - 5 = 4
So, the difference is 41.
4. Subtraction with Regrouping
When a digit in the minuend is smaller than the corresponding digit in the subtrahend, borrow from the next higher place value.
Example: Subtract 398 from 1531.
Steps:
- Ones: 1 < 8, borrow 1 from tens (11 - 8 = 3), tens becomes 2
- Tens: 2 < 9, borrow 1 from hundreds (12 - 9 = 3), hundreds becomes 4
- Hundreds: 4 - 3 = 1
- Thousands: 1 - 0 = 1
So, 1531 - 398 = 1133.
Example with Thousands: Subtract 2598 from 5240.
Steps:
- Ones: 0 < 8, borrow 1 from tens (10 - 8 = 2), tens becomes 3
- Tens: 3 < 9, borrow 1 from hundreds (13 - 9 = 4), hundreds becomes 1
- Hundreds: 1 < 5, borrow 1 from thousands (11 - 5 = 6), thousands becomes 4
- Thousands: 4 - 2 = 2
So, 5240 - 2598 = 2642.
5. Mental Addition and Subtraction
Mental strategies simplify calculations by breaking numbers into manageable parts.
Mental Addition: Add 48 and 13.
- Method 1: 48 + 10 = 58, then 58 + 3 = 61
- Method 2: 48 + 2 = 50, then 50 + 11 = 61 (13 = 2 + 11)
So, 48 + 13 = 61.
Mental Subtraction: Subtract 37 from 81.
- Method 1: 81 - 40 = 41, then 41 + 3 = 44 (37 = 40 - 3)
- Method 2: 37 + 3 = 40, 40 + 41 = 81, so 3 + 41 = 44
So, 81 - 37 = 44.
6. Word Problems
Word problems apply addition and subtraction to real-world situations, often requiring multiple steps.
Example 1: Eve had 1427 beads. Her mother gave her 1359 more beads. How many beads did Eve have altogether?
Solution: 1427 + 1359 = 2786
So, Eve had 2786 beads altogether.
Example 2: There were 296 boys and 197 girls in a swimming club. 125 children left. How many children were there at first? How many were there in the end?
Solution:
- At first: 296 + 197 = 493
- In the end: 493 - 125 = 368
So, there were 493 children at first and 368 in the end.
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