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\\January 8, 2024 4:53 PM Bharat Arora Proof-3 Reader _________________________ Date: ___________________74

Encapsulate
math
ADDiTiON AND SuBTrACTiON

Addition of Bigger Numbers Subtraction of Bigger Numbers

Addition of bigger numbers without regrouping Subtraction of bigger numbers without regrouping

TTh Th H T O TTh Th H T O
3 2 4 7 5 Addend 1 7 9 8 9 5 Minuend
+ 2 4 3 1 2 Addend 2 – 3 6 7 4 3 Subtrahend
4 3 1 5 2 Difference
5 6 7 8 7 Sum
5 ones – 3 ones = 2 ones
Addition of bigger numbers with regrouping 9 tens – 4 tens = 5 tens
8 hundreds – 7 hundreds = 1 hundred
L TTh Th H T O 9 thousands – 6 thousands = 3 thousands
7 ten thousands – 3 ten thousands
1 1 1 1
= 4 ten thousands
8 7 1 9 9 9 Subtraction of bigger numbers with regrouping
+ 1 9 9 9 9 L TTh Th H T O
8 9 1 9 9 8 14 12 15
6 4 2 5 12
4 7 5 3 6 2
Properties of Addition – 2 2 9 7 6 4
1. Order property (Commutative Property): 2 4 5 5 9 8
E.g., 21,425 + 32,147 = 32,147 + 21,425
2. Grouping property (Associative Property):
E.g., 2,150 + (32,140 + 54,789) = (2,150 + 32,140) + 54,789 Properties of Subtraction
3. Property of 1: E.g., 87,540 + 1 = 87,541 1. One subtracted from any number gives its
4. Property of 0: E.g., 67,532 + 0 = 67,532 predecessor.
E.g., 32,541 – 1 = 32,540
2. Zero subtracted from any number gives the
number itself.
Estimating Sum and Difference E.g., 90,531 – 0 = 90,531
3. The number subtracted from itself gives zero.
Estimating the sum of 25,138 and 63,848 E.g., 59,531 – 59,531 = 0

Estimated Sum Actual Sum
TTh Th H T O TTh Th H T O
3 0 0 0 0 2 5 1 3 8 Addition and Subtraction Together
+ 6 0 0 0 0 + 6 3 8 4 8
9 0 0 0 0 8 8 9 8 6 Solve: 1,55,423 + 15,067 – 37,643.

Estimating the difference of 11,782 and 38,741 L TTh Th H T O L TTh Th H T O
1 1 9
Estimated Difference Actual Difference 1 5 5 4 2 3 6 10 14 8 10
TTh Th H T O TTh Th H T O + 1 5 0 6 7 Sum 1 7 0 4 9 0
4 0 0 0 0 16 13 1 7 0 4 9 0 – 3 7 6 4 3
– 1 0 0 0 0 7 6 3 11 Add the numbers 1 3 2 8 4 7
3 0 0 0 0 3 8 7 4 1 having + sign Subtract the number
– 1 1 7 8 2 having – sign from the
2 6 9 5 9 sum obtained.

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