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Addition - Addition of 4-digit Numbers with carrying

Grade 3ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Place Value Alignment: To add 4-digit numbers, we must arrange the digits in columns according to their place value: Thousands (Th), Hundreds (H), Tens (T), and Ones (O). Imagine a grid where the number 4,5624,562 has 44 in the Th column, 55 in the H column, 66 in the T column, and 22 in the O column. Proper alignment ensures we add digits of the same value together.

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Order of Addition: Always begin adding from the rightmost column (Ones) and work your way to the left (Tens, then Hundreds, then Thousands). Visually, this looks like moving from the 'back' of the numbers to the 'front'.

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Concept of Carrying (Regrouping): If the sum of digits in any column is 1010 or more, we cannot write a two-digit number in a single column. We must 'regroup' or 'carry over' the extra value to the next column on the left. For example, if the Ones column adds up to 1414, we write 44 in the Ones place and carry 11 to the Tens place.

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Carrying from Ones to Tens: When the sum of the digits in the Ones column is greater than 99, for every 1010 ones, we carry over 11 to the Tens column. Visualize this as trading 1010 small single blocks for 11 long 'ten' rod.

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Carrying from Tens to Hundreds: When the sum of digits in the Tens column (including any carry-over from the Ones) is 1010 or more, we carry 11 to the Hundreds column. This is like trading 1010 'ten' rods for 11 large 'hundred' square.

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Carrying from Hundreds to Thousands: If the total in the Hundreds column is 1010 or more, we carry 11 to the Thousands column. In visual base-10 blocks, this is like trading 1010 'hundred' squares for 11 large 'thousand' cube.

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The Identity Property: Adding 00 to any 4-digit number does not change its value. For example, 4,321+0=4,3214,321 + 0 = 4,321. Visually, if a column contains a 00, the sum of that column is just the other digit plus any carry-over.

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Commutative Property: The order of numbers being added (addends) does not change the total (sum). 1,234+5,6781,234 + 5,678 will result in the same sum as 5,678+1,2345,678 + 1,234.

📐Formulae

Addend+Addend=Sum\text{Addend} + \text{Addend} = \text{Sum}

10 Ones=1 Ten10 \text{ Ones} = 1 \text{ Ten}

10 Tens=1 Hundred10 \text{ Tens} = 1 \text{ Hundred}

10 Hundreds=1 Thousand10 \text{ Hundreds} = 1 \text{ Thousand}

a+b=b+aa + b = b + a

(a+b)+c=a+(b+c)(a + b) + c = a + (b + c)

💡Examples

Problem 1:

Add 4,5784,578 and 3,6453,645.

Solution:

\begin{array}{r@{\quad}cccc} & \text{Th} & \text{H} & \text{T} & \text{O} \\ & \text{(1)} & \text{(1)} & \text{(1)} & \\ & 4 & 5 & 7 & 8 \\ + & 3 & 6 & 4 & 5 \\ \hline & 8 & 2 & 2 & 3 \\ \hline \end{array}

Explanation:

Step 1: Add the Ones (8+5=138 + 5 = 13). Write 33 in the Ones column and carry 11 to the Tens column. Step 2: Add the Tens (7+4+1 carry=127 + 4 + 1 \text{ carry} = 12). Write 22 in the Tens column and carry 11 to the Hundreds column. Step 3: Add the Hundreds (5+6+1 carry=125 + 6 + 1 \text{ carry} = 12). Write 22 in the Hundreds column and carry 11 to the Thousands column. Step 4: Add the Thousands (4+3+1 carry=84 + 3 + 1 \text{ carry} = 8). The final sum is 8,2238,223.

Problem 2:

Find the sum of 2,8942,894 and 1,3061,306.

Solution:

\begin{array}{r@{\quad}cccc} & \text{Th} & \text{H} & \text{T} & \text{O} \\ & \text{(1)} & \text{(1)} & \text{(1)} & \\ & 2 & 8 & 9 & 4 \\ + & 1 & 3 & 0 & 6 \\ \hline & 4 & 2 & 0 & 0 \\ \hline \end{array}

Explanation:

Step 1: Add the Ones (4+6=104 + 6 = 10). Write 00 in the Ones column and carry 11 to the Tens column. Step 2: Add the Tens (9+0+1 carry=109 + 0 + 1 \text{ carry} = 10). Write 00 in the Tens column and carry 11 to the Hundreds column. Step 3: Add the Hundreds (8+3+1 carry=128 + 3 + 1 \text{ carry} = 12). Write 22 in the Hundreds column and carry 11 to the Thousands column. Step 4: Add the Thousands (2+1+1 carry=42 + 1 + 1 \text{ carry} = 4). The final sum is 4,2004,200.