krit.club logo

Addition - Addition of 4-digit Numbers without carrying

Grade 3ICSE

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

🔑Concepts

•

Place Value Alignment: In 4-digit addition, numbers are composed of Thousands (ThTh), Hundreds (HH), Tens (TT), and Ones (OO). Imagine a table with four vertical columns; each digit must sit perfectly inside its designated column so that ones are under ones, tens under tens, and so on.

•

The Right-to-Left Rule: Always begin the addition process from the rightmost column (the Ones column). Visualize an arrow starting at the Ones and pointing leftwards through Tens, Hundreds, and finally Thousands.

•

Column-by-Column Addition: You add the digits in each column independently. For example, if the Thousands column has a 22 and a 33, you simply add them to get 55. In this specific topic, the sum of digits in any column will never exceed 99.

•

Addends and the Sum: The two or more numbers being added together are called 'Addends'. The final answer you calculate is called the 'Sum'. Visually, you can think of the sum as the total value shown at the bottom of the addition stack.

•

Zero Property in Addition: When one of the digits in a column is 00, the sum for that column is equal to the other digit. For instance, if the Tens column has 44 and 00, the resulting digit in the sum's Tens place is 44.

•

No-Carrying Concept: This type of addition is known as 'Simple Addition' because no column produces a value greater than 99. This means you do not need to pass or 'carry' any value over to the next column on the left.

📐Formulae

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

Digit at Ones+Digit at Ones=Sum Digit at Ones\text{Digit at Ones} + \text{Digit at Ones} = \text{Sum Digit at Ones}

Digit at Tens+Digit at Tens=Sum Digit at Tens\text{Digit at Tens} + \text{Digit at Tens} = \text{Sum Digit at Tens}

Digit at Hundreds+Digit at Hundreds=Sum Digit at Hundreds\text{Digit at Hundreds} + \text{Digit at Hundreds} = \text{Sum Digit at Hundreds}

Digit at Thousands+Digit at Thousands=Sum Digit at Thousands\text{Digit at Thousands} + \text{Digit at Thousands} = \text{Sum Digit at Thousands}

💡Examples

Problem 1:

Add 32543254 and 46124612.

Solution:

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

  1. Add the Ones: 4+2=64 + 2 = 6
  2. Add the Tens: 5+1=65 + 1 = 6
  3. Add the Hundreds: 2+6=82 + 6 = 8
  4. Add the Thousands: 3+4=73 + 4 = 7

Explanation:

The numbers are arranged in columns by place value. We start from the right (Ones) and work our way to the left (Thousands). Since no individual column sum is greater than 99, we simply write the total of each column directly below the line.

Problem 2:

Find the sum of 50835083 and 29142914.

Solution:

\begin{array}{r@{\quad}cccc} & Th & H & T & O \\ & 5 & 0 & 8 & 3 \\ + & 2 & 9 & 1 & 4 \\ \hline & 7 & 9 & 9 & 7 \\ \hline \end{array}

  1. Ones: 3+4=73 + 4 = 7
  2. Tens: 8+1=98 + 1 = 9
  3. Hundreds: 0+9=90 + 9 = 9
  4. Thousands: 5+2=75 + 2 = 7

Explanation:

Aligning the digits 50835083 and 29142914 in their respective place value columns allows us to add each set of digits. In the hundreds column, adding 00 to 99 results in 99, following the identity property of addition.