Why is it important to align the columns from right to left?

Step-by-step solution

Idea: In the Indian place-value system the value of a digit depends on its position, counted from the right. Only the rightmost digit is always the units digit, so the numbers must be lined up from the right.

1. A digit’s value depends on its place: in 473 the 4 means 4 hundreds, the 7 means 7 tens and the 3 means 3 units. Places are counted from the right: the last digit is always the units digit, whatever the length of the number.½ mark
2. The addition algorithm adds one column at a time. This is correct only if each column holds digits of the same place value, so we add units to units, tens to tens, and so on.½ mark
3. Aligning from the right puts the units digits in one column, the tens digits in the next, and so on. Aligning from the left would not, unless both numbers have the same number of digits.½ mark
4. Example: 473 + 25. Aligned from the right: 3 + 5 = 8, 7 + 2 = 9, 4 → 498 ✓. Aligned from the left, 25 sits under 47 and acts like 250: 3 + 0 = 3; 7 + 5 = 12, write 2, carry 1; 4 + 2 + 1 = 7 → 723, which is wrong.½ mark

Answer to write in the exam

Common mistakes that cost marks

• Saying “to make it look neat”. The reason is place value, not neatness.
• Thinking the alignment matters only for numbers with different lengths and then misaligning decimals later (decimals are aligned at the decimal point for the same reason).
• Not giving an example; a short example showing a wrong answer earns the reasoning mark.

How this can come in the exam

Try one yourself

Riya added 3045 + 62 and got 9245. What did she do wrong, and what is the correct answer?

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• Try to execute the algorithm to compute the divisors of 15, 135, and 775. How does the amount of work increase as the numbers grow?

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