Add two 4-digit numbers using the steps we have written down. Make sure you follow the steps precisely; do not perform any action that is not explicitly mentioned. Are you able to obtain the correct result?

Step-by-step solution

Idea: Follow each step exactly as written, like a machine would. Then look for a case the steps do not cover: the rules say “less than 10” and “more than 10”, so nothing is said about a sum of exactly 10.

1. Step 1: write 4785 above 3692 with the units digits in the same column.
2. Step 2 (units): 5 + 2 = 7. This is less than 10, so write 7 and set carry = 0.½ mark
3. Step 3 (tens): 8 + 9 + 0 = 17. This is more than 10, so write 7 and set carry = 1.
   Step 4 says repeat Step 3. Hundreds: 7 + 6 + 1 = 14, more than 10, write 4, carry = 1.
   Thousands: 4 + 3 + 1 = 8, less than 10, write 8, carry = 0. No more digits on the left.1 mark
4. Step 5: carry is 0, so nothing more is written. Result: 8477. Check: 4785 + 3692 = 8477 ✓. So for these numbers the steps give the correct result.½ mark
5. But try 3456 + 2154. Units: 6 + 4 = 10. The steps say what to do if the sum is less than 10 or more than 10, but not if it equals 10. Following the steps precisely, we are stuck. So the steps do not always give the correct result.1 mark
6. Fix: change “more than 10” to “10 or more” (equal to or more than 10) in Steps 2 and 3. Then 3456 + 2154 gives 0 (carry 1), 5 + 5 + 1 = 11 (write 1, carry 1), 4 + 1 + 1 = 6, 3 + 2 = 5: 5610 ✓.

Check: 4785 + 3692 = 8477 and 3456 + 2154 = 5610 (by calculator or by counting up: 3456 + 2000 = 5456, + 154 = 5610).

Answer to write in the exam

Common mistakes that cost marks

• Doing what we “know” instead of what is written: carrying 1 when a column gives exactly 10, even though the steps never say so. The question asks you to follow the steps precisely.
• Forgetting to add the carry in Step 3 (for example writing 7 + 6 = 13 in the hundreds column instead of 7 + 6 + 1 = 14).
• Choosing only numbers with no carries at all, so the test never checks the carry rules.

How this can come in the exam

Try one yourself

Follow the steps to add 6857 + 2496. Write the carry after each column.

More questions like this

• What happens if you add a 5-digit number to a 3-digit number. Do our steps handle this situation correctly?
• Why is it important to align the columns from right to left?
• In Step 3, why cannot the value of carry be more than 1?
• What happens if we do not include the fifth step in the algorithm above? Give examples where the algorithm will work correctly and where it will fail to work.
• 1. See if you can complete the argument about grouping by units, tens, hundreds, … to justify why the addition algorithm works.
  2. How would you modify the algorithm to add two decimal fractions?

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