CBSE Class 5 Mathematics Addition and Subtraction of Large Numbers Notes Set 01

Adding and subtracting large numbers

Big numbers appear everywhere: the people in a town, the books in a library, the money a school collects. To work with them we use the same ideas you already know for small numbers, but we take more care with place value. In this chapter we work with numbers up to five digits and their sums and differences.

Key words

1. The numbers that are added are called addends, and the result is the sum.
2. In subtraction, the number we start with is the minuend, the number taken away is the subtrahend, and the result is the difference.
3. Addition and subtraction are opposites: if 5 + 3 = 8, then 8 − 3 = 5.

How to add

1. Write the addends one below the other so that ones are under ones, tens under tens, hundreds under hundreds, and so on.
2. Start from the ones column and add. If the total is 10 or more, write the ones digit and carry the tens digit to the next column.
3. Move left column by column, adding the carried digit too.
4. Write the sum below the line.

How to subtract

1. Write the bigger number (minuend) on top and the smaller number (subtrahend) below it, with digits in the correct places.
2. Start from the ones column. If the top digit is smaller than the bottom digit, borrow 1 from the next column on the left. That 1 becomes 10 in the column you are working on.
3. Subtract column by column and write the difference below the line.

Worked examples

Example 1. Add 45,678 and 23,456.
Ones: 8 + 6 = 14, write 4 carry 1. Tens: 7 + 5 + 1 = 13, write 3 carry 1. Hundreds: 6 + 4 + 1 = 11, write 1 carry 1. Thousands: 5 + 3 + 1 = 9. Ten thousands: 4 + 2 = 6.
Sum = 69,134.

Example 2. Subtract 47,869 from 82,305.
Ones: 5 is less than 9, so borrow and take 15 − 9 = 6. Continue the same way for each column, borrowing wherever the top digit is smaller.
Difference = 34,436. Check: 34,436 + 47,869 = 82,305.

Example 3. A shop earned ₹36,450 in one month and ₹28,775 in the next month. How much did it earn in all, and how much more did it earn in the first month?
Total = 36,450 + 28,775 = ₹65,225. Difference = 36,450 − 28,775 = ₹7,675.

Common mistakes to avoid

1. Writing digits in the wrong columns, which gives a wrong place value.
2. Forgetting a carried digit while adding.
3. Forgetting that a column was borrowed from, so it is now one less.
4. Subtracting the bigger digit from the smaller one in a column instead of borrowing.

Useful tips

1. Always estimate first. Round each number to the nearest thousand to see roughly what the answer should be.
2. In a word problem, words like "in all", "together" and "total" usually mean add; words like "how many more", "left" and "difference" usually mean subtract.
3. Always check subtraction by adding the answer to the number you subtracted.

Quick Check Questions