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What is subtraction?
Subtraction means taking away or finding how much is left after some part is removed. If you have 9 mangoes and give 4 to a friend, the number left is 9 − 4 = 5. Subtraction tells us the difference between two numbers. We call the number we start with the minuend and the number we take away the subtrahend. The result is the difference.
Place value review
Every digit in a number has a place value. In a three-digit number we have hundreds, tens and units. For example 345 = 3 hundreds + 4 tens + 5 units. When we subtract, digits must be in the correct columns. If tens are under units, the answer will be wrong. Good alignment helps us know which digits to subtract.
How to write neatly
Write numbers in two rows with the minuend on top and the subtrahend below it. Draw a line and work from the rightmost column (units) to the left (tens, then hundreds). If the top digit is greater than or equal to the bottom digit, subtract directly. If it is smaller, use borrowing. Showing each step, crossing out a digit when you borrow, and writing the new digit helps prevent mistakes and lets others follow your work.
Subtract when digits allow direct subtraction
When each digit of the minuend (top number) is equal to or greater than the corresponding digit of the subtrahend (bottom number), you can subtract each column without borrowing. This is the simplest case and helps build confidence. Always work from right to left: units first, then tens, then hundreds. If a column gives zero, write 0 or leave a clear blank space to show the place.
Steps to follow
1. Write the numbers one under another, aligning units, tens and hundreds. 2. Start with the units column: subtract the bottom digit from the top digit. 3. Move to the tens column and subtract. 4. Finally subtract the hundreds column. Check that no column required borrowing; if it did, you have to use regrouping rules.
Examples and tips
For 374 − 142: units 4−2=2, tens 7−4=3, hundreds 3−1=2 so result 232. For 86 − 23: units 6−3=3, tens 8−2=6 giving 63. Use a ruler or straight edge if students find alignment hard. Practise many such problems to become fast and accurate before moving on to borrowing cases.
When direct subtraction is not possible
Sometimes a digit in the minuend is smaller than the digit beneath it. For example in 52 − 37 the units digit 2 is less than 7. You cannot take 7 from 2 in the units column without regrouping. To solve such problems we use borrowing (also called regrouping), which moves value from a higher place to a lower place in order to make subtraction possible.
How borrowing works
Borrowing means taking one from the next higher place value and adding ten to the current place. In base ten, one ten equals ten units. So when you borrow one ten, you decrease the tens place by one and increase the units place by ten. The value of the whole number stays the same because you remove ten units from tens and add them to units.
Practical explanation and signs
When borrowing, cross out the digit in the higher place and write the new reduced digit. Then add 10 to the current place's digit and subtract. Always work from right to left so that needed borrows are in place before you reach the tens or hundreds columns. Using objects—sticks for tens and pebbles for units—helps children see that one stick removed becomes ten pebbles added to the units pile.
Borrowing when only tens are available
For two-digit subtraction like 73 − 48, borrowing comes from the tens column. Write the numbers one below another: 73 on top, 48 below, units under units, tens under tens. Look first at the units column. If the top unit is smaller than the bottom unit (3 < 8), you must borrow one ten. That ten comes from the tens digit 7. Reduce 7 by 1 to make 6 tens and add 10 units to the units place, changing 3 into 13. Now you can subtract the units column: 13 − 8 = 5.
Finish tens column
After units are done, move to tens. Now tens are 6 (after borrowing) minus 4 = 2. The final answer is 25. Always show the crossing out of the tens digit and write the new reduced digit so the child knows where the borrow came from. Writing the 13 above the units column helps visualise the new value.
Classroom aids and practice
Use ten-sticks and single counters: take away one stick from the tens pile and place ten counters in the units pile. Practise many such problems so students learn to borrow correctly and understand why borrowing does not change the total value, it only reorganises it.
Why zeros cause extra steps
When the tens place of the minuend is 0, you cannot borrow from it. For example with 102 − 38, the units 2 is smaller than 8, and the tens digit is 0 so there is nothing to borrow from in tens. You must go to the next higher place that has a non-zero digit, usually the hundreds place. Borrowing across a zero requires two moves: first change the higher non-zero digit, then make the tens non-zero so you can borrow to units.
Step-by-step method
Write 102 above 38 aligned. To make units big enough, go to the hundreds digit 1. Reduce hundreds by 1 (1→0). Add 10 to the tens place: tens 0→10. Now borrow 1 ten from those 10 tens to give to units: tens 10→9 and units 2→12. Now do units subtraction 12−8=4. Tens subtraction 9−3=6. Hundreds 0−0=0. Answer 64. Always cross out each changed digit and write the new digit clearly.
Teaching tips
Use physical objects to show conversion: one hundred sheet becomes ten ten-sticks, then one ten-stick becomes ten unit counters. Practise many examples with zeros so students become comfortable with multi-step borrowing and do not get confused when zeros appear in the middle of a number.
Applying the same rules to three digits
Borrowing in three-digit problems like 425 − 187 follows the same right-to-left rule used in smaller problems, but sometimes needs more than one borrow. Always write the minuend over the subtrahend in three neat columns: hundreds, tens and units. Start with the units column. If the units digit in the minuend is smaller, borrow from the tens column. If the tens digit is zero or smaller than needed, you must borrow from the hundreds column and then from tens to units as necessary. Each borrow reduces the higher place by one and adds ten to the next lower place.
Detailed worked example
Consider 425 − 187. Units: 5 < 7 so borrow 1 ten from tens. Change tens 2→1 and units 5→15. Now units 15−7=8. Move to tens: tens 1 < 8, so borrow 1 hundred. Change hundreds 4→3 and tens 1→11. Now tens 11−8=3. Finally hundreds 3−1=2. The answer is 238. Write each crossing out and new number so each step is clear and check by addition.
When tens are zero
If you meet a number like 305 − 178, tens are 0 so you borrow from hundreds: 3→2 and tens 0→10, then borrow 1 ten to units if needed. This can create a sequence of borrows; follow them one at a time from right to left and always show the changes.
Teaching tips and practice
Use place-value charts and blocks: hundreds sheets, ten-sticks and unit counters. Let students physically convert one hundred into ten tens and then tens into units to see why borrowing works. Give many mixed problems so students become fluent and learn to check each result by adding difference and subtrahend to get the minuend.
Why checking helps
Checking subtraction by addition is a reliable way to find mistakes. The rule is simple: minuend = subtrahend + difference. After you subtract, add the difference to the subtrahend. If the result equals the minuend, your subtraction is likely correct. This method helps catch errors made during borrowing or misalignment of digits.
How to check step-by-step
Take your subtraction result and write it under the subtrahend for column addition. Add units first, then tens, then hundreds, carrying where needed. For example, if you find 642 − 279 = 363, add 279 + 363. Units 9 + 3 = 12, write 2 carry 1. Tens 7 + 6 + 1carry = 14, write 4 carry 1. Hundreds 2 + 3 + 1carry = 6. Sum 642 which matches the minuend, so subtraction is correct.
Class routine
Teach students to check every subtraction, especially when borrowing was used. Checking trains carefulness and helps students trust their answers. For small numbers they can also check by mentally adding, but learning column addition properly is important for checking larger answers. Always align digits before adding to check subtraction.
Turn words into numbers
In word problems, first understand what the story says. Identify the starting amount (minuend) and what is taken away (subtrahend). Convert words into a subtraction sentence and line up digits correctly. If the problem involves money, objects or counts, remember to keep units in the final answer (rupees, pencils, apples).
Use borrowing when needed
Many word problems need borrowing because numbers do not always subtract directly. For example: "Ria had 120 rupees and bought a toy for 87 rupees. How much is left?" Convert to 120 − 87. Because the tens digit is 2 and units is 0, you must borrow from hundreds. Show each step of crossing out and regrouping and then subtract to get the left amount. Always show work so the answer is easy to follow.
Steps to solve
1. Read and underline important numbers. 2. Write subtraction sentence with alignment. 3. Use borrowing rules if top digits are smaller. 4. Check your answer by addition. 5. State the answer with the correct unit. Practise many word problems so students learn both to set up and to compute correctly.