Numbers — Class 3 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 3 Mathematics. Place value to 999, the four operations, and word problems.
1. Place value up to 999
Every digit in a number has a place, and the place decides what the digit is worth.
Take 473. The 4 sits in the hundreds place, the 7 in the tens place, the 3 in the ones place.
Written out: 4 hundreds, 7 tens and 3 ones. That is the expanded form.
The same digit is worth different amounts in different places. In 582 the 5 is worth 500. In 258 the 5 is worth only 50.
A zero still holds a place. In 305 there are 3 hundreds, 0 tens and 5 ones. Dropping the zero gives 35, a completely different number. The zero is doing real work: it keeps the 3 in the hundreds column.
2. Comparing numbers
To compare two numbers, look at the leftmost place first.
- 512 and 489: the first has 5 hundreds, the second only 4, so 512 > 489.
- 367 and 361: hundreds match and tens match, so compare the ones. 7 beats 1, so 367 > 361.
The symbols are > for greater than, < for less than and = for equal.
3. Adding and subtracting
Always start from the ones column, on the right.
Adding 456 + 278. Ones: 6 + 8 = 14, write 4 and carry 1. Tens: 5 + 7 + 1 = 13, write 3 and carry 1. Hundreds: 4 + 2 + 1 = 7. The answer is 734.
Starting from the left does not work, because you cannot know a carry before adding the column to its right.
Subtracting across a zero: 500 − 237. Ones: 0 − 7 will not go, so borrow from the tens. The tens are 0 too, so borrow from the hundreds first.
Now 5 hundreds becomes 4 hundreds and 10 tens, and one of those tens becomes 10 ones. The sum reads 4 hundreds, 9 tens, 10 ones, and subtracting 237 leaves 263.
4. Multiplication
Learn the tables from 2 to 10 by heart. They are the tool everything else here rests on.
To multiply a 2-digit number by a 1-digit number, do the ones first, then the tens, carrying as you go.
24 × 3. Ones: 4 × 3 = 12, write 2 and carry 1. Tens: 2 × 3 = 6, plus the carried 1 makes 7. The answer is 72.
5. Division and remainders
Division asks how many equal groups can be made.
45 ÷ 3 = 15, exactly, with nothing left over.
47 ÷ 3 = 15 remainder 2. Three fifteens make 45, and 2 are left. Write it as "15 remainder 2" or "15 R 2".
At this stage a remainder is a whole number left over, never a decimal. Writing 47 ÷ 3 = 15.67 hides what the question is asking. If 47 sweets are shared among 3 children, each child gets 15 and 2 stay in the packet.
6. Worked examples
Example 1. Write 806 in expanded form.
800 + 0 + 6, that is 8 hundreds, 0 tens and 6 ones. The tens digit is zero and must still be written inside the number.
Example 2. Compute 623 − 387.
Ones: 3 − 7 will not go, so borrow to make 13 − 7 = 6. Tens: after the borrow the 1 will not take 8, so borrow again to make 11 − 8 = 3. Hundreds: 5 − 3 = 2. The answer is 236.
Example 3. Compute 36 × 5.
Ones: 6 × 5 = 30, write 0 and carry 3. Tens: 3 × 5 = 15, plus 3 makes 18. The answer is 180.
Example 4. A shopkeeper has 95 pencils and packs them in boxes of 8. How many full boxes, and how many pencils are left?
95 ÷ 8 = 11 remainder 7, so 11 full boxes with 7 pencils left over.
7. Practice
- Write 347 in expanded form.
- Which is greater, 519 or 591?
- Compute 389 + 145.
- Compute 741 − 359.
- Compute 48 × 3.
- Compute 82 ÷ 6 and state the remainder.
- Amma buys 235 g of one spice and 168 g of another. What is the total weight?
8. Answers
- 300 + 40 + 7.
- 591, because once the hundreds match the tens decide, and 9 beats 1.
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- 13 remainder 4.
- 403 g.
9. Summary
- A 3-digit number is hundreds × 100 + tens × 10 + ones, so 473 = 400 + 70 + 3.
- A zero holds its place: 305 is not 35.
- Compare from the leftmost place and move right only while places match.
- Add and subtract starting from the ones column, so carries and borrows come out right.
- To borrow across a zero, borrow first from the next column that has something to give.
- Tables 2 to 10 are worth memorising; every multiplication here rests on them.
- A remainder is a whole number left over, written "R 2", never a decimal.
