Year 6 Maths: Long Division

What is Long Division?

Long division is a method used to divide larger numbers into smaller parts. It’s like sharing something fairly among friends. Instead of dividing right away, we break it down into easier steps.

Steps to Long Division

1. Set Up the Problem: Write the large number (the dividend) inside the division bracket and the smaller number (the divisor) outside.
2. Divide: Look at the first number or set of numbers in the dividend. See how many times the divisor can fit into it. Write this number above the division line.
3. Multiply: Multiply the divisor by the number you just wrote. Write this answer below the number you divided.
4. Subtract: Subtract the number you just wrote from the dividend. Write the answer below.
5. Bring Down: If there are more numbers in the dividend, bring down the next digit next to the result from the subtraction.
6. Repeat: Repeat the divide, multiply, subtract, and bring down steps until you’ve worked through all the digits.
7. Remainder: If there’s anything left that cannot be divided anymore, that’s your remainder.

Example of Long Division

Let’s divide 154 by 7.

1. Set Up: $$\text{7} , | , \text{154}$$
2. Divide:How many times does 7 fit into 15? It fits 2 times.Write 2 above the 15.
3. Multiply: $$7 \times 2 = 14$$ Write 14 below 15.
4. Subtract: $$15 – 14 = 1$$ Write 1 below.
5. Bring Down:Bring down the 4, making it 14.
6. Repeat:How many times does 7 fit into 14? It fits 2 times again.Write 2 above the 4.
7. Multiply: $$7 \times 2 = 14$$ Write 14 below 14.
8. Subtract: $$14 – 14 = 0$$ Nothing is left to bring down.

So,

Key Rules for Long Division

• Always start with the leftmost digits of the dividend.
• Write down the quotient (the answer) above the division bracket.
• Make sure to line up your numbers correctly.
• If the divisor is larger than the number you’re dividing, move to the next digit.
• Practice helps! The more you do, the easier it becomes.

Tips and Tricks

• Use estimation! Before you start, think about how many times the divisor can go into the first few digits.
• If you get stuck, don’t be afraid to start over.
• Remember to check your work by multiplying back.

Practice Questions

Easy Level Questions

1. $$24 \div 6$$
2. $$36 \div 9$$
3. $$45 \div 5$$
4. $$56 \div 7$$
5. $$63 \div 9$$
6. $$81 \div 9$$
7. $$72 \div 8$$
8. $$18 \div 3$$
9. $$30 \div 5$$
10. $$40 \div 5$$

Medium Level Questions

1. $$144 \div 12$$
2. $$225 \div 15$$
3. $$576 \div 24$$
4. $$132 \div 11$$
5. $$294 \div 7$$
6. $$120 \div 10$$
7. $$360 \div 18$$
8. $$256 \div 16$$
9. $$462 \div 6$$
10. $$390 \div 13$$

Hard Level Questions

1. $$987 \div 3$$
2. $$1,234 \div 4$$
3. $$1,560 \div 12$$
4. $$2,520 \div 35$$
5. $$1,689 \div 9$$
6. $$1,875 \div 25$$
7. $$3,456 \div 12$$
8. $$2,789 \div 17$$
9. $$4,236 \div 18$$
10. $$5,432 \div 24$$

Answers and Explanations

Easy Level Answers

1. 4
2. 4
3. 9
4. 8
5. 7
6. 9
7. 9
8. 6
9. 6
10. 8

Medium Level Answers

1. 12
2. 15
3. 24
4. 12
5. 42
6. 12
7. 20
8. 16
9. 77
10. 30

Hard Level Answers

1. 329
2. 308
3. 130
4. 72
5. 187
6. 75
7. 288
8. 163
9. 235
10. 226

By practicing these long division problems, you will become more comfortable with the method. Remember, practice makes perfect! Happy dividing!