**Division: The Basics**
Dividend ÷ Divisor = Quotient (N ÷ D = Q)
With remainder: N = D × Q + R
**Connection to Multiplication**
Every multiplication fact gives TWO division facts.
If 5 × 7 = 35, then 35 ÷ 5 = 7 AND 35 ÷ 7 = 5
**Place Value Patterns in Division**
1000 ÷ 10 = 100 (remove one zero)
1000 ÷ 100 = 10 (remove two zeros)
Pattern: Dividing by 10, 100, or 1000 removes zeros from the number.
**Mental Strategies**
1. Splitting: 1248 ÷ 6 = (1200 ÷ 6) + (48 ÷ 6) = 200 + 8 = 208
2. Near numbers: 1992 ÷ 4 = (2000 ÷ 4) - (8 ÷ 4) = 500 - 2 = 498
3. Repeated halving (for divisor 4): 128 ÷ 4 = half of 128 = 64, half of 64 = 32
4. Repeated subtraction: Subtract equal groups until 0 or remainder remains
**Division with Remainder**
97 coconuts ÷ 25 per bag = 3 bags with 22 left over
97 = 25 × 3 + 22
**Don't Confuse**: Remainder must always be LESS than the divisor. If remainder = 5 and divisor = 4, you made an error.
**Everyday Example**: ₹5500 shared by 5 employees = ₹5500 ÷ 5 = ₹1100 each
Q1. In the division problem 35 ÷ 7 = 5, which number is the Divisor?
Answer: B — The divisor is the number we divide by (the number of groups), which is 7.
Q2. If 6 × 8 = 48, which of these is NOT a correct division fact?
Answer: C — 48 ÷ 6 = 8, not 6, because 6 × 8 = 48 gives us two correct division facts: 48 ÷ 6 = 8 and 48 ÷ 8 = 6.
Q3. What is 1200 ÷ 6?
Answer: A — Since 6 × 200 = 1200, we know that 1200 ÷ 6 = 200.
Q4. Sabina cycles 160 km in 20 days at the same distance each day. How many kilometres does she cycle each day?
Answer: B — 160 ÷ 20 = 8 km per day, because she cycles the same distance each day.
Q5. What pattern do you see when dividing by 10? 100 ÷ 10 = ____, 1000 ÷ 10 = ____, 1200 ÷ 10 = ____
Answer: A — When dividing by 10, one zero is removed from the end of the number: 100 ÷ 10 = 10, 1000 ÷ 10 = 100, 1200 ÷ 10 = 120.
Q6. To divide 128 by 4 using the halving strategy, what is the first step?
Answer: B — To divide by 4, you halve twice: half of 128 is 64, then half of 64 is 32, so 128 ÷ 4 = 32.
Q7. How many ₹100 notes does Seema need to carry if she wants to buy coconuts worth ₹4200?
Answer: A — 4200 ÷ 100 = 42 notes, because 100 × 42 = 4200.
Q8. In the division 1248 ÷ 6 = 208, what is the Quotient?
Answer: C — The quotient is the answer to the division problem, which is 208.
Q9. Fill in the blank: 630 ÷ 63 = ____
Answer: B — 630 ÷ 63 = 10, following the pattern where you can cancel common factors: 630 ÷ 63 = (63 × 10) ÷ 63 = 10.
Q10. When 97 coconuts are packed into bags that hold 25 coconuts each, how many complete bags can be filled and what is left over?
Answer: A — 97 ÷ 25 = 3 remainder 22, because 25 × 3 = 75 and 97 - 75 = 22 leftover.
What is the Dividend in a division problem?
The dividend is the total number being divided or split into groups.
What is the Divisor in a division problem?
The divisor is the number that tells us how many groups we are making or dividing by.
What is the Quotient in a division problem?
The quotient is the answer we get after dividing—how many are in each group.
If 5 × 7 = 35, write two division facts from this.
35 ÷ 5 = 7 and 35 ÷ 7 = 5 are the two division facts from 5 × 7 = 35.
What is the formula that shows dividend, divisor, quotient, and remainder?
N = D × Q + R, where N is dividend, D is divisor, Q is quotient, and R is remainder.
How do you divide 1248 by 6 using splitting?
Split 1248 into 1200 + 48, then divide: 1200 ÷ 6 = 200 and 48 ÷ 6 = 8, so 1248 ÷ 6 = 208.
What strategy can you use to divide 128 by 4?
Halve twice: half of 128 is 64, half of 64 is 32, so 128 ÷ 4 = 32.
If 900 ÷ 10 = 90, what pattern do you see?
When dividing by 10, the quotient is the same number but with one zero removed from the end.
Sabina cycles 160 km in 20 days equally. How far does she cycle each day?
160 ÷ 20 = 8 km per day.
If 582 ÷ 6 is done using repeated subtraction, what fact helps you?
You can subtract groups of 60 (or 120) repeatedly from 582 to find how many groups of 6 fit in.
Write the two division facts from the multiplication fact 9 × 8 = 72. [1 mark]
If 9 × 8 = 72, then 72 ÷ 9 = 8 AND 72 ÷ 8 = 9. Every multiplication fact creates exactly two division facts.
Solve 1248 ÷ 6 by splitting the number into convenient parts. Show your working. [2 marks]
Split 1248 into 1200 and 48. Divide each part by 6 separately, then add the quotients. 1200 ÷ 6 = 200, and 48 ÷ 6 = 8, so answer = 200 + 8 = 208.
The owner of a store wants to distribute ₹5500 equally among 5 employees as a gift. (a) How much will each employee get? (b) If he distributes the same amount among 10 employees instead, will each get more or less? Explain. [3 marks]
Part (a): Divide 5500 ÷ 5 = 1100. Part (b): When you divide the same amount among more people, each person gets less. Use: 5500 ÷ 10 = 550, which is less than 1100.
Susie harvested 1117 coconuts in April. She sold 582 to 6 customers equally. (a) How many coconuts did each customer get? (b) How many coconuts were left? (c) She needs to pack the remaining coconuts in bags holding 25 each. How many complete bags can she fill and how many are left over? Show all working using the division formula N = D × Q + R. [5 marks]
Part (a): 582 ÷ 6 = 97. Part (b): 1117 - 582 = 535 left. Part (c): 535 ÷ 25 gives quotient 21 and remainder 10. Use formula: 535 = 25 × 21 + 10. She needs 21 complete bags and has 10 coconuts left.
True or False? When dividing 1000 by 100, the quotient is 10. Give a reason for your answer. [2 marks]
True. Because 100 × 10 = 1000, following the place value pattern that dividing by 100 removes two zeros from the number.
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