Division • Topic 4 of 6

Quotient and Remainder

Real life rarely divides evenly, so children must meet the leftover -- the remainder -- and learn to name the four parts of a division. In 17 divided by 5 you write quotient 3, remainder 2: here 17 is the dividend (the number being divided), 5 is the divisor (the number you divide by), 3 is the quotient (the result of the division), and 2 is the remainder (what is left over). The relationship that ties them together, and that CTET tests directly, is Dividend equals Divisor times Quotient plus Remainder. Check it: 5 times 3 plus 2 is 15 plus 2, which is 17. The golden rule is that the remainder is always less than the divisor; if it ever equals or exceeds the divisor, the quotient was too small and you can fit in at least one more. When the remainder is 0 we say the dividend is exactly, or completely, divisible by the divisor. The same idea works for both stories: share 23 mangoes among 4 friends and each gets 5 with 3 left over, or pack 50 eggs into trays of 6 and you fill 8 trays with 2 eggs left.

✅ Solved examples

1. Riya has 23 mangoes to share equally among 4 friends. How many does each friend get and how many are left over?
Since 4 x 5 = 20 and 4 x 6 = 24 (too high), the quotient is 5 and the remainder is 23 - 20 = 3. Each friend gets 5 mangoes and 3 are left over. Check: 4 x 5 + 3 = 23, and the remainder 3 is less than the divisor 4.
2. In 50 / 6, find the quotient and remainder and verify your answer.
Since 6 x 8 = 48 and 6 x 9 = 54 (too high), the quotient is 8 and the remainder is 50 - 48 = 2. Verify: 6 x 8 + 2 = 48 + 2 = 50, and 2 is less than 6.
3. A child writes 29 / 5 = 4 remainder 9. Without dividing again, how can you tell this is wrong?
The remainder 9 is not less than the divisor 5, so it must be wrong -- another 5 still fits. The correct answer is 5 remainder 4 (5 x 5 + 4 = 29).
4. Name the four parts of the division 38 / 7 = 5 remainder 3.
Dividend = 38, Divisor = 7, Quotient = 5, Remainder = 3. Check: 7 x 5 + 3 = 35 + 3 = 38.

✏️ Practice — try these, take hints as needed

1. Find the quotient and remainder for 27 / 4.
Largest multiple of 4 not above 27.
4 x 6 = 24.
Quotient 6, remainder 3 (4 x 6 + 3 = 27)
2. When 45 is divided by a number, the quotient is 7 and the remainder is 3. What is the divisor?
Dividend = Divisor x Quotient + Remainder.
45 - 3 = 42, then divide by the quotient.
6 (since 6 x 7 + 3 = 45)
3. A pupil gets a remainder of 8 when dividing by 6. Explain why this cannot be a final answer.
Compare the remainder with the divisor.
The remainder must be less than the divisor; 8 is bigger than 6, so the quotient is too small and one more group fits.

📝 Topic test — 8 questions

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