9. Coconut Farm

35 ÷ 7 = 5 and 35 ÷ 5 = 7

35 ÷ 1 = 35

The array has 4 rows with 7 coconuts in each row.

4 × 7 = 28

28 ÷ 4 = 7

28 ÷ 7 = 4

Products: 72 = 36 × 2 (given), 60 = 6 × 10, 48 = 6 × 8, 36 = 4 × 9, 24 = 4 × 6, 40 = 5 × 8

Quotients: 54 = 108 ÷ 2, 42 = 84 ÷ 2, 56 = 112 ÷ 2

54 ÷ 6 = 9, 42 ÷ 7 = 6, 56 ÷ 8 = 7

30 × 30 = 900; 900 ÷ 30 = 30 (both division statements are the same)

15 × 60 = 900; 900 ÷ 15 = 60; 900 ÷ 60 = 15

400 × 8 = 3,200; 3,200 ÷ 400 = 8; 3,200 ÷ 8 = 400

200 × 16 = 3,200; 3,200 ÷ 200 = 16; 3,200 ÷ 16 = 200

50 × 3 = 150, so 150 ÷ 3 = 50
80 ÷ 4 = 20
5 × 100 = 500, so 500 ÷ 5 = 100

100 ÷ 10 = 10
300 ÷ 100 = 3
500 ÷ 50 = 10

200 ÷ 20 = 10
44 × 10 = 440, so 440 ÷ 44 = 10
630 ÷ 63 = 10

Pattern: When the dividend is 10 times the divisor, the quotient is 10.

10 × 100 = 1,000
37 × 100 = 3,700

1,000 ÷ 10 = 100
1,000 ÷ 100 = 10
1,600 ÷ 4 = 400

2,000 ÷ 2 = 1,000
2,000 ÷ 20 = 100
3,700 ÷ 37 = 100

3,300 ÷ 3 = 1,100
3,300 ÷ 300 = 11
4,000 ÷ 40 = 100

Pattern: When the dividend becomes 10 times bigger and the divisor stays the same, the quotient also becomes 10 times bigger. The digits move one place to the left.

160 ÷ 20 = 8 km each day

4,200 ÷ 100 = 42 notes

Each of 5 employees gets ₹5,500 ÷ 5 = ₹1,100.

Among 10 employees, each gets ₹5,500 ÷ 10 = ₹550. That is less.

For 10 employees to get ₹1,100 each, he needs 10 × ₹1,100 = ₹11,000.

Answer 1: 6 ÷ 3 = 2; 6 − 5 = 1; 2 × 4 = 8; 1 + 7 = 8

Answer 2: 8 ÷ 4 = 2; 8 − 7 = 1; 2 × 3 = 6; 1 + 5 = 6

Yes, there is more than one answer.

How to think: Start with the division. The first number must be divisible by the second, so try 6 ÷ 3, 8 ÷ 4, 6 ÷ 2, 8 ÷ 2. Then check if the other boxes can be filled with the remaining numbers.

(a) 1,800 ÷ 18 = 100
(b) 6,100 ÷ 10 = 610
(c) 7,200 ÷ 100 = 72
(d) 1,000 ÷ 100 = 10

(e) 870 ÷ 10 = 87
(f) 7,000 ÷ 100 = 70
(g) 200 ÷ 100 = 2
(h) 130 ÷ 10 = 13

848 ÷ 4 = 800 ÷ 4 + 48 ÷ 4 = 200 + 12 = 212

963 ÷ 3 = 900 ÷ 3 + 63 ÷ 3 = 300 + 21 = 321

2,448 ÷ 12 = 2,400 ÷ 12 + 48 ÷ 12 = 200 + 4 = 204

1,575 ÷ 5 = 1,500 ÷ 5 + 75 ÷ 5 = 300 + 15 = 315

3,624 ÷ 6 = 3,600 ÷ 6 + 24 ÷ 6 = 600 + 4 = 604

It works for divisors 2, 4, 8, 16 and so on. To divide by 8, halve three times. To divide by 16, halve four times.

1. 64 ÷ 4 = (40 + 24) ÷ 4 = 10 + 6 = 16

2. 265 ÷ 5 = (250 + 15) ÷ 5 = 50 + 3 = 53

3. 1,560 ÷ 8 = (1,600 − 40) ÷ 8 = 200 − 5 = 195

4. 4,824 ÷ 24 = (4,800 + 24) ÷ 24 = 200 + 1 = 201

5. 168 ÷ 8: Halve 168 → 84, halve 84 → 42, halve 42 → 21

6. 144 ÷ 4: Halve 144 → 72, halve 72 → 36

(a) 256 ÷ 4 = 64 (halve twice: 128, 64)
(b) 545 ÷ 5 = 500 ÷ 5 + 45 ÷ 5 = 109

(c) 147 ÷ 7 = 140 ÷ 7 + 7 ÷ 7 = 21
(d) 1,212 ÷ 6 = 1,200 ÷ 6 + 12 ÷ 6 = 202

(e) 648 ÷ 12 = 600 ÷ 12 + 48 ÷ 12 = 50 + 4 = 54
(f) 9,648 ÷ 48 = 9,600 ÷ 48 + 48 ÷ 48 = 201

(g) 775 ÷ 25 = 750 ÷ 25 + 25 ÷ 25 = 31
(h) 796 ÷ 4 = 800 ÷ 4 − 4 ÷ 4 = 199

582 ÷ 6 = 97 coconuts each.

Yes, Sunitha’s method is better. She took away bigger groups (90 groups of 6), so she needed only 2 steps. Susie needed 6 steps.

535 ÷ 25 = 21, remainder 10.

21 bags are full, and 1 more bag is needed for the 10 coconuts left. They need 22 bags.

726 ÷ 4: 726 − 400 (100) = 326; 326 − 320 (80) = 6; 6 − 4 (1) = 2. Quotient = 100 + 80 + 1 = 181, Remainder = 2.

We could not write 200, because 4 × 200 = 800 is more than 726.

902 ÷ 16: 902 − 800 (50) = 102; 102 − 96 (6) = 6. Quotient = 56, Remainder = 6.

We could not use 60, because 16 × 60 = 960 is more than 902.

Is 726 = 4 × 181? No. So, 726 = 4 × 181 + 2.

Is 902 = 16 × 56? No. So, 902 = 16 × 56 + 6.

Dividend (N) = Divisor (D) × Quotient (Q) + Remainder (R)

Packs of 6: 250 ÷ 6 = 41 R 4. She needs 42 packs = 252 samosas. Only 2 extra.

Packs of 8: 250 ÷ 8 = 31 R 2. She needs 32 packs = 256 samosas. 6 extra.

She should buy 42 packs of 6, because fewer samosas will be left over.

342 ÷ 41 = 8, remainder 14.

8 buses carry 328 students. 14 students need one more bus. So, 9 buses are needed.

Total = ₹157 + ₹124 + ₹136 = ₹417

Each pays ₹417 ÷ 3 = ₹139

(a) 887 ÷ 3 = 295 R 2 → 3 × 295 + 2 = 887 ✓

(b) 283 ÷ 8 = 35 R 3 → 8 × 35 + 3 = 283 ✓

(c) 745 ÷ 5 = 149 R 0 → 5 × 149 = 745 ✓

(d) 767 ÷ 26 = 29 R 13 → 26 × 29 + 13 = 767 ✓

(e) 530 ÷ 41 = 12 R 38 → 41 × 12 + 38 = 530 ✓

(f) 888 ÷ 67 = 13 R 17 → 67 × 13 + 17 = 888 ✓

4,376 ÷ 8 = 547 l of oil

Earnings = 547 × ₹175 = 547 × 100 + 547 × 75 = 54,700 + 41,025 = ₹95,725

9,913 ÷ 23 = 400 + 30 + 1 = 431 kg

8,890 ÷ 35 = 200 + 50 + 4 = 254 tender coconuts

(8,890 − 7,000 = 1,890; 1,890 − 1,750 = 140; 140 − 140 = 0)

Cost of 254 coconuts at ₹20 each = 254 × ₹20 = ₹5,080

Extra amount = ₹8,890 − ₹5,080 = ₹3,810

62 ÷ 5 = 12, remainder 2

75 ÷ 8 = 9, remainder 3 (7 tens cannot be shared among 8, so regroup into 75 ones)

324 ÷ 3 = 108. We put 0 in the tens place because 2 tens cannot be shared into 3 equal parts.

136 ÷ 6 = 22, remainder 4

Yes. Look at the first digit of the dividend.

If the first digit is equal to or more than the divisor, the quotient has as many digits as the dividend. For example, 324 ÷ 3 → 3 digits (108).

If the first digit is less than the divisor, the quotient has one digit less. For example, 136 ÷ 6 → 2 digits (22).

Partial quotients: 7,032 − 6,000 (1,000) = 1,032; − 600 (100) = 432; − 420 (70) = 12; − 12 (2) = 0

Quotient = 1,000 + 100 + 70 + 2 = 1,172

3,005 − 3,000 (600) = 5; 5 − 5 (1) = 0. Quotient = 601

By place value: 30 hundreds ÷ 5 = 6 hundreds; 0 tens ÷ 5 = 0 tens; 5 ones ÷ 5 = 1. We write 0 in the tens place to keep the places correct.

2,874 − 2,800 (200) = 74; 74 − 70 (5) = 4

Quotient = 205, Remainder = 4. (7 tens cannot be divided by 14, so we write 0 in the tens place.)

9,805 − 9,600 (300) = 205; 205 − 192 (6) = 13

Quotient = 306, Remainder = 13. Check: 32 × 306 + 13 = 9,805

4)480(120 → 480 ÷ 4 = 120

3)906(302 → 906 ÷ 3 = 302

20)400(20 → 400 ÷ 20 = 20

50)1000(20 → 1,000 ÷ 50 = 20

4)848(212 → 848 ÷ 4 = 212 (or 868 ÷ 4 = 217)

3)936(312 → 936 ÷ 3 = 312

4)88(22 → 88 ÷ 4 = 22 (or 88 ÷ 2 = 44, 88 ÷ 8 = 11)

3)960(320 → 960 ÷ 3 = 320 (or 900 ÷ 2 = 450)

1)180(180 → 180 ÷ 1 = 180

8)6,480(810 → 6,480 ÷ 8 = 810 (or 6,480 ÷ 9 = 720)

5 × 42 = 210 and 420 ÷ 2 = 210. The number is 210.

(a) 475 ÷ 45 = 10 R 25. 10 shows seat 450 people. 25 more need 1 more show. So, 11 shows are needed.

(b) 2 shows a day: 11 ÷ 2 = 5 R 1. So, 6 days are needed.

Ice cream eaten = 5,000 g − 400 g = 4,600 g

Each friend ate 4,600 g ÷ 23 = 200 g

Total biscuits = 15 × 8 = 120

Each person gets 120 ÷ 6 = 20 biscuits

Each day = 20 ÷ 4 = 5 biscuits

(a) 9,045 ÷ 5 = 1,809 R 0 → 5 × 1,809 = 9,045 ✓

(b) 1,034 ÷ 4 = 258 R 2 → 4 × 258 + 2 = 1,034 ✓

(c) 2,504 ÷ 7 = 357 R 5 → 7 × 357 + 5 = 2,504 ✓

(d) 8,900 ÷ 15 = 593 R 5 → 15 × 593 + 5 = 8,900 ✓

(e) 9,876 ÷ 32 = 308 R 20 → 32 × 308 + 20 = 9,876 ✓

(f) 7,506 ÷ 24 = 312 R 18 → 24 × 312 + 18 = 7,506 ✓

A. (b) 340 ÷ 17 = 20 (c) 680 ÷ 17 = 40 (d) 680 ÷ 34 = 20 (e) 170 ÷ 17 = 10 (f) 680 ÷ 68 = 10

B. (b) 192 ÷ 8 = 24 (c) 384 ÷ 8 = 48 (d) 384 ÷ 4 = 96 (e) 384 ÷ 8 = 48 (f) 86 ÷ 2 = 43

C. (b) 704 ÷ 22 = 32 (c) 704 ÷ 11 = 64 (d) 352 ÷ 22 = 16 (e) 1,408 ÷ 44 = 32

Relation: Doubling the dividend doubles the quotient. Doubling the divisor halves the quotient. Doubling both keeps the quotient the same.

(a) Distance each day = 576 ÷ 12 = 48 km

(b) Ratnagiri to Goa = 232 km. In 4 days: 232 ÷ 4 = 58 km each day

(a) Missing: the price of one mango. If one mango costs ₹10: 6 × 12 = 72 mangoes, 72 × ₹10 = ₹720.

(b) Missing: the total number of desks. If there are 240 desks: 240 ÷ 8 = 30 desks in each classroom.

(c) Nothing is missing. One bat costs ₹3,500 ÷ 5 = ₹700.

(d) Missing: the price of one idli. One plate costs ₹6,250 ÷ 125 = ₹50. If one idli costs ₹25, each plate has 50 ÷ 25 = 2 idlis.

The large clips are enough for only 30 bookshelves. So, the carpenter can make 30 bookshelves.

The table records the name of each vegetable, the cost of 1 kg, the quantity supplied and the total amount.

(a) 8 × 9 = 70 + 2 → 72 = 72 → T

(b) 20 − 6 = 7 × 3 → 14 ≠ 21 → F

(c) 48 ÷ 3 = 4 × 4 → 16 = 16 → T

(d) 89 − 9 = 90 + 0 → 80 ≠ 90 → F

(e) 25 + 10 = 45 − 10 → 35 = 35 → T

(a) 7 × 6 = 25 + 17
(b) 87 + 6 = 3 × 31
(c) 63 + 7 = 74 − 4
(d) 72 ÷ 9 = 16 ÷ 2