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NCERT Solutions for Class 5th Maths Chapter 6 Practise Nida's, John's and Mili's father's methods — Let Us Solve

Book page 83–84 Updated on2026-09-19

Q1.
Solve the following problems like Nida. a) 548 × 6 b) 682 × 3 c) 324 × 18 d) 507 × 23 e) 190 × 65
Answer

Nida's grid: split both numbers into place values, multiply every box, add everything.

a) 548 × 6 = 3,288

×500408
63,00024048
3,000 + 240 + 48 = 3,288

b) 682 × 3 = 2,046

×600802
31,8002406
1,800 + 240 + 6 = 2,046

c) 324 × 18 = 5,832

×300204Row total
103,000200403,240
82,400160322,592
3,240 + 2,592 = 5,832

d) 507 × 23 = 11,661

×50007Row total
2010,000014010,140
31,5000211,521
10,140 + 1,521 = 11,661

e) 190 × 65 = 12,350

×10090Row total
606,0005,40011,400
5500450950
11,400 + 950 = 12,350
Do not skip the zero. In d) the middle digit of 507 is 0, so those two boxes are 0. Many students forget the tens column altogether and lose a place — keep the empty box in the grid to remind yourself.
Q2.
Solve the following problems like John. a) 123 × 84 b) 368 × 32 c) 159 × 324 d) 239 × 401 e) 592 × 5 f) 101 × 22
Answer

John's way: one line for each digit of the multiplier, with that line's pieces already added.

a) 123 × 84 = 10,332
Step 1. 4 × 123 → 400 + 80 + 12 = 492
Step 2. 80 × 123 → 8,000 + 1,600 + 240 = 9,840
Step 3. 492 + 9,840 = 10,332
b) 368 × 32 = 11,776
Step 1. 2 × 368 → 600 + 120 + 16 = 736
Step 2. 30 × 368 → 9,000 + 1,800 + 240 = 11,040
Step 3. 736 + 11,040 = 11,776
c) 159 × 324 = 51,516
Step 1. 4 × 159 → 400 + 200 + 36 = 636
Step 2. 20 × 159 → 2,000 + 1,000 + 180 = 3,180
Step 3. 300 × 159 → 30,000 + 15,000 + 2,700 = 47,700
Step 4. 636 + 3,180 + 47,700 = 51,516
d) 239 × 401 = 95,839
Step 1. 1 × 239 = 239
Step 2. 0 × 239 = 0
Step 3. 400 × 239 → 80,000 + 12,000 + 3,600 = 95,600
Step 4. 239 + 0 + 95,600 = 95,839
e) 592 × 5 = 2,960
Step 1. 5 × 592 → 2,500 + 450 + 10 = 2,960
f) 101 × 22 = 2,222
Step 1. 2 × 101 → 200 + 0 + 2 = 202
Step 2. 20 × 101 → 2,000 + 0 + 20 = 2,020
Step 3. 202 + 2,020 = 2,222
Check f) in your head: 101 × 22 = 100 × 22 + 1 × 22 = 2,200 + 22 = 2,222 ✓ A number times 101 is that number with itself added on at the end.
Q3.
Let us solve a few questions like Mili's father: 806 × 9, 455 × 26, and 143 × 208 (fill the boxes and circles).
Answer

806 × 9 = 7,254; 455 × 26 = 11,830; 143 × 208 = 29,744. Here is every box filled.

First puzzle: 806 × 9

  1. 9 × 6 = 54. Write 4 in ones, carry 5 into the tens circle.
  2. 9 × 0 tens = 0. Add the carry: 0 + 5 = 5. Write 5 in tens.
  3. 9 × 8 hundreds = 72 hundreds. Write 2 in hundreds and 7 in thousands.
  4. Answer: 7,254

Second puzzle: 455 × 26

Row 1 — the 6
6 × 5 = 30 → write 0, carry 3
6 × 5 tens = 30 tens, add carry 3 tens = 33 tens → write 3, carry 3
6 × 4 hundreds = 24 hundreds, add carry 3 hundreds = 27 hundreds
Row 1 = 2,730

Row 2 — the 2 tens
20 × 455 = 9,100
Row 2 = 9,100

Total = 2,730 + 9,100 = 11,830

Third puzzle: 143 × 208

Row 1 — the 8
8 × 3 = 24 → write 4, carry 2
8 × 4 tens = 32 tens, add 2 tens = 34 tens → write 4, carry 3
8 × 1 hundred = 8 hundreds, add 3 hundreds = 11 hundreds
Row 1 = 1,144

Row 2 — the 0 tens
0 × 143 = 0

Row 3 — the 2 hundreds
200 × 143 = 28,600

Total = 1,144 + 0 + 28,600 = 29,744
Check the second one: 455 × 26 = 455 × 25 + 455 = 11,375 + 455 = 11,830 ✓
The circles hold the carries. Writing them in a circle above the column keeps them separate from the digits of the number, so you never mistake a carry for part of the answer.
Q4.
Now use Mili's father's method to solve the following questions. (a) 807 × 5 (b) 143 × 28 (c) 309 × 9
Answer
(a) 807 × 5 = 4,035
Step 1. 5 × 7 = 35 → write 5, carry 3
Step 2. 5 × 0 tens = 0, add carry 3 → write 3
Step 3. 5 × 8 hundreds = 40 hundreds → write 0 in hundreds, 4 in thousands
Answer: 4,035
(b) 143 × 28 = 4,004
Row 1 — the 8
8 × 3 = 24 → write 4, carry 2
8 × 4 tens = 32 tens + 2 tens = 34 tens → write 4, carry 3
8 × 1 hundred = 8 hundreds + 3 hundreds = 11 hundreds
Row 1 = 1,144

Row 2 — the 2 tens
20 × 143 = 2,860

Total = 1,144 + 2,860 = 4,004
(c) 309 × 9 = 2,781
Step 1. 9 × 9 = 81 → write 1, carry 8
Step 2. 9 × 0 tens = 0, add carry 8 → write 8
Step 3. 9 × 3 hundreds = 27 hundreds → write 7 in hundreds, 2 in thousands
Answer: 2,781
Check (b): 143 × 28 = 143 × 30 − 143 × 2 = 4,290 − 286 = 4,004 ✓
Q5.
(d) 450 × 38 (e) 584 × 23 (f) 302 × 13
Answer
(d) 450 × 38 = 17,100
Row 1 — the 8: 8 × 450 = 3,600
Row 2 — the 3 tens: 30 × 450 = 13,500
Total = 3,600 + 13,500 = 17,100
(e) 584 × 23 = 13,432
Row 1 — the 3
3 × 4 = 12 → write 2, carry 1
3 × 8 tens = 24 tens + 1 ten = 25 tens → write 5, carry 2
3 × 5 hundreds = 15 hundreds + 2 hundreds = 17 hundreds
Row 1 = 1,752

Row 2 — the 2 tens: 20 × 584 = 11,680

Total = 1,752 + 11,680 = 13,432
(f) 302 × 13 = 3,926
Row 1 — the 3: 3 × 302 = 906
Row 2 — the 1 ten: 10 × 302 = 3,020
Total = 906 + 3,020 = 3,926
Check (d) with doubling and halving: 450 × 38 = 900 × 19 = 900 × 20 − 900 = 18,000 − 900 = 17,100 ✓
Q6.
(g) 604 × 54 (h) 112 × 23 (i) 237 × 19
Answer
(g) 604 × 54 = 32,616
Row 1 — the 4: 4 × 604 = 2,416
Row 2 — the 5 tens: 50 × 604 = 30,200
Total = 2,416 + 30,200 = 32,616
(h) 112 × 23 = 2,576
Row 1 — the 3: 3 × 112 = 336
Row 2 — the 2 tens: 20 × 112 = 2,240
Total = 336 + 2,240 = 2,576
(i) 237 × 19 = 4,503
Row 1 — the 9
9 × 7 = 63 → write 3, carry 6
9 × 3 tens = 27 tens + 6 tens = 33 tens → write 3, carry 3
9 × 2 hundreds = 18 hundreds + 3 hundreds = 21 hundreds
Row 1 = 2,133

Row 2 — the 1 ten: 10 × 237 = 2,370

Total = 2,133 + 2,370 = 4,503
Check (i) with the nearest multiple: 237 × 20 = 4,740. That is one group of 237 too many. 4,740 − 237 = 4,503 ✓
Watch the zero in (g): 604 has 0 tens. So in the first row, 4 × 0 tens = 0, and only the carry from 4 × 4 = 16 goes into the tens place. Skipping the zero column is how answers lose a whole place value.
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