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NCERT Solutions for Class 5th Maths Chapter 6 Same answers without calculating, easy ways, and using a known product — Let Us Do

Book page 86–87 Updated on2026-09-19

Q1.
Identify the problems that have the same answer as the one given at the top of each box. Do not calculate. (12 × 17; 26 × 11; 18 × 4; 55 × 9; 101 × 42; 247 × 8; 1001 × 5; 1999 × 2)
Answer

Here is every box, with the matching problems marked and the reason given.

BoxOptionSame?Reason
12 × 1711 × 18NoNeither number was halved or doubled; this is a different product
12 × 176 × 34Yes12 halved is 6, 17 doubled is 34
26 × 1126 × 10 and 26 × 1Yes11 = 10 + 1
26 × 1120 × 11 and 6 × 11Yes26 = 20 + 6
18 × 49 × 8Yes18 halved is 9, 4 doubled is 8
18 × 420 × 4 − 8Yes18 is 2 less than 20, and 2 × 4 = 8
55 × 950 × 9 and 5 × 9Yes55 = 50 + 5
55 × 954 × 10NoYou may not change both numbers like that
55 × 955 × 10 − 55Yes9 is one less than 10, so take away one 55
101 × 42100 × 42 and 100NoThe extra piece is one 42, not one 100
101 × 42100 × 42 and 42Yes101 = 100 + 1, so add one 42
247 × 8250 × 8 − 24Yes247 is 3 less than 250, and 3 × 8 = 24
247 × 8247 × 10 − 247NoThat gives 247 × 9, not 247 × 8
1001 × 51,000 × 6NoBoth numbers were changed with nothing to balance it
1001 × 51,000 × 5 and 5Yes1001 = 1000 + 1, so add one 5
1999 × 22,000 × 2 − 4No1999 is only 1 less than 2000, so we must take away one 2, not 4
1999 × 22,000 × 2 − 2Yes1999 = 2000 − 1, so take away one 2
Test the last box by hand
1999 × 2 = 3,998
2,000 × 2 − 4 = 4,000 − 4 = 3,996 ✗
2,000 × 2 − 2 = 4,000 − 2 = 3,998 ✓
The one to watch: in the last box only 2,000 × 2 − 2 matches. The option 2,000 × 2 − 4 gives 3,996, which is two too small. Always ask: how many groups did I overshoot by, and how big is each group?
The rule behind every box: You may change a multiplication only if you put back exactly what you took away. Halve one number and you must double the other. Go up to the nearest ten and you must come back down by the whole groups you added.
Q2.
Find easy ways of solving these problems. (a) 16 × 25 (b) 12 × 125 (c) 24 × 250
Answer

All three become easy if you climb to 100, 500 or 1,000 by doubling.

(a) 16 × 25 = 400
Step 1. Halve 16 to 8, double 25 to 50 → 8 × 50
Step 2. Halve 8 to 4, double 50 to 100 → 4 × 100
Step 3. 4 × 100 = 400
(b) 12 × 125 = 1,500
Step 1. Halve 12 to 6, double 125 to 250 → 6 × 250
Step 2. Halve 6 to 3, double 250 to 500 → 3 × 500
Step 3. 3 × 500 = 1,500
(c) 24 × 250 = 6,000
Step 1. Halve 24 to 12, double 250 to 500 → 12 × 500
Step 2. Halve 12 to 6, double 500 to 1,000 → 6 × 1,000
Step 3. 6 × 1,000 = 6,000
Why 25, 125 and 250 love doubling: 25 doubled twice is 100. 125 doubled three times is 1,000. 250 doubled twice is 1,000. Each of them is hiding inside a friendly round number.
Q3.
(d) 36 × 25 (e) 28 × 75 (f) 300 × 15
Answer
(d) 36 × 25 = 900
Step 1. Halve 36 to 18, double 25 to 50 → 18 × 50
Step 2. Halve 18 to 9, double 50 to 100 → 9 × 100
Step 3. 9 × 100 = 900
(e) 28 × 75 = 2,100
Step 1. Notice 75 is three 25s, and 28 is four 7s.
Step 2. 28 × 75 = 7 × 4 × 75 = 7 × 300
Step 3. 7 × 300 = 2,100
(f) 300 × 15 = 4,500
Step 1. Set the zeros aside: 3 × 15 = 45
Step 2. 300 has two zeros, so put two zeros back.
Step 3. Answer = 4,500
Check (e) another way: 28 × 75 = 28 × 100 − 28 × 25 = 2,800 − 700 = 2,100 ✓
Q4.
(g) 50 × 78 (h) 199 × 63 (i) 128 × 35
Answer
(g) 50 × 78 = 3,900
Step 1. Double 50 to 100, halve 78 to 39 → 100 × 39
Step 2. 100 × 39 = 3,900
(h) 199 × 63 = 12,537
Step 1. 199 is one less than 200, so use the nearest multiple.
Step 2. 200 × 63 = 12,600
Step 3. That is one group of 63 too many.
Step 4. 12,600 − 63 = 12,537
(i) 128 × 35 = 4,480
Step 1. Halve 128 to 64, double 35 to 70 → 64 × 70
Step 2. 64 × 7 = 448
Step 3. Put back the zero from 70: 4,480
Check (i) with another halving: 64 × 70 = 32 × 140 = 16 × 280 = 8 × 560 = 4 × 1,120 = 2 × 2,240 = 4,480 ✓ Every step keeps the same answer.
Q5.
Write 5 other examples for which you can find easy ways of getting products.
Answer

Sample answer: the easiest problems are the ones where a number is close to 10, 100 or 1,000, or where doubling turns it into one of those.

My exampleThe easy wayProduct
32 × 2516 × 50 = 8 × 100800
98 × 45100 × 45 − 2 × 45 = 4,500 − 904,410
64 × 12532 × 250 = 16 × 500 = 8 × 1,0008,000
1,001 × 71,000 × 7 + 77,007
45 × 2090 × 10900
How to spot an easy one: Look for 5, 25, 50, 125, 250 (they double up to round numbers), or for 9, 19, 49, 98, 99, 199, 1,001 (they sit right next to round numbers).
Q6.
Find the answers to the following questions based on the given information. (a) 17 × 23 = 391 (b) 17 × 24 = ___ (c) 17 × 22 = ___ (d) 16 × 23 = ___
Answer

(b) 408 (c) 374 (d) 368. You do not need to multiply again — just add or take away one whole group.

  1. (b) 17 × 24. This is one more group of 17 than 17 × 23. So 391 + 17 = 408.
  2. (c) 17 × 22. This is one group of 17 fewer. So 391 − 17 = 374.
  3. (d) 16 × 23. Here the other number went down by 1, so we lose one group of 23. So 391 − 23 = 368.
17 × 23 = 391 one more column = 17 23 columns, each 17 tall 17 × 24 = 391 + 17 = 408
One more column means one more 17. One more row would mean one more 23.
Which number do you add? Ask what changed. If the number of groups went up by 1, add one group size. In 17 × 24, the 23 became 24, so one more group of 17 was added.
Q7.
(e) 8 × 9 = 72 (f) 18 × 9 = ___ (g) 28 × 9 = ___ (h) 108 × 9 = ___ (i) 18 × 23 = ___
Answer

(f) 162 (g) 252 (h) 972 (i) 414.

  1. (f) 18 × 9. 18 is 8 + 10, so add ten more 9s. 72 + 90 = 162.
  2. (g) 28 × 9. 28 is 18 + 10, so add ten more 9s again. 162 + 90 = 252. (Or from 8 × 9: 72 + 180 = 252.)
  3. (h) 108 × 9. 108 is 8 + 100, so add a hundred 9s. 72 + 900 = 972.
  4. (i) 18 × 23. Go back to 17 × 23 = 391. One more row of 23 gives 391 + 23 = 414.
Check (g) directly
28 × 9 = 28 × 10 − 28 = 280 − 28 = 252 ✓

Check (i) directly
18 × 23 = 18 × 20 + 18 × 3 = 360 + 54 = 414 ✓
Did you notice? Every time the first number grows by 10, the answer grows by 10 × 9 = 90. Growing by 100 makes the answer grow by 900. The change is always the size of the jump multiplied by the other number.
Q8.
To find 17 × 24, how much is to be added to 17 × 23 — 17 or 23?
Answer

Add 17.

  1. Look at what changed. The 23 became 24. The 17 stayed the same.
  2. Read the picture. The block is 17 squares tall and 23 columns wide. Going to 24 columns adds one more column.
  3. Count the new column. It is as tall as the block, so it holds 17 squares.
  4. So 17 × 24 = 391 + 17 = 408.
Why not 23: The 23 tells you how many columns there are, not how tall each one is. Adding a column adds a column's worth, and a column here is 17 squares.
Q9.
To find 18 × 23, how much is to be added to 17 × 23 — 17 or 23?
Answer

Add 23.

  1. Look at what changed. This time the 17 became 18. The 23 stayed the same.
  2. Read the picture. The block grows from 17 rows to 18 rows — one extra row along the bottom.
  3. Count the new row. It runs the whole width, so it holds 23 squares.
  4. So 18 × 23 = 391 + 23 = 414.
Remember the pair: one more column adds the height (17); one more row adds the width (23). Look at which number changed, then add the other one.
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