NCERT Solutions for Class 4th Maths Chapter 13 Constructing Tables — Constructing Tables

Book page 186 Updated on2026-09-19

Q1.
Recall the times-tables that we created in Grade 3. Now construct a times-15 table. You may use the arrangement given below and split the columns into 10 and 5 for ease of counting, as shown on the previous page. (1 × 15 = ___, 2 × 15 = ___, … 10 × 15 = ___)
1510
The pebble arrangement printed on page 186 — 15 pebbles across and 10 rows down.
Answer
105
The 10 x 15 pebble arrangement, with each row split into 10 and 5.

Take one row at a time. Each row is 10 pebbles and 5 pebbles.

10 × part5 × partAnswer
1 × 1510515
2 × 15201030
3 × 15301545
4 × 15402060
5 × 15502575
6 × 15603090
7 × 157035105
8 × 158040120
9 × 159045135
10 × 1510050150
So the times-15 table is:
15, 30, 45, 60, 75, 90, 105, 120, 135, 150
Why it happens: Every new row adds one more 10 and one more 5, that is 15 more pebbles each time.
Q2.
1. What patterns do you see in this table?
1510
The pebble arrangement printed on page 186 — 15 pebbles across and 10 rows down.
1 × 15 =6 × 15 =2 × 15 =7 × 15 =3 × 15 =8 × 15 =4 × 15 =9 × 15 =5 × 15 =10 × 15 =
The times-15 table printed on page 186, with every answer still to be filled in.
Answer

Three patterns are easy to see.

  • The ones digit goes 5, 0, 5, 0, 5, 0 … again and again.
  • Each answer is 15 more than the one before it.
  • Every second answer (30, 60, 90, 120, 150) is a multiple of 30 — it is double the one two steps back’s neighbour.
15, 30, 45, 60, 75, 90, 105, 120, 135, 150
15 + 15 = 30   30 + 15 = 45   45 + 15 = 60 …
Why it happens: Adding 15 is adding 10 and then 5. Adding 5 twice makes 10, so the ones digit keeps flipping between 5 and 0.
Q3.
2. Compare the times-15 table with the times-5 table. What similarities and differences do you notice?
Times - 5Times - 15
1 × 5 = 51 × 15 = 15
2 × 5 = 102 × 15 = 30
3 × 5 = 153 × 15 = 45
4 × 5 = ______4 × 15 = ______
5 × 5 = ______5 × 15 = ______
6 × 5 = ______6 × 15 = ______
7 × 5 = ______7 × 15 = ______
8 × 5 = ______8 × 15 = ______
9 × 5 = ______9 × 15 = ______
10 × 5 = ______10 × 15 = ______
The Times-5 and Times-15 box printed on page 186. The book fills in the first three lines of each column.
Answer

Both tables filled in, side by side:

Times - 5Times - 15Difference
1 × 5 = 51 × 15 = 1515 − 5 = 10
2 × 5 = 102 × 15 = 3030 − 10 = 20
3 × 5 = 153 × 15 = 4545 − 15 = 30
4 × 5 = 204 × 15 = 6060 − 20 = 40
5 × 5 = 255 × 15 = 7575 − 25 = 50
6 × 5 = 306 × 15 = 9090 − 30 = 60
7 × 5 = 357 × 15 = 105105 − 35 = 70
8 × 5 = 408 × 15 = 120120 − 40 = 80
9 × 5 = 459 × 15 = 135135 − 45 = 90
10 × 5 = 5010 × 15 = 150150 − 50 = 100

Same:

  • Both end in 5 or 0 every time.
  • Both go up by a fixed jump — 5 in one, 15 in the other.

Different:

  • Every times-15 answer is 3 times the times-5 answer. (3 × 5 = 15)
  • The times-15 answers grow much faster: 5 reaches only 50, but 15 reaches 150.
Why it happens: 15 is 3 fives. So 7 fifteens are just 3 lots of 7 fives — 105 instead of 35.
Q4.
What times-table is this? ____ How did we get this? (15 – 5 = 10, 30 – 10 = 20, 45 – 15 = 30, ____________ …)
Times - 5Times - 15
1 × 5 = 51 × 15 = 15
2 × 5 = 102 × 15 = 30
3 × 5 = 153 × 15 = 45
4 × 5 = ______4 × 15 = ______
5 × 5 = ______5 × 15 = ______
6 × 5 = ______6 × 15 = ______
7 × 5 = ______7 × 15 = ______
8 × 5 = ______8 × 15 = ______
9 × 5 = ______9 × 15 = ______
10 × 5 = ______10 × 15 = ______
The Times-5 and Times-15 box printed on page 186. The book fills in the first three lines of each column.
Answer

It is the times-10 table.

Times - 15Times - 5Difference
15510
301020
451530
602040
752550
903060
1053570
1204080
1354590
15050100
The blank lines are filled like this:
60 − 20 = 40   75 − 25 = 50   90 − 30 = 60
105 − 35 = 70   120 − 40 = 80
135 − 45 = 90   150 − 50 = 100

How we got it: we took each times-15 answer and subtracted the times-5 answer above it.

Why it happens: 15 is 5 and 10 together. Take the 5 away and only the 10 is left, so the differences make the times-10 table.
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