NCERT Solutions for Class 4th Maths Chapter 9 Patterns in the multiplication chart — In-text Questions
Book page 136 Updated on2026-09-19
Q1.
Colour the common multiples of the following numbers. Use different colours for each item. a) 2 and 3 b) 4 and 8 c) 7 and 9. Share your observations regarding the numbers that are common multiples in each case.The multiplication chart from the book: 10 rows and 10 columns, with the green squares and the diagonal line marked.
Answer
×
1
2
3
4
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7
8
9
10
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1
2
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6
7
8
9
10
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2
4
6
8
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18
20
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3
6
9
12
15
18
21
24
27
30
4
4
8
12
16
20
24
28
32
36
40
5
5
10
15
20
25
30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
20
30
40
50
60
70
80
90
100
The completed multiplication chart.
a) Common multiples of 2 and 3 are the numbers in the 6 times table.
b) Common multiples of 4 and 8 are the numbers in the 8 times table: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80.
c) Common multiples of 7 and 9: only 63 appears in this chart (7 × 9 and 9 × 7). The next one is 126, which is bigger than 100.
Why it happens: A number that is in both lists must hold whole groups of each. For 2 and 3 the smallest such number is 6, for 4 and 8 it is 8, and for 7 and 9 it is 63.
Q2.
Observe the pattern in the ones digits of the products in row 5? Observe the ones digit of the products in other rows also. What patterns do you notice?The multiplication chart from the book: 10 rows and 10 columns, with the green squares and the diagonal line marked.
Answer
×
1
2
3
4
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1
2
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9
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2
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6
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18
20
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3
6
9
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15
18
21
24
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30
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4
8
12
16
20
24
28
32
36
40
5
5
10
15
20
25
30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
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100
Row 5 of the chart.
In row 5 the ones digit goes 5, 0, 5, 0, 5, 0, 5, 0, 5, 0 — it repeats after two steps.
Row
Ones digits of the products
2
2, 4, 6, 8, 0, 2, 4, 6, 8, 0
4
4, 8, 2, 6, 0, 4, 8, 2, 6, 0
5
5, 0, 5, 0, 5, 0, 5, 0, 5, 0
6
6, 2, 8, 4, 0, 6, 2, 8, 4, 0
10
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
The ones digits repeat in every row.
Why it happens: After 10 steps of the same size we come back to a ten, so the ones digits start over. Rows 2, 4, 6 and 8 repeat after 5 steps; row 5 after 2 steps.
Q3.
Here is row 8 of the chart: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80. The ones digit of the products are: 8, 6, 4, 2, 0, 8, 6, 4, 2, 0. Do you see a repeating pattern here? Guess the ones digit of the following products. Verify your answer by multiplying. 11 × 8 _____ 12 × 8 _____ 13 × 8 _____The multiplication chart from the book: 10 rows and 10 columns, with the green squares and the diagonal line marked.
Why it happens: Adding 8 each time changes the ones digit in the same order again and again, so the pattern never breaks.
Q4.
In row 8 of the chart, there is no number whose ones digit is 1. What other digits do not appear as the ones digit?The multiplication chart from the book: 10 rows and 10 columns, with the green squares and the diagonal line marked.
Answer
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1
2
3
4
5
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7
8
9
10
1
1
2
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4
5
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8
9
10
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2
4
6
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12
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18
20
3
3
6
9
12
15
18
21
24
27
30
4
4
8
12
16
20
24
28
32
36
40
5
5
10
15
20
25
30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
20
30
40
50
60
70
80
90
100
Row 8 of the chart.
The digits 1, 3, 5, 7 and 9 never appear as the ones digit in row 8.
Why it happens: Every number in row 8 is a group of 8s, so it is even. Even numbers can never end in an odd digit.
Q5.
Is there a row in which all the digits from 0 to 9 appear as the ones digit? Which rows have this property?The multiplication chart from the book: 10 rows and 10 columns, with the green squares and the diagonal line marked.
Answer
×
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
6
7
8
9
10
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2
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6
8
10
12
14
16
18
20
3
3
6
9
12
15
18
21
24
27
30
4
4
8
12
16
20
24
28
32
36
40
5
5
10
15
20
25
30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
20
30
40
50
60
70
80
90
100
The completed multiplication chart.
Yes. Rows 1, 3, 7 and 9 have all ten digits as ones digits.
Row
Ones digits
1
1, 2, 3, 4, 5, 6, 7, 8, 9, 0
3
3, 6, 9, 2, 5, 8, 1, 4, 7, 0
7
7, 4, 1, 8, 5, 2, 9, 6, 3, 0
9
9, 8, 7, 6, 5, 4, 3, 2, 1, 0
Each of these rows uses every digit from 0 to 9 exactly once.
Why it happens: 1, 3, 7 and 9 share no factor with 10. So their jumps land on a fresh ones digit each time until all ten are used.
Q6.
It can be seen in row 8 that 0 appears as the ones digit two times. ___ × 8 gives 0 as the ones digit. What numbers can go in the box? Give 5 examples of such numbers.The multiplication chart from the book: 10 rows and 10 columns, with the green squares and the diagonal line marked.
Answer
×
1
2
3
4
5
6
7
8
9
10
1
1
2
3
4
5
6
7
8
9
10
2
2
4
6
8
10
12
14
16
18
20
3
3
6
9
12
15
18
21
24
27
30
4
4
8
12
16
20
24
28
32
36
40
5
5
10
15
20
25
30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
20
30
40
50
60
70
80
90
100
Row 8 of the chart.
Any multiple of 5 can go in the box.
Number in the box
× 8
Ones digit
5
40
0
10
80
0
15
120
0
20
160
0
25
200
0
Five numbers that work.
Why it happens: 5 × 8 = 40 already ends in 0. Every extra group of 5 eights adds another 40, so the answer keeps ending in 0.
Q7.
Is there a row in which 0 appears as the ones digit only once? Which rows have this property?The multiplication chart from the book: 10 rows and 10 columns, with the green squares and the diagonal line marked.
Answer
×
1
2
3
4
5
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7
8
9
10
1
1
2
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8
9
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2
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3
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4
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36
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5
10
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30
35
40
45
50
6
6
12
18
24
30
36
42
48
54
60
7
7
14
21
28
35
42
49
56
63
70
8
8
16
24
32
40
48
56
64
72
80
9
9
18
27
36
45
54
63
72
81
90
10
10
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30
40
50
60
70
80
90
100
The completed multiplication chart.
Yes. In rows 1, 3, 7 and 9 the digit 0 appears only once — at the last number.
Row
Numbers ending in 0
1
10
3
30
7
70
9
90
2
10 and 20 (twice)
5
10, 20, 30, 40, 50 (five times)
Only the rows 1, 3, 7 and 9 have a single 0 ending.
Why it happens: A product ends in 0 only when it is a whole number of tens. For rows 1, 3, 7 and 9 that first happens at the 10th step, and the row stops there.
Q8.
What do you notice about the answers for Questions 11 and 13? Share in the grade.
Answer
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7
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56
63
70
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8
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48
56
64
72
80
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9
18
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36
45
54
63
72
81
90
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100
The completed multiplication chart.
Both questions give the same four rows: 1, 3, 7 and 9.
All ten digits appear → rows 1, 3, 7, 9 0 appears only once → rows 1, 3, 7, 9
Why it happens: If a row uses each digit just once, then 0 also comes just once. So the two answers have to be the same rows.