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NCERT Solutions for Class 4th Maths Chapter 10 Reading patterns in the addition table — Addition Chart

Book page 150 Updated on2026-09-19

Q1.
Look at the table given below and discuss how the table is made.
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
Answer
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.

Every box is made by adding the row number and the column number.

The box in row 6 and column 5
= 6 + 5 = 11

The pink corner (+) sign tells us that. The blue strip on top gives one number, the pink strip on the left gives the other.

Why it happens: The chart is a ready-made answer sheet. Instead of adding every time, we just look where the row and the column meet.
Q2.
Identify some patterns in the table.
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
Answer
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.

Here are four easy patterns.

  • Move one step right and the number goes up by 1.
  • Move one step down and the number goes up by 1.
  • Move one step down and one step left and the number stays the same. So the slanting lines (↗) carry equal numbers.
  • The chart is the same on both sides of the main slant, because 6 + 5 and 5 + 6 are equal.
Why it happens: Going right adds 1 to the column number and going down adds 1 to the row number, so the total goes up by 1 each time.
Q3.
Observe the cells where the number 9 appears in the table. How many times do you see number 9? What about other numbers?
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
Answer
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.

The number 9 appears 10 times.

0 + 9, 1 + 8, 2 + 7, 3 + 6, 4 + 5,
5 + 4, 6 + 3, 7 + 2, 8 + 1, 9 + 0
That is 10 boxes, and they lie on one slanting line.

Other numbers behave like this:

NumberHow many times
01
56
910
1213 (the most)
187
241
Why it happens: Up to 12, a number appears one more time than itself. After 12 the count falls again, because the chart stops at 12.
Q4.
Are there any rows or columns that contain only even numbers or only odd numbers? Explain your observation.
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
Answer
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.

No. There is no such row and no such column.

Row 3 → 3, 4, 5, 6, 7, 8, 9, …
even, odd, even, odd … one after the other

Every row is a line of numbers that go up by 1. So odd and even keep taking turns.

Why it happens: Adding 1 changes an even number into an odd number and an odd number into an even number, every single time.
Q5.
Look at the window frame highlighted in red colour in the table. Find the sum of the two numbers in each row.
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
Answer
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.

The red window holds four numbers.

10    11
11    12

Row sums:

Top row: 10 + 11 = 21
Bottom row: 11 + 12 = 23
Why it happens: The bottom row is 1 more in each box, so its sum is 2 more than the top row’s sum.
Q6.
Find the sum of the two numbers in each column. What do you notice?
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
Answer
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
Left column: 10 + 11 = 21
Right column: 11 + 12 = 23

They are the same two sums as the rows — 21 and 23.

Why it happens: In this chart 10 + 11 and 11 + 10 give the same answer, so the row sums and the column sums must match.
Q7.
Now, find the sum of the numbers in each of the two diagonals marked by arrows. What do you notice?
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
Answer
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
One slant: 10 + 12 = 22
Other slant: 11 + 11 = 22

Both slants give the same sum, 22.

Why it happens: One slant takes 1 less and 1 more than the middle number; the other takes the middle number twice. So both come to the same total.
Q8.
Now, put the red window frame in other places and find the sums as above. What do you notice?
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
Answer
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.

Try the window on rows 2–3 and columns 8–9.

10    11
11    12
Rows: 10 + 11 = 21, 11 + 12 = 23
Columns: 10 + 11 = 21, 11 + 12 = 23
Slants: 10 + 12 = 22, 11 + 11 = 22

Now try rows 7–8 and columns 3–4.

10    11
11    12
Same three answers again: 21, 23 and 22.

Wherever you put the window, the two row sums equal the two column sums, and the two slant sums are equal.

Why it happens: Every 2 by 2 window has the shape n, n+1 on top and n+1, n+2 below. So the answers always come out in the same way.
Q9.
Identify some patterns and relationships among the numbers in the blue window frame.
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.
Answer
+0123456789101112
00123456789101112
112345678910111213
2234567891011121314
33456789101112131415
445678910111213141516
5567891011121314151617
66789101112131415161718
778910111213141516171819
8891011121314151617181920
99101112131415161718192021
1010111213141516171819202122
1111121314151617181920212223
1212131415161718192021222324
The addition chart. The pink block of four is the red window frame; the blue block of nine is the blue window frame.

The blue window holds nine numbers.

7    8    9
8    9    10
9    10    11
  • Each row goes up by 1. Each column goes up by 1.
  • The slant going up to the right is 9, 9, 9 — all the same.
  • The two opposite corners give equal sums: 7 + 11 = 18 and 9 + 9 = 18.
  • Add all nine numbers: 7 + 8 + 9 + 8 + 9 + 10 + 9 + 10 + 11 = 81. And 9 × 9 = 81, so the total is nine times the middle number.
Why it happens: The middle number 9 sits exactly in between. Every number that is a little less has a partner that is just as much more.
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