The step size between the first two consecutive tick marks is 7670 - 7645 = 25. We verify this with Tick 5: 7645 + 4 × 25 = 7745, which matches the given value. Thus, the missing values are: Tick 3: 7695, Tick 4: 7720, Tick 6: 7770, Tick 7: 7795, and Tick 8: 7820.

The step size between the first two consecutive tick marks is 7670 - 7645 = 25. We verify this with Tick 5: 7645 + 4 × 25 = 7745, which matches the given value. Thus, the missing values are: Tick 3: 7695, Tick 4: 7720, Tick 6: 7770, Tick 7: 7795, and Tick 8: 7820.

4. Look at the window frame highlighted in red colour in the table. a) Find the sum of the two numbers in each row. b) Find the sum of the two numbers in each column. What do you notice? c) Now, find the sum of the numbers in each of the two diagonals marked by arrows. What do you notice? d) Now, put the red window frame in other places and find the sums as above. What do you notice? 5. Identify some patterns and relationships among the numbers in the blue window frame. Reverse and Add a) Take a 2-digit number say, $27$ . Reverse its digits ( $72$ ). Add them ( $99$ ). Repeat for different 2-digit numbers. b) What sums can we get when we add a 2-digit number with its reverse? c) List down all numbers which when added to their reverse give i) $55$ ii) $88$ d) Can we get a 3-digit sum? What is the smallest 3-digit sum that we can get? Fill in the blanks with appropriate numbers. a) A sequence of trees with numbers inside: Tree 1: $2540$ Tree 2: $2590$ Tree 3: [blank] Tree 4: [blank] Tree 5: [blank] Tree 6: [blank] b) A sequence of capsules/bread shapes with numbers inside: Shape 1: $354$ Shape 2: $1354$ Shape 3: [blank] Shape 4: [blank] Shape 5: [blank] Shape 6: [blank] Shape 7: [blank] c) A number line with equal intervals, a kangaroo positioned on the 4th tick mark, and tick marks having labels or boxes: - Tick 1: $7645$ - Tick 2: $7670$ - Tick 3: [blank box] - Tick 4: [blank box] - Tick 5: $7745$ - Tick 6: [blank box] - Tick 7: [blank box] - Tick 8: [blank box]

Answer: 4 & 5: Underdetermined without page 150 table. Reverse & Add: b) Multiples of 11 (from 11 to 198); c) i) 14, 23, 32, 41, 50; ii) 17, 26, 35, 44, 53, 62, 71, 80; d) Yes, smallest 3-digit sum is 110. Fill in the blanks: a) 2640, 2690, 2740, 2790; b) 2354, 3354, 4354, 5354, 6354; c) 7695, 7720, 7770, 7795, 7820.

Step-by-step solution

Step 1: Analyze Questions 4 and 5

Questions 4 and 5 refer to specific red and blue window frames placed over a number grid located on the preceding page (page 150). Because the table containing those numbers is not visible in this image, Questions 4 and 5 are mathematically underdetermined without that reference grid.

Step 2: Reverse and Add: General Structure and Parts (a) and (b)

For any $2$ -digit number with tens digit $a$ and units digit $b$ , the number is $10a + b$ and its reverse is $10b + a$ . Their sum is $(10a + b) + (10b + a) = 11(a + b)$ . Therefore, any sum obtained by adding a $2$ -digit number to its reverse is always a multiple of $11$ , ranging from $11 \times (1 + 0) = 11$ up to $11 \times (9 + 9) = 198$ .

Step 3: Reverse and Add: Parts (c) and (d)

For part (c)(i), $11(a + b) = 55 \implies a + b = 5$ . With digits $a \in \{1, \dots, 9\}$ and $b \in \{0, \dots, 9\}$ , the possible $2$ -digit numbers are $14, 23, 32, 41, 50$ . For (c)(ii), $11(a + b) = 88 \implies a + b = 8$ , giving $17, 26, 35, 44, 53, 62, 71, 80$ . For part (d), yes, we can get a $3$ -digit sum when $a + b \ge 10$ . The smallest sum occurs when $a + b = 10$ , which gives $11 \times 10 = 110$ (for instance, $19 + 91 = 110$ or $28 + 82 = 110$ ).

Step 4: Fill in the Blanks: Pattern (a)

The difference between the first two terms is $2590 - 2540 = 50$ . Continuing to add $50$ to each successive term yields: Tree 3: $2590 + 50 = 2640$ , Tree 4: $2640 + 50 = 2690$ , Tree 5: $2690 + 50 = 2740$ , and Tree 6: $2740 + 50 = 2790$ .

Step 5: Fill in the Blanks: Pattern (b)

The difference between the first two terms is $1354 - 354 = 1000$ . Adding $1000$ to each successive term gives: Shape 3: $2354$ , Shape 4: $3354$ , Shape 5: $4354$ , Shape 6: $5354$ , and Shape 7: $6354$ .

Step 6: Fill in the Blanks: Number Line (c)

The step size between the first two consecutive tick marks is $7670 - 7645 = 25$ . We verify this with Tick 5: $7645 + 4 \times 25 = 7745$ , which matches the given value. Thus, the missing values are: Tick 3: $7695$ , Tick 4: $7720$ , Tick 6: $7770$ , Tick 7: $7795$ , and Tick 8: $7820$ .

Solve your own maths question free →