Samacheer Kalvi Class 4 Maths Solutions Term 1 Chapter 3 Patterns Exercise 3.4

Tamilnadu Samacheer Kalvi 4th Maths Solutions Term 1 Chapter 3 Patterns Ex 3.4

Fill in the blanks:

(i) 90, 180, 270, ____, ____, ____
(ii) A9, B18, C27, 836, ____, ____, ____, E45 F54, G63.
Answer:
(i) 90, 180, 270, 360, 450, 540.
(ii) A9, B18, C27, D36, E45, F54, G63. This sequence follows a pattern where the letter moves to the next alphabet and the number increases by 9 each time (9, 18, 27, 36, 45, 54, 63).
In simple words: For (i), add 90 each time. For (ii), the letter goes up by one, and the number goes up by nine.

🎯 Exam Tip: Look for both numerical and alphabetical patterns. For numbers, check if they are adding, subtracting, multiplying, or dividing by a fixed amount.

B. Circle the Multiples of 9:

25, 27, 35, 36, 45, 46, 54, 55
Answer: The multiples of 9 from the list are 27, 36, 45, and 54. A number is a multiple of 9 if it can be divided by 9 without any remainder, or if the sum of its digits is a multiple of 9.
In simple words: Find all the numbers in the list that you can divide by 9 exactly. These are 27, 36, 45, and 54.

🎯 Exam Tip: To quickly check if a number is a multiple of 9, add up its digits. If that sum is a multiple of 9, the original number is also a multiple of 9.

C. Complete the Following Sequence:

Question 1. Complete the sequence: 125, 150, 175, ____, ____, ____
Answer: The pattern in this sequence is adding 25 to the previous number. So, the sequence continues as 125, 150, 175, 200, 225, 250. This is an arithmetic progression with a common difference of 25.
In simple words: Each number is 25 more than the one before it. So, just keep adding 25.

🎯 Exam Tip: For number sequences, first check the difference between consecutive numbers. If it's constant, it's an arithmetic progression.

Question 2. Complete the sequence: 100, 400, 700, ____, ____, ____
Answer: This sequence shows a pattern of adding 300 to the previous number. So, the complete sequence is 100, 400, 700, 1000, 1300, 1600. Finding the difference between terms is key to solving such problems.
In simple words: Each new number is found by adding 300 to the last number. Just keep adding 300.

🎯 Exam Tip: Always calculate the difference between the first few terms to quickly identify the rule for the sequence.

Question 3. Complete the following sequence in the table: A100 C300 E50, ____, ____, ____, ____
Answer: The pattern in the sequence is that the letter skips one alphabet (A, C, E, G, I, K), and the number increases by 200 each time (100, 300, 500, 700, 900, 1100). The completed sequence is shown in the table below:

In simple words: Letters skip one (like A to C), and numbers go up by 200.

🎯 Exam Tip: For patterns with letters and numbers, look for rules in both parts: how letters change and how numbers change.

Question 4. Complete the following sequence in the table: 200, 400, 600, ____, ____, ____
Answer: This sequence follows a pattern where each number increases by 200 from the previous one. The completed sequence is:

In simple words: Each number is 200 more than the one before it. Keep adding 200 to find the next numbers.

🎯 Exam Tip: Always look for a constant difference or a multiplication factor in number patterns.

Complete the Following Sequence:

Question 1. Complete the following sequence:
9 x 6 = 54
9 × 66 = 594
9 x 666 = 5994
9 × 6666 = 5____4
9 × 666666 = ____
Answer: The pattern shows that as the number of 6s increases in the multiplier, the number of 9s in the middle of the answer also increases. The last digit remains 4 and the first digit remains 5. This is a special property of multiplying by numbers consisting of repeated sixes.
9 × 6666 = 59994
9 × 666666 = 5999994
In simple words: When you multiply 9 by numbers like 6, 66, 666, the answer always starts with 5 and ends with 4. In between, there are many 9s, one less than the number of 6s in the number you multiplied by.

🎯 Exam Tip: Observe how the number of repeating digits in the multiplier affects the repeating digits in the product.

Question 2. Complete the following sequence:
9 × 111 = 999
9 × 222 = ____
9 × 333 = 2997
9 × 444 = ____
9 × 555 = ____
9 × 666 = ____
Answer: The pattern shows that multiplying 9 by a three-digit number with repeating digits (like 111, 222) results in a product where the product of 9 and the repeating digit is then replicated. More simply, 9 times 'x' hundred eleven is 'x' times 999. So, 9 x 222 = 2 x 999 = 1998, 9 x 444 = 4 x 999 = 3996, and so on. This pattern is useful for quick mental calculations.
9 × 111 = 999
9 × 222 = 1998
9 × 333 = 2997
9 × 444 = 3996
9 × 555 = 4995
9 × 666 = 5994.
In simple words: Look at the first digit of the number being multiplied by 9 (like '1' in 111 or '2' in 222). Then multiply that digit by 999 to get the answer.

🎯 Exam Tip: When a pattern involves multiplication by a number like 9, look for properties like \( 9 \times (n \times 111) = n \times (9 \times 111) = n \times 999 \).

E. Answer the Following Questions:

Question 1. The school bell rings once every hour to mark the end or start of a session. Breaks are 20 minutes long. Complete the time table below:

Answer: Each period lasts one hour, and breaks are 20 minutes. Starting from 9:00 AM, the periods and breaks will be as follows: Period 1 (9:00-10:00), Period 2 (10:00-11:00), Break (11:00-11:20), Period 3 (11:20-12:20), Period 4 (12:20-1:20), Break (1:20-1:40), Period 5 (1:40-2:40). The completed table is:

In simple words: Periods are one hour long. Breaks are 20 minutes. Fill in the times by adding one hour for periods and 20 minutes for breaks.

🎯 Exam Tip: Pay close attention to the duration of each interval (period and break) when filling out a timetable.

Question 2. Imagine you are a traffic inspector. Design the traffic signal timings. Here is the time table to complete:

Answer: As a traffic inspector, the timings for signals can be designed with a consistent flow. Based on the provided solution, the pattern for signal changes is a few minutes per phase. The completed table shows: Red (7:30 am), Yellow/orange (7:32 am), Green (7:33 am), Red (7:35 am), Green (7:37 am). This helps manage traffic safely and efficiently.

In simple words: The traffic lights change colors after a few minutes. We fill in the times based on the pattern shown.

🎯 Exam Tip: When setting up a timetable, ensure logical progression and realistic durations for each event.

Question 3. A city is planned in such a way that every 5km has a circle and has 4 signals around. How many signals are needed for a 20 km distance?
Answer: If there is a circle with 4 signals every 5 km, then for a 20 km distance, we need to find how many 5 km segments there are. There are \( \frac{20 \text{ km}}{5 \text{ km}} = 4 \) segments of 5 km. Since each segment has 4 signals, the total number of signals needed is \( 4 \times 4 = 16 \) signals. This pattern helps city planners design efficient traffic flow.
\( \implies \) For 5 km: 4 signals
\( \implies \) For 10 km: 4 + 4 = 8 signals
\( \implies \) For 15 km: 4 + 4 + 4 = 12 signals
\( \implies \) For 20 km: 4 + 4 + 4 + 4 = 16 signals.
Therefore, 16 signals are needed for a 20 km distance.
In simple words: Every 5 kilometers needs 4 signals. For 20 kilometers, which is like four groups of 5 kilometers, you need 4 times 4 signals, which is 16 signals in total.

🎯 Exam Tip: Break down word problems into smaller, manageable steps. Identify the rate (signals per km) and then multiply by the total distance.