Samacheer Kalvi Class 6 Maths Solutions Term 1 Chapter 1 Numbers Exercise 1.3

Question 1. Fill in the blanks.
Answer:
1. If Arulmozhi saves Rs 12 per day then she saves Rs 360 in 30 days. To find this, we multiply her daily savings by the number of days.
2. If a person 'A' earns Rs 1800 in 12 days, then he earns Rs 150 in a day. We divide the total earnings by the number of days to get the daily earning.
3. \( 45 \div (7 + 8) - 2 = 1 \). First, we add the numbers in the bracket, then divide, and finally subtract.
In simple words: For fill-in-the-blanks, you need to do calculations like multiplying daily savings by days, dividing total earnings by days, or using the order of operations for math problems.

🎯 Exam Tip: Always read fill-in-the-blank questions carefully to understand the operation required (addition, subtraction, multiplication, or division).

Question 2. Say True or False
Answer:
1. \( 3 + 9 \times 8 = 96 \) is False. According to the order of operations, multiplication is done before addition. So, \( 3 + (9 \times 8) = 3 + 72 = 75 \), which is not 96.
2. \( 7 \times 20 - 4 = 136 \) is True. Following the order of operations, multiply first: \( (7 \times 20) - 4 = 140 - 4 = 136 \). This matches the given value.
3. \( 40 + (56 - 6) \div 2 = 45 \) is False. We first solve the bracket: \( 40 + (50) \div 2 \). Then we divide: \( 40 + 25 = 65 \), which is not 45.
In simple words: To check if a statement is true or false, always follow the correct order of operations (like BIDMAS/BODMAS). Do operations inside brackets first, then multiplication or division, and finally addition or subtraction.

🎯 Exam Tip: Remember BIDMAS/BODMAS (Brackets, Indices/Orders, Division, Multiplication, Addition, Subtraction) to correctly evaluate mathematical expressions.

Question 3. The number of people who visited the Public Library for the past 5 months was 1200, 2000, 2450, 3060 and 3200 respectively. How many people visited the library in the last 5 months.
Answer: To find the total number of people who visited the library in the last 5 months, we add up the visitors from each month. We simply combine all the given numbers to find the grand total.
People visited the library for past 5 months = \( 1200 + 2000 + 2450 + 3060 + 3200 = 11910 \)
Total people visited = 11910.
In simple words: We add up the visitors from each of the five months to get the total number of people who visited the library.

🎯 Exam Tip: For "how many total" questions, addition is usually the operation needed. Carefully list all numbers and sum them.

Question 4. Cheran had a bank savings of Rs 7,50,250. He withdrew Rs 5,34,500 for educational purposes. Find the balance amount in his account.
Answer: To find the balance amount, we need to subtract the amount Cheran withdrew from his initial bank savings. This shows how much money is left after taking some out.
Bank Savings of Cheran = Rs 7,50,250
Withdrew Amount = Rs 5,34,500
Balance Amount = Rs \( 7,50,250 - 5,34,500 = 2,15,750 \)
In simple words: We take the money Cheran had in his bank and subtract the money he took out. The remaining amount is his balance.

🎯 Exam Tip: "Balance amount" or "amount left" usually signals a subtraction problem. Ensure you subtract the smaller number from the larger number.

Question 5. In a cycle factory, 1560 bicycles were manufactured every day. Find the number of bicycles manufactured in 25 days.
Answer: To find the total number of bicycles manufactured in 25 days, we multiply the number of bicycles made each day by the total number of days. This gives us the total production over that period.
Bicycles manufactured in one day = 1560
Bicycles manufactured in 25 days = \( 1560 \times 25 \)
= 39,000 bicycles
In simple words: We multiply the number of cycles made daily by the total number of days to find how many cycles were made in total.

🎯 Exam Tip: When a problem gives a rate "per day" and asks for a total over "many days," multiplication is the correct operation.

Question 6. Rs 62,500 was equally distributed as a New Year bonus for 25 employees of a company. How much did each receive?
Answer: To find out how much each employee received, we divide the total bonus amount by the number of employees. This ensures an equal share for everyone.
Total amount = Rs 62,500
Total number of employees = 25
Bonus amount received by each employee = Rs \( 62,500 \div 25 \)
= Rs 2,500
In simple words: We divide the total bonus money by the number of employees to find out how much money each person got.

🎯 Exam Tip: "Equally distributed" or "share for each" problems always require division to find the individual amount.

Question 7. Simplify the following numerical expressions:
(i) \( (10 + 17) \div 3 \)
(ii) \( 12 - [3 - \{6 - (5 - 1)\}] \)
(iii) \( 100 + 8 \div 2 + \{(3 \times 2) - 6 \div 2\} \)
Answer:
(i) \( (10 + 17) \div 3 \)
We first add the numbers inside the parentheses.
\( = 27 \div 3 \)
Next, we perform the division.
\( = 9 \)
(ii) \( 12 - [3 - \{6 - (5 - 1)\}] \)
We start by solving the innermost parentheses.
\( = 12 - [3 - \{6 - 4\}] \)
Next, we solve the curly brackets.
\( = 12 - [3 - 2] \)
Then, we solve the square brackets.
\( = 12 - 1 \)
Finally, we perform the subtraction.
\( = 11 \)
(iii) \( 100 + 8 \div 2 + \{(3 \times 2) - 6 \div 2\} \)
We begin by solving the operations inside the curly brackets, following the order of operations.
\( = 100 + 8 \div 2 + \{6 - 3\} \)
Now, we complete the curly bracket operation.
\( = 100 + 8 \div 2 + 3 \)
Next, we perform the division operation outside the brackets.
\( = 100 + 4 + 3 \)
Finally, we add all the numbers.
\( = 107 \)
In simple words: When simplifying complex math problems, always remember to follow the order of operations: start with innermost brackets (like parentheses, then curly, then square), then do multiplication and division from left to right, and finally addition and subtraction from left to right.

🎯 Exam Tip: Be very careful with the order of operations (BIDMAS/BODMAS), especially when dealing with multiple types of brackets. Work from the innermost brackets outwards.

Objective Type Questions

Question 8. The value of 3 + 5 – 7 x 1 is
(a) 0
(b) 7
(c) 8
(d) 1
Answer: (d) 1
In simple words: First, multiply 7 by 1, which gives 7. Then, do the addition: 3 plus 5 equals 8. Finally, subtract 7 from 8, which leaves 1.

🎯 Exam Tip: In expressions without brackets, always perform multiplication or division before addition or subtraction.

Question 9. The value of 24 ÷ {8 − (3 × 2)} is
(a) 0
(b) 12
(c) 3
(d) 4
Answer: (b) 12
In simple words: First, solve the innermost part: 3 multiplied by 2 is 6. Next, subtract 6 from 8, which is 2. Finally, divide 24 by 2, which gives 12.

🎯 Exam Tip: Remember to work from the innermost brackets outwards. In this case, first the multiplication, then subtraction within the curly braces, and finally the division.

Question 10. Use BIDMAS and put the correct operator in the box.
2 ..... 6 - 12 ÷ (4 + 2) = 10
(a) +
(b) –
(c) x
(d) ÷
Answer: (c) x
In simple words: If we put 'x' (multiplication) in the blank, the equation becomes 2 x 6 - 12 ÷ (4 + 2) = 10. Following BIDMAS, first calculate (4+2)=6. Then, 12 ÷ 6 = 2. Also, 2 x 6 = 12. So, 12 - 2 = 10, which is correct.

🎯 Exam Tip: When choosing an operator, test each option by applying the BIDMAS/BODMAS rule until the equation balances correctly.