Samacheer Kalvi Class 6 Maths Solutions Term 2 Chapter 5 Information Processing Exercise 5.2

Miscellaneous Practice Problems

 

Question 1. Write the missing numbers in the trees.
Answer:

(i) First, calculate \( 9 \div 3 = 3 \). Then, multiply \( 15 \times 3 = 45 \). The top number is the result of multiplying the first number by the outcome of dividing the other two numbers.
(ii) First, calculate \( 9 + 3 = 12 \). Then, divide \( 65 \div 12 = 5.416... \). The calculation involves dividing the initial number by the sum of the other two.
(iii) First, calculate \( 8 + 5 = 13 \) and \( 9 + 2 = 11 \). Then, subtract \( 13 - 11 = 2 \). This expression shows how to find the difference between two sums.
In simple words: Look at the bottom numbers and their operation first. Calculate that part. Then, use that answer with the next number and its operation, moving up the tree until you find the final missing number.

🎯 Exam Tip: Always start solving tree diagrams from the bottom-most operations (like addition or division) before moving upwards to the operations at the top of the tree.

 

Question 2. Write the missing operations in the trees.
Answer:

(i) We need to find the operation between 6 and 2 that results in 3, which is then added to 8 to give 11. Since \( 6 \div 2 = 3 \), the missing operation is division. The tree shows that \( 8 + (6 \div 2) = 8 + 3 = 11 \).
(ii) We need to find the operation between 6 and 5 that results in 30, which is then subtracted from 39 to give 9. Since \( 6 \times 5 = 30 \), the missing operation is multiplication. The tree shows that \( 39 - (6 \times 5) = 39 - 30 = 9 \).
In simple words: Look at the numbers at the bottom first. Think about what math operation (like plus, minus, times, divide) makes them equal the number above them. Once you find that, use the new number and the next operation to keep going up the tree.

🎯 Exam Tip: To find missing operations, always work backwards from the result or downwards from the known numbers to logically deduce the operator.

 

Question 3. Check whether the Tree diagrams are equal or not.
Answer:

The first tree diagram represents the expression \( c \div (a \div b) \). Here, \( a \) is divided by \( b \) first, and then \( c \) is divided by that result.
The second tree diagram represents the expression \( a \div (b \div c) \). Here, \( b \) is divided by \( c \) first, and then \( a \) is divided by that result.
These two expressions are not equal. For example, if \( a=1, b=2, c=3 \), then \( 3 \div (1 \div 2) = 3 \div 0.5 = 6 \). But \( 1 \div (2 \div 3) = 1 \div 0.666... = 1.5 \). Since division is not associative, the order of operations matters greatly in these types of tree diagrams, and the results will typically be different.
In simple words: The two tree diagrams are not equal. The way the numbers are grouped for division is different in each tree, and this changes the final answer.

🎯 Exam Tip: Remember that division is not an associative operation, meaning \( (a \div b) \div c \neq a \div (b \div c) \), so the order of operations in tree diagrams for division must be carefully evaluated.

Challenge Problems

 

Question 4. Convert the following questions into tree diagrams:
(i) The number of people who visited a library in the last 5 months were 1210, 2100, 2550, 3160 and 3310. Draw the tree diagram of the total number of people who had used the library for the 5 months.
(ii) Ram had a bank deposit of Rs. 7,55,250 and he had withdrawn Rs. 5,34,500 for educational purpose. Find the amount left in his account. Draw a tree diagram for this.
(iii) In a cycle factory, 1,600 bicycles were manufactured on a day. Draw tree diagram to find the number of bicycle produced in 20 days.
(iv) A company with 30 employees decided to distribute Rs. 90, 000 as a special bonus equally among its employees. Draw tree diagram to show how much will each receive?
Answer:
(i) To find the total number of people, we need to add all the given numbers:

The total number of people who visited the library over 5 months is \( 1210 + 2100 + 2550 + 3160 + 3310 = 12330 \). A tree diagram helps visualize the sum of these individual monthly visits to find the grand total.

(ii) To find the amount left, we subtract the withdrawn amount from the initial deposit:Amount left in Ram's account is \( 7,55,250 - 5,34,500 = \text{Rs. } 2,20,750 \). This tree diagram represents a simple subtraction problem to find the remaining balance after a withdrawal.

(iii) To find the total number of bicycles produced in 20 days, we multiply the daily production by the number of days:Number of bicycles produced in 20 days is \( 1600 \times 20 = 32000 \). The tree diagram clearly shows the multiplication of the daily output by the number of days to get the total production.

(iv) To find how much each employee receives, we divide the total bonus amount by the number of employees:Each employee will receive \( 90,000 \div 30 = \text{Rs. } 3000 \). This tree diagram illustrates the division of a total amount equally among a number of people, which is a common way to calculate individual shares.
In simple words: For each problem, think about the main math step needed (like adding, subtracting, multiplying, or dividing). Then, draw a tree that shows this calculation, with the answer at the top and the numbers at the bottom.

🎯 Exam Tip: When converting word problems to tree diagrams, first identify the operation (addition, subtraction, multiplication, or division) needed to solve the problem, then arrange the numbers accordingly.

 

Question 5. Write the numerical expression which gives the answer 10 and also convert into tree diagram.
Answer: The numerical expression that gives the answer 10 can be \( 2 + (4 \times 2) \). This calculation involves multiplying two numbers first, and then adding another number to the product.

Another example could be \( 15 - (3 + 2) \). This demonstrates using parentheses to prioritize addition before subtraction.
In simple words: You need to create a math problem that equals 10. Then, draw a tree showing how you solve it, with the answer 10 at the very top.

🎯 Exam Tip: When creating expressions for a target number, use different combinations of operations (like addition, subtraction, multiplication, division) and always remember the order of operations (PEMDAS/BODMAS).

 

Question 6. Use brackets in appropriate place to the expression 3 x 8 – 5 which gives 19 and convert it into tree diagram for it.
Answer: To get the answer 19 from \( 3 \times 8 - 5 \), we need to place brackets around \( 3 \times 8 \). This means we perform the multiplication first.
The expression becomes \( (3 \times 8) - 5 \).
First, calculate the multiplication inside the brackets: \( 3 \times 8 = 24 \).
Next, perform the subtraction: \( 24 - 5 = 19 \).
The tree diagram for \( (3 \times 8) - 5 \) is shown below:

In simple words: To get 19, we first multiply 3 and 8 to get 24. Then, we subtract 5 from 24. The tree diagram shows this order: multiply first, then subtract.

🎯 Exam Tip: Always use brackets to clarify the order of operations when you want to change the natural priority (like multiplication before subtraction), and show each step clearly in your tree diagram.

 

Question 7. A football team gains 3 and 4 points for successive 2 days and loses 5 points on the third day. Find the total points scored by the team and also represent this in tree diagram.
Answer: First, let's find the total points gained by the team. They gained 3 points on one day and 4 points on the next. So, \( 3 + 4 = 7 \) points. After gaining these points, the team then lost 5 points on the third day. So, we subtract 5 from the total gained: \( 7 - 5 = 2 \) points. The final total points scored by the team is 2. This kind of sequential scoring is common in sports, where positive gains and negative losses determine the final standing.
The tree diagram for this sequence of operations \( (3 + 4) - 5 \) is:

In simple words: The team first adds up the points they gained (3 + 4). Then, they take away the points they lost (minus 5) from that total to find their final score. The tree diagram shows these two steps.

🎯 Exam Tip: When dealing with combined gains and losses, always add up all gains first, then subtract all losses to find the net change, and ensure the tree diagram reflects this order.