NCERT Solutions Class 6 Maths Chapter 10 The Other Side of Zero Exercise 10.4

Class 6 Maths Chapter 10 – The Other Side of Zero closes with Exercise 10.4 which allows students to practice positive and negative numbers, comparisons with integers, number lines, and real life examples. This final exercise brings together all of the key concepts and gives students significant practice for exam readiness.

NCERT Solutions Class 6 Maths Chapter 10 The Other Side of Zero Exercise 10.4, designed by expert educators and trusted by institutes like Allen, simplifies each question into simple, easy-to-follow steps. These solutions are ideal for exam time because they provide useful content for revision, clarifying doubts and solidifying confidence in the ability to solve integer problems correctly.

1.0Download NCERT Solutions of Class 6 Maths Chapter 10 The Other Side of Zero Exercise 10.4: Free PDF

Download NCERT Solutions for Class 6 Maths Chapter 10 The Other Side of Zero Exercise 10.4 in a handy PDF format. Content includes full solutions and explanations by Allen as an independent provider to ensure you master integers confidently.

2.0Key Concepts of Exercise 10.4

• Mixed Operations with Integers: To solve problems that involve addition and subtraction of integers.
• Real-Life Problem Solving: Applying positive and negative integer concepts to word problems within contexts of everyday experiences (elevation, banks, temperature, etc.).
• Understanding and Interpreting Integer Statements: Considering and expressing verbal statements in mathematical notation with integers.
• Comparison and Ordering in Context: Using integer quantities and comparisons to respond to questions based on a scenario from real-life contexts.
• Review of all Integer Concepts: This activity will often serve as a review to make sure that students can see the complete topic on integers from throughout the whole chapter.

3.0NCERT Exercise Solutions Class 6 Maths Chapter 10 The Other Side of Zero : All Exercises 

4.0NCERT Class 6 Maths Chapter 10 Exercise 10.4 : Detailed Solutions

• Do the calculations for the given grid and find the border sum
  
  Sol. Let's analyze the given grid and find the border sum. Understanding the grid. The given grid is a $3\times 3$ arrangement of numbers. The sum of numbers in each row and column should be the same. Calculating the Border Sum: Top row: $5+(-3)+(-5)=-3$ Bottom row: $(-8)+(-2)+7=-3$ Left column: $5+0+(-8)=-3$ Right column: $(-5)+(-5)+7=-3$ Therefore, the border sum of the given grid is -3
• Complete the grids to make the required border sum:
  
  Sol. Here is the completed grid:
  
  The border sum is +4 Explanation: We filled in the missing numbers to ensure the sum of each row and column is equal to the given border sum. e.g. in the first grid, to get a border sum of +4 , the missing number in the top row should be 12 and 2 . (Since $-10+12+2=4$ ). Attempt the remaining two grids by yourself.
• For the last grid above, find more than one way of filling the numbers to get border sum - 4 . Sol. There are multiple ways to fill the last grid with a border sum of -4 , here are two examples:
  
• Which other grids can be filled in multiple ways? What could be the reason? Sol. Grid with a larger size (more rows and columns) is likely to have multiple solutions. This is because there are more degrees of freedom to distribute numbers while maintaining the border sum.
• Make a border integer square puzzle and challenge your classmates. Sol. Do it yourself
• Try afresh, choose different numbers this time. What sum did you get? Was it different from the first time? Try a few more times! Sol. Let's circle the number 3. Lets strike out the row and column with the number 3.
  
  Again lets circle the number-1 Let's strike out the row and column with the number-1
  
  Let's circle the number -5 . Now as per the game, let's strike out the row and column with the number -5 .
  
  Let's circle the number 2. Now as per the game, let's strike out the row and column with the number 2.
  
  Now let's add the circled numbers $=3+(-1)+(-5)+2=-1$ Hence, we get the value ( -1 ). Now try yourself
• Play the same game with the grids below. What answer did you get?
  
  Sol. (a) Lets circle the number 1. Now as per the game, let's strike out the row and column with number 1.
  
  Again let's circle the number 13. Let's strike out the row and column with the number 13.
  
  Again let's circle the number -20. Let's strike out the row and column with the number -20.
  
  Again let's circle the number -2. Let's strike out the row and column with the number -2.
  
  Now let's add the circled numbers $=1+13+(-20)+(-2)=-8$ which is the required answer. (b) Let's strike out the row and column with the number -5 . Let's strike out the row and column with the number -5 .
  
  Again let's circle the number 1. Let's strike out the row and column with the number 1.
  
  Let's strike out the row and column with the number -10 . Again let's circle the balance number -10 .
  
  Let's strike out the row and column with the number 0 . Again let's circle the balance number 0 .
  
  Now let's add the circled numbers $=(-5)+1+(-10)+0=-14$ which is the required answer.
• What could be so special about these grids? Is the magic in the numbers or the way they are arranged or both? Can you make more such grids? Sol. Grids can be fascinating because of both the numbers and the way they are arranged. Here's why:

• Numbers: The numbers in a grid can follow specific patterns or sequences, such as magic squares where the sums of numbers in each row, column, and diagonal are the same.
• Arrangement: When you organize things in an orderly way, the result is called an arrangement. If you admire your friend's arrangement of his living room furniture, you might go home and make a similar arrangement

• Write all the integers between the given pairs, in increasing order. a. 0 and - 7 b. -4 and 4 c. -8 and -15 d. -30 and -23 Sol. a. The integers between 0 and -7 , in increasing order, are: $-6,-5,-4,-3,-2,-1$ b. The integers between -4 and 4 , in increasing order, are: $-3,-2,-1,0,1,2,3$ c. The integers between -8 and -15 , in increasing order, are: $-14,-13,-12,-11,-10,-9$ d. The integers between -30 and -23 , in increasing order, are: $-29,-28,-27,-26,-25,-24$
• Give three numbers such that their sum is -8 . Sol. Three numbers that add up to -8 are $-10,-1$, and 3 . When we add them together, we get $(-10)+(-1)+3=-8$
• There are two dice whose faces have these numbers: $-1,2,-3,4,-5,6$. The smallest possible sum upon rolling these dice is $-10=(-5)+(-5)$ and the largest possible sum is $12=(6)+(6)$. Some numbers between ( -10 ) and ( +12 ) are not possible to get by adding numbers on these two dice. Find those numbers. Sol. Let's find the sums that are not possible when rolling these two dice. The faces of the dice are: $-1,2,-3,4,-5$, and 6 . First, let's list all possible sums: The sum of two negative numbers:

• $(-1)+(-1)=-2$
• $(-1)+(-3)=-4$
• $(-1)+(-5)=-6$
• $(-3)+(-3)=-6$
• $(-3)+(-5)=-8$
• $(-5)+(-5)=-10$ The sum of one negative and one positive number:
• $(-1)+2=1$
• $(-1)+4=3$
• $(-1)+6=5$
• $(-3)+2=-1$
• $(-3)+4=1$
• $(-3)+6=3$
• $(-5)+2=-3$
• $(-5)+4=-1$
• $(-5)+6=1$ The sum of two positive numbers:
• $2+2=4$
• $2+4=6$
• $2+6=8$
• $4+4=8$
• $4+6=10$
• $6+6=12$ Now, let's list all the possible sums in ascending order: $-10,-8,-6,-4,-3,-2,-1,1,3,4,5,6,8,10,12$ The sum of numbers between -10 and 12 that are not possible to get are: $-9,-7,-5,0,2,7,9,11$

• Solve these:

Sol. (a) $8-13=-5$ (b) $-8-(13)=-8-13=-21$ (c) $-13-(-8)=-13+8=-5$ (d) $(-13)+(-8)=-13-8=-21$ (e) $8+(-13)=8-13=-5$ (f) $-8-(-13)=-8+13=5$ (g) $(13)-8=13-8=5$ (h) $13-(-8)=13+8=21$

• Find the years below. a. From the present year, which year was it 150 years ago? b. From the present year, which year was it 2200 years ago? Hint: Recall that there was no year 0. c. What will be the year 320 years after 680 BCE? Sol. a. 150 years ago from the present year (2024): [2024-150=1874] So, 150 years ago, it was the year 1874. b. 2200 years ago from the present year (2024): Since there was no year 0 , we need to account for this in our calculation: [2024-2200 = -176]. The year -176 corresponds to 177 BCE (Before the Common Era). So, 2200 years ago, it was the year 177 BCE. c. As BCE is before Christ, hence Let's write 680 BCE $=-680$ Hence, 320 years after $680\mathrm{BCE}=-680+320=-360=360\mathrm{BCE}$.
• Complete the following sequences: a. $(-40),(-34),(-28),(-22)$, , , b. $3,4,2,5,1,6,0,7$, , c. , 12, 6, 1, (-3), (-6), , , Sol. a. Let's subtract a last number of the sequence with the preceding number. $\begin{array}{rl}& \because (-22)-(-28)=-22+28=6\\ & (-28)-(-34)=-28+34=6\\ & -(34)-(-40)=-34+40=6\end{array}$ Hence, this is a sequence where each term increases by 6 . $\therefore$ Next term $=-22+6=-16$ $\therefore$ Following term $=-16+6=-10$ $\therefore$ Final term $=-10+6=-4$ Hence, the sequence is $(-40),(-34),(-28),(-22),(-16),(-10),(-4)$ b. Let's subtract the last number of the sequence with the preceding number. $7-0=7$ $0-6=-6$ $6-1=5$ $1-5=-4$ $5-2=3$ $2-4=-2$ $4-3=1$ Hence in this sequence, numbers are decreasing by 1 with alternate positive and negative integers. Hence the next number $7+(-8)=-1$ $-1+9=8$ $8-10=-2$ $-2+11=9$ and so on. Hence complete sequence is $3,4,2,5,1,6,0,7,-1,8,-2,9,\dots \dots$. Let us check $-1-7=-8$ $8+1=9$ $-2-8=-10$ c. Let's subtract the last number of the sequence from the preceding number $(-6)-(-3)=-6+3=-3$ $(-3)-(1)=-3-1=-4$ $1-6=-5$ $6-12=-6$ Hence in this sequence, 1 negative integer is added to each number. Let's take the first number of the sequence as x and the second number as y . 2nd number = $12-\mathrm{y}=-7$ Hence $y=12+7=19$ 1st number, let it be x 2nd number $19-\mathrm{x}=-8$ $\Rightarrow \mathrm{x}=19+8=27$ Now let's find the 8th number, let it be a. Hence, $\mathrm{a}-(-6)=-2$ $\Rightarrow \mathrm{a}=-2-6=-8$ Now let's find the 9 th number, let it be b . Hence b - (-8) = -1 $\Rightarrow \mathrm{b}=-1-8=-9$ Hence, the sequence is: $27,19,12,6,1,(-3),(-6),(-8),(-9),(-9)$
• Here are six integer cards: $(+1),(+7),(+18),(-5),(-2),(-9)$. You can pick any of these and make an expression using addition(s) and subtraction(s). Here is an expression: $(+18)+(+1)-(+7)-(-2)$ which gives a value $(+14)$. Now, pick cards and make an expression such that its value is closer to ( -30 ). Sol. Let's try to create an expression that gets as close to ( -30 ) as possible using the given cards: $(+1,+7,+18,-5,-2,-9)$. One possible expression is: $(-9)+(-5)+(-2)-(-18)+(+1)$ Let's calculate the value step by step: 1.$(-9)+(-5)=-14$ 2.$-14+(-2)=-16$ 3.$-16-(+18)=-34$ 4.$-34+(+1)=-33$ Hence, the value of this expression is ( -33 ), which is quite close to ( -30 ).
• The sum of two positive integers is always positive but a (positive integer) - (positive integer) can be positive or negative. What about a. (positive) - (negative) b. (positive) + (negative) c. (negative) + (negative) d. (negative) - (negative) e. (negative) - (positive) f. (negative) + (positive) Sol. a. (Positive) - (Negative): Subtracting a negative number is the same as adding its positive counterpart. So, this will always be positive. For example, $5-(-3)=5+3=8$. b. (Positive) + (Negative) This depends on the magnitudes of the numbers. If the positive number is larger, the result is positive; if the negative number is larger, the result is negative. For example, $7+(-4)=3$ (positive) $4+(-7)=-3$ (negative) c. (Negative) + (Negative) Adding two negative numbers always results in a negative number. For example, $-2+(-3)=-5$. d. (Negative) - (Negative) This is like adding the positive counterpart of the second number to the first negative number. If the first negative number is larger in magnitude, the result is negative. However, if the first negative number is smaller than the second negative number, then it is positive. For example, $(-5)-(-2)=-3$ (negative) $(-2)-(-5)=3$ (positive) e. (Negative) - (Positive) This will always be negative because you're subtracting a positive number from a negative number. For example, $-4-2=-6$. f. (Negative) + (Positive) Similar to (Positive) + (Negative), it depends on the magnitudes. If the positive number is larger, the result is positive; if the negative number is larger, the result is negative. For example, $-3+5=2$ (positive) $-5+3=-2$ (negative)
• This string has a total of 100 tokens arranged in a particular pattern. What is the value of the string?
  
  Sol. Let's analyze the sequence of the string: $3,-2,3,-2,3,-2$
  
  Let's take a set of 5 tokens as it is repeating, total is $3-2=1$ There are 100 tokens in the string. Hence total sets $=100÷5=20$ sets Total of 1 set = 1 Hence, the value of the string $=1\times 20=20$

5.0Key Features and Benefits Class 6 Maths Chapter 10 The Other Side of Zero : Exercise 10.4

• Step by Step NCERT Solutions for total concept clarity 
• Easy-to-read student-friendly explanations and visuals 
• Aligned with CBSE Class 6 - syllabus and exam pattern 
• Highly recommended by Allen as a great way to revise concepts, and practice 
• A helpful tool for homework, revision, or exam prep.
• A robust way for students to build, create, and reverse manipulate their knowledge of integers.