Question 11 Mark
Find an integer x such that:
$7 + x = 0$
$7 + x = 0$
Answer
View full question & answer→$7 + x = 0$
$\Rightarrow 7 + x - 7 = 0 - 7$
$x = -7$
$\Rightarrow 7 + x - 7 = 0 - 7$
$x = -7$
Questions
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Question 21 Mark
Find the value of: $(-1) + (-304) + 304 + 304 + (-304) + 1$
Answer
View full question & answer→$(-1) + (-304) + 304 + 304 + (-304) + 1 = -1 + 1 - 304 + 304 - 304 + 304 = 0$
Question 31 Mark
Find the predecessor of each of the following integers:-$125$
Answer
View full question & answer→Predecessor of $-125$ is $= -125 - 1 = -126$
Question 41 Mark
Write the absolute value of the following: $a - 7$, if a is greater than $7$
Answer
View full question & answer→Absolute value of $(a - 7)$ is $(a - 7)$ if a is greater than $7$, that is, $a - 7 > 0.$
Question 51 Mark
Replace * by $'<'$ or $'>'$ in each of the following to make the statement true: $28 - (-10) * (-16) - (-76)$
Answer
View full question & answer→$28 - (-10) < (-16) - (-76) 30 < 60$
Question 61 Mark
Subtract the first integer from the second of the following:$-12, 8$
Answer
View full question & answer→In order to subtract $-12$ from $8, 8 – (–12) = 8 + 12 = 20.$
Question 71 Mark
The largest negative integer is .
Answer
View full question & answer→The numbers $.... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, .....$ form the set of integers.
Thus, the largest negative integer is $− 1.$
Thus, the largest negative integer is $− 1.$
Question 81 Mark
How many integers are between? $-4$ and $3$
Answer
View full question & answer→Integers between $-4$ and $3$ are $-3, -2, -1, 0, 1, 2$.
$\therefore$ No of integers between $-4$ and $3$ are $6.$
$\therefore$ No of integers between $-4$ and $3$ are $6.$
Question 91 Mark
Find the successor of the following integers:
$0$
$0$
Answer
View full question & answer→Successor of $0$ is $= 0 + 1$
$= 1$
$= 1$
Question 101 Mark
Which of the following statements are true:
The negative of a negative integer is positive.
The negative of a negative integer is positive.
Answer
View full question & answer→For example:$ -(-2) = 2$
Question 111 Mark
$(-3)(-4)(12)(-1) =$ ............
Answer
View full question & answer→$(-3)(-4)(12)(-1) = (-3)(-4)(-12)$
[$\because$ $(12)(-1) = (-12)] = (-3)(48)$
[$\because$ $(-4)(-12) = 48] = -(3 × 48) = -144$
Hence, $(-3)(-4)(12)(-1) = -144$
[$\because$ $(12)(-1) = (-12)] = (-3)(48)$
[$\because$ $(-4)(-12) = 48] = -(3 × 48) = -144$
Hence, $(-3)(-4)(12)(-1) = -144$
Question 121 Mark
Find the additive inverse of the following integers: $52$
Answer
View full question & answer→Additive inverse of $52$ is $-52.$
Question 131 Mark
Using the number line, write integer which is: $5$ less than $3$
Answer
View full question & answer→We want an integer five less than $3.$ So, on the number line, we will start from $3$ and move $5$ units to the left to obtain $-2$, as shown on the number line.
Question 141 Mark
Write the opposite of the following: $25$
Answer
View full question & answer→$-25$
Question 151 Mark
Write the following integers in decreasing order: $-15, 0, -2, -9, 7, 6, -5, 8$
Answer
View full question & answer→$8, 7, 6, 0, 2, -5, -9, -15$
Question 161 Mark
Which of the following statements are true: If a and b are two integers such that $a > b$, then a $- b$ is always positive integer,
Answer
View full question & answer→$a > b$
Question 171 Mark
Write the absolute value of each of the following: $-|-5|$
Answer
View full question & answer→$-|-5|$ is $-5$ and its absolute value is $5.$
Question 181 Mark
Write all integers between: $-7$ and $3$
Answer
View full question & answer→Integers between $-7$ and $3$ are $-6, -5, -4, -3, -2, -1, 0, 1, 2.$
Question 191 Mark
Replace * by $'<'$ or $'>'$ in each of the following to make the statement true: $(-20) - (-20) * 20 - (65)$
Answer
View full question & answer→$(-20) - (-20) > 20 - (65) 0 > -45$
Question 201 Mark
Indicate the following by using intergers:
$3\ km$ above sea level
$3\ km$ above sea level
Answer
View full question & answer→$3\ km$ above sea level $= +3$
Question 211 Mark
Write the absolute value of the following: $14$
Answer
View full question & answer→Absolute value of $14$ is $14.$
Question 221 Mark
Find the additive inverse of each of the following integers:$1$
Answer
View full question & answer→Additive inverse of $1$ is $-1.$
Question 231 Mark
Which of the following statements are true: $-13 > -8 - (-2)$
Answer
View full question & answer→It should be $-13 < -8 + 2 = -6$
Question 241 Mark
Find the predecessor of each of the following integers:$1$
Answer
View full question & answer→Predecessor of $1$ is $= 1 - 1 = 0$
Question 251 Mark
Replace * of the following by $<$ or $>$ so that the statement is true: $0 * -7$
Answer
View full question & answer→$0 > -7$
Question 261 Mark
Find the predecessor of each of the following integers: $0$
Answer
View full question & answer→Predecessor of $0$ is $= 0 - 1 = -1$
Question 271 Mark
Find an integer $x$ such that: $x + (-8) = 0$
Answer
View full question & answer→$x + (-8) = 0 \Rightarrow x - 8 = 0 \Rightarrow x - 8 + 8 = 0 + 8$ [adding 8 on both sides] $x = 8$
Question 281 Mark
Which number of the following pairs is smaller? $-15, -27$
Answer
View full question & answer→We know that on the number line $-27$ is to left of $-15.$ So $-27 < -15 -27$ is smaller.
Question 291 Mark
Write the absolute value of each of the following: $a + 4,$ if a is greater than $-4$
Answer
View full question & answer→Absolute value of $(a + 4)$ is $(a + 4)$ if a is greater than $-4$, that is, $a > -4 \Rightarrow a + 4 > 0.$
Question 301 Mark
$(-1)(-1)(-1)(-1)(-1) =$ ............
Answer
View full question & answer→Here, $-1$ is multiplied $5$ times and since, $5$ is an odd integer, therefore $(-1)(-1)(-1)(-1)(-1) = -1$
Question 311 Mark
Indicate the following by using intergers:
$25^\circ $ above zero
$25^\circ $ above zero
Answer
View full question & answer→$25^\circ $ above zero is $= +25^\circ $
Question 321 Mark
Which number in each of the following pairs is larger? $12, -18$
Answer
View full question & answer→We know that on the number line $-18$ is to left of $12.$ So $12 > -18 12$ is larger.
Question 331 Mark
Replace * by $'<'$ or $'>'$ in each of the following to make the statement true:
$(-12) - (-12) * (-12) + (-12)$
$(-12) - (-12) * (-12) + (-12)$
Answer
View full question & answer→$(-12) - (-12) > (-12) + (-12)$
$0 > -24$
$0 > -24$
Question 341 Mark
Which number in each of the following pairs is larger? $3, -4$
Answer
View full question & answer→We know that on the number line $3$ is to right of $-4.$ So $3 > -4. 3$ is larger.
Question 351 Mark
Which of the following statements are true? Zero is not an integer.
Answer
View full question & answer→$0$ is simply an integer that is neither positive nor negative.
Question 361 Mark
The smallest positive integer is .
Answer
View full question & answer→The collection ..... $-4, -3, -2, -1, 0, 1, 2, 3, 4,$ ..... forms the set of integers.
Thus, the smallest positive integer is $1.$
Thus, the smallest positive integer is $1.$
Question 371 Mark
Find the successor of the following integers:$-99$
Answer
View full question & answer→Successor of $-99$ is $= -99 + 1 = -98$
Question 381 Mark
Replace * of the following by $<$ or $>$ so that the statement is true:$ -235 * -532$
Answer
View full question & answer→$-235 > -532$
Question 391 Mark
How many integers are between? $5$ and $12$
Answer
View full question & answer→Integers between $-9$ and $-2$ are $-8, -7, -6, -5, -4, -3.$
$\therefore$ No of integers between $-9$ and $-2$ are $6.$
$\therefore$ No of integers between $-9$ and $-2$ are $6.$
Question 401 Mark
Write the opposite of the following:
Increase in population.
Increase in population.
Answer
View full question & answer→ Decrease of population.
Question 411 Mark
Write all integers between: $-2$ and $2$
Answer
View full question & answer→Integers between $-2$ and $2$ are $-1, 0, 1.$
Question 421 Mark
Write the opposite of the following: Going North
Answer
View full question & answer→Going South
Question 431 Mark
Write the absolute value of the following:$-248$
Answer
View full question & answer→Absolute value of $-248$ is $248.$
Question 441 Mark
Write all integers whose absolute values are less than $5.$
Answer
View full question & answer→Integers whose absolute values less than $5$ are: $-4, -3, -2, -1, 0, 1, 2, 3, 4.$
Question 451 Mark
Find an integer $x$ such that: $x + 0 = 0$
Answer
View full question & answer→$x + 0 = 0 x = 0$
Question 461 Mark
Write the absolute value of each of the following: $a + 4$, if a is less than $-4$
Answer
View full question & answer→Value of $(a + 4)$ is $-(a + 4)$ if a is less than $-4$, that is, $a < -4 \Rightarrow a + 4 < 0.$
Question 471 Mark
Mark the following integers on a number line:
$i.\ 7$
$ii.\ -4$
$iii.\ 0$
$i.\ 7$
$ii.\ -4$
$iii.\ 0$
Answer
View full question & answer→Integers are as shown in the number line.
Question 481 Mark
Indicate the following by using intergers: A profit of $Rs. 800$
Answer
View full question & answer→A profit of $800 = +800$
Question 491 Mark
Replace * by $'<'$ or $'>'$ in each of the following to make the statement true: $(-6) + (-9) * (-6) - (-9)$
Answer
View full question & answer→$(-6) + (-9) < (-6) - (-9) -15 < 3$
Question 501 Mark
Replace * of the following by $<$ or $>$ so that the statement is true: $-8 * 15$
Answer
View full question & answer→$-8 < 15$
Question 511 Mark
Write all integers between: $0$ and $3$
Answer
View full question & answer→Integers between $0$ and $3$ are $1, 2.$
Question 521 Mark
Which of the following statements are true:
$-4 + (-2) < 2$
$-4 + (-2) < 2$
Answer
View full question & answer→$-4 - 2 = -6 < 2$
Question 531 Mark
Find the value of: $1 + (-475) + (-475) + (-475) + (-475) + 1900$
Answer
View full question & answer→$1 - 475 - 475 - 475 + 1900 = 1 - 950 - 950 + 1900 = 1900 + 1 - 1900 = 1$
Question 541 Mark
Following statement are true? The sum of a number and its opposite zero.
Answer
View full question & answer→It is the definition of additive inverse; for example, $5 + (−5) = 0.$
Question 551 Mark
Subtract the first integer from the second of the following:-$812, 3126$
Answer
View full question & answer→$3126 - (-812) = 3126 + 812 = 3938.$
Question 561 Mark
Subtract the first integer from the second of the following:$-225, -135$
Answer
View full question & answer→$-135 – (-225) = 225 - 135 = 90$
Question 571 Mark
Replace * of the following by $<$ or $>$ so that the statement is true: $-20 * 20$
Answer
View full question & answer→$-20 < 20$
Question 581 Mark
How many integers are between? $0$ and $5$
Answer
View full question & answer→Integers between $0$ and $5$ are $1, 2, 3, 4.$
$\therefore$ No of integers between $0$ and $5$ are $4.$
$\therefore$ No of integers between $0$ and $5$ are $4.$
Question 591 Mark
Write the absolute value of the following:$0$
Answer
View full question & answer→Absolute value of $0$ is $0.$
Question 601 Mark
Find an integer $x$ such that: $x + 1 = 0$
Answer
View full question & answer→$x +1 = 0 \Rightarrow x + 1 - 1 = 0 - 1$ [subtract $-1$ on both sides] $\Rightarrow x = -1$
Question 611 Mark
Which of the following is false:
$|4 - 2| = |4| - |2|$
$|4 - 2| = |4| - |2|$
Answer
View full question & answer→$|4 - 2| = 2 = |4| - |2| = 2;$ True
Question 621 Mark
Write the following integers in decreasing order:
$-154, 123, -205, -89, -74$
$-154, 123, -205, -89, -74$
Answer
View full question & answer→$124, -74, -89, -154, -205$
Question 631 Mark
Replace * of the following by $<$ or $>$ so that the statement is true: $2 * 5$
Answer
View full question & answer→$2 < 5$
Question 641 Mark
Find the value of:
$-27 - (-23)$
$-27 - (-23)$
Answer
View full question & answer→$-27 - (-23) = -27 + 12$
$= 23 - 27$
$= -4$
$= 23 - 27$
$= -4$
Question 651 Mark
Find an integer $x$ such that: $x + 5 = 0$
Answer
View full question & answer→$x + 5 = 0 \Rightarrow x + 5 - 5 = 0 - 5$ [subtract $-5$ on both sides] $\Rightarrow x + 0 = -5 x = -5$
Question 661 Mark
Write the absolute value of the following:$-125$
Answer
View full question & answer→Absolute value of $-125$ is $125.$
Question 671 Mark
Find the value of: $-17 - 18 - (-35)$
Answer
View full question & answer→$-17 - 18 - (-35) = -35 + 35 = 0$
Question 681 Mark
Find the successor of the following integers: $-1$
Answer
View full question & answer→Successor of $-1$ is $= -1 + 1 = 0$
Question 691 Mark
Find an integer $x$ such that: $-3 + x = 0$
Answer
View full question & answer→$-3 + x = 0 \Rightarrow 3 - 3 + x = 0 + 3$ [adding $3$ on both sides] $x = 3$
Question 701 Mark
Replace * of the following by $<$ or $>$ so that the statement is true:
$0 * 3$
$0 * 3$
Answer
View full question & answer→$0 < 3$
Question 711 Mark
Subtract the first integer from the second of the following:$7560, -8$
Answer
View full question & answer→$-8 - 7560 = -7568$
Question 721 Mark
Find the additive inverse of the following integers: $-176$
Answer
View full question & answer→Additive inverse of $-176$ is $176.$
Question 731 Mark
Which of the following statements are true? The opposite of zero is zero.
Answer
View full question & answer→True.Solution:
$0$ is neither positive nor negative.
$0$ is neither positive nor negative.
Question 741 Mark
Using the number line, write integer which is: $4$ more than $-9$
Answer
View full question & answer→We want an integer four more than $−9.$ So, on the number line, we will start from $−9$ and move $4$ units to the right to obtain $−5$, as shown on the number line. 
Question 751 Mark
Write the following integers in increasing order: $-8, 5, 0, -12, 1, -9, 15$
Answer
View full question & answer→$-12, -9 , -8, 0, 1, 5, 15.$
Question 761 Mark
Write $4$ negative integers less than $-10.$
Answer
View full question & answer→$-9, -8, -7$ and $-6$ are the four negative integers less than $-10.$
Question 771 Mark
Write the opposite of the following: $-15$
Answer
View full question & answer→$15$
Question 781 Mark
Write the absolute value of each of the following:
$a - 7$, if a $- 2$ is less than $7$
$a - 7$, if a $- 2$ is less than $7$
Answer
View full question & answer→If $a - 2$ is less than $7$, that is, $a - 2 < 7 ⇒ a < 9$ or $a - 7 < 2$
So absolute value of $a - 7 = a - 7$ if $7 < a < 9$ that is $a - 2$ is less than $7$ but $a - 2$ is greater than $5.$
and absolute value will be $-(a - 7)$ if $a < 7$ if $a - 7$ is less than $5.$
So absolute value of $a - 7 = a - 7$ if $7 < a < 9$ that is $a - 2$ is less than $7$ but $a - 2$ is greater than $5.$
and absolute value will be $-(a - 7)$ if $a < 7$ if $a - 7$ is less than $5.$
Question 791 Mark
Indicate the following by using intergers: $5^\circ $ below zero
Answer
View full question & answer→$5^\circ $ below zero is $= -5^\circ $
Question 801 Mark
The sum of two integers is $-233$. If one of the integers is $172$, find the other.
Answer
View full question & answer→Required integer $= -223 - 172$
$= -395$
$= -395$
Question 811 Mark
Which number of the following pairs is smaller? $0, -4$
Answer
View full question & answer→since $'0'$ is greater than all negative integers. Therefore, $-4 < 0 -4$ is smaller.
Question 821 Mark
Which number of the following pairs is smaller?
$-3, 13$
$-3, 13$
Answer
View full question & answer→Every positive integer is greater than every negative integer.Therefore, $-3 < 12$
$-3$ is smaller.
$-3$ is smaller.
Question 831 Mark
Which number of the following pairs is smaller? $8, 13$
Answer
View full question & answer→We know that on the number line $8$ is to left of $13$. So $8 < 13 8$ is smaller.
Question 841 Mark
Write the absolute value of each of the following:
$|12 - 5|$
$|12 - 5|$
Answer
View full question & answer→$|12 - 5 | = | 7|$ and its absolute value is $7.$
Question 851 Mark
Write the opposite of the following: Gaining a weight of $4\ kg$
Answer
View full question & answer→Losing weight of $4\ kg$
Question 861 Mark
Write the opposite of the following:
Earning money
Earning money
Answer
View full question & answer→ Spending money
Question 871 Mark
How many integers are between? $5$ and $12$
Answer
View full question & answer→Integers between $5$ and $12$ are $6, 7, 8, 9, 10, 11.$
$\therefore$ No of integers between $5$ and $12$ are $6.$
$\therefore$ No of integers between $5$ and $12$ are $6.$
Question 881 Mark
Write the absolute value of each of the following: $|-3|$
Answer
View full question & answer→Absolute value of $-3$ is $3.$
Question 891 Mark
Subtract the first integer from the second of the following:-$3978, -4109$
Answer
View full question & answer→$-4109 - (-3978) = -4109 + 3978 = -131$
Question 901 Mark
Write the opposite of the following:
Depositing money in a bank.
Depositing money in a bank.
Answer
View full question & answer→ Withdrawing money from a bank.
Question 911 Mark
Indicate the following by using intergers: A deposit of $Rs. 2500$
Answer
View full question & answer→A deposit of Rs. $2500 = +2500$
Question 921 Mark
Find the additive inverse of the following integers:
$0$
$0$
Answer
View full question & answer→Additive inverse of $0$ is $0.$
Question 931 Mark
Write all integers between: $-4$ and $0$
Answer
View full question & answer→Integers between $-4$ and $0$ are $-3, -2, -1.$
Question 941 Mark
Find the predecessor of each of the following integers:$-1$
Answer
View full question & answer→Predecessor of $-1$ is $= -1 - 1 = -2$
Question 951 Mark
Write the absolute value of the following:$-25$
Answer
View full question & answer→Absolute value of $-25$ is $25.$
Question 961 Mark
Indicate the following by using intergers: $2\ km$ below sea level
Answer
View full question & answer→$2\ km$ below sea level $= -2$
Question 971 Mark
Using the number line, write integer which is: $2$ more than $3$
Answer
View full question & answer→We want an integer two more than $3$. So, on the number line, we will start from $3$ and move $2$ units to the right to obtain $5$, as shown on the number line. 
Question 981 Mark
Find the successor of the following integers: $-42$
Answer
View full question & answer→Successor of $-42$ is $= -42 + 1 = -41$
Question 991 Mark
Write $6$ negative integers just greater than $-12.$
Answer
View full question & answer→$-11, -10, -9, -8, -7$ and $-6$ are the six negative integers just greater than $-12.$
Question 1001 Mark
Subtract the first integer from the second in each of the following:$12, -5$
Answer
View full question & answer→Using the rule for sub traction, we have $-5 - 12 = –17.$
Question 1011 Mark
Write the opposite of the following: A loss of $Rs. 1000$
Answer
View full question & answer→A gain of $Rs. 1000$
Question 1021 Mark
Find the predecessor of each of the following integers:$1000$
Answer
View full question & answer→Predecessor of $1000$ is $= 1000 - 1 = 999$
Question 1031 Mark
$(-22) + 21 + (-22) + 21 + ....... + 20$ terms is equal to .......
Answer
View full question & answer→$\because$ $(-22) + 21 = -(22 - 21) = -1$
$\therefore$ $(-22) + 21 + (-22) + 21 + ... + 20$
terms $= (-1) + (-1) + (-1) + ... + 10$
terms $= 10 × (-1) = -10$
$\therefore$ $(-22) + 21 + (-22) + 21 + ... + 20$
terms $= (-1) + (-1) + (-1) + ... + 10$
terms $= 10 × (-1) = -10$
Question 1041 Mark
Write the following integers in increasing order:
$-106, 107, -320, -7, 185$
$-106, 107, -320, -7, 185$
Answer
View full question & answer→$-320, -106, -7, 107, 186$
Question 1051 Mark
Subtract the first integer from the second of the following:$0, -1005$
Answer
View full question & answer→$-1005 - 0 = -1005$
Question 1061 Mark
Which number in each of the following pairs is larger? $-12, -8$
Answer
View full question & answer→We know that on the number line $-12$ is to left of $-8$. So $-12 < -8 -8$ is larger.
Question 1071 Mark
Subtract the first integer from the second of the following:$1001, 101$
Answer
View full question & answer→$101 - 1001 = -900$
Question 1081 Mark
Find the successor of the following integers:-$200$
Answer
View full question & answer→Successor of $-200$ is $= -200 + 1 = -199$
Question 1091 Mark
Which number in each of the following pairs is larger?
$0, 7$
$0, 7$
Answer
View full question & answer→Since $'0'$ is less than all positive integers.
Therefore, $7 > 0$
$7$ is larger.
Therefore, $7 > 0$
$7$ is larger.
Question 1101 Mark
Find the value of:
$-12 - (-5) - (-125) + 270$
$-12 - (-5) - (-125) + 270$
Answer
View full question & answer→$-17 - 18 - (-35) = -35 + 35$
$= 0$
$= 0$