Q: Fill in the blank.\$(-4)+\$______\$=-12\$.

Let \$x\$ be the unknown \$(-4)+ x = -12\$\$x= -12- (-4)\$\$x = -12+ 4\$\$x= -8\$\$(-4)+ (-8)=(-12)\$

Q: The sum of two integers is -16. If one of them is 53, find the other.

By assuming Closure property of addition [a+b=c],Let,\$a=53,\ assume\ b=x, c=-16\$\$=53+x=-16\$\$= x =-16-53\$( By sending 53 from left hand side to the right hand side, it changes to -53)\$= x = -69\$By the calculation we got another integer is \$-69\$

Q: Find the sum of the first \$1000\$ positive integers.

Sum of n positive integers\$=\cfrac{n(n+1)}{2}\$For 1000 integers, \$n=1000\$\$=\cfrac{1000(1000+1)}{2}\$\$=500\times 1001\$\$=500500\$

Q: In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack's scores in five successive rounds were \$ 25, -5, -10, 15\$ and \$10\$, what was his total at the end?

Scores of jack \$= 25, -5, -10, 15, 10\$\$\text{Total at end }= 25 + (-5) + (-10) + 15 + 10\$\$=25 - 5 - 10 + 15 + 10\$\$=35\$

Q: In a class test containing \$10\$ questions, '\$3\$' marks are awarded for every correct answer and \$(-1)\$ mark is for every incorrect answer and '\$0\$' for questions not attempted.(i) Gopi gets \$5\$ correct and \$5\$ incorrect answers. What is his score?(ii) Reshma gets \$7\$ correct answer and \$3\$ incorrect answers. What is her score?(iii) Reshma gets \$3\$ correct and \$4\$ incorrect answers out of seven questions she attempts. What is her score?

i) Gopi gets \$5\$ correct and \$5\$ incorrect answers To find his score Since for every correct answer '\$3\$ marks are awarded ' For every incorrect answer '\$(-1)\$ marks are awarded ' Total Score \$ = 5 \times 3 + 5 \times (-1)\$ \$ = 15 - 5 \$ \$ = 10 \$ii) Reshma gets \$7\$ correct answer and \$3\$ incorrect answers To find his score Since for every correct answer '\$3\$ marks are awarded' For Every Incorrect Answer ' (-1) marks are awarded ' Total score \$ = 7 \times 3 + 3 \times (-1)\$ \$ = 21 - 3 \$ \$ = 18 \$iii) Reshma gets \$3\$ correct answer and \$4\$ incorrect answers To find his score Since for every correct answer '\$3\$ marks are awarded ' For every incorrect answer '\$(-1)\$ marks are awarded ' Total score \$ = 3 \times 3 + 4 \times (-1)\$ \$ = 9 - 4 \$ \$ = 5 \$

Q: Taking today as zero on the number line, if the day before yesterday is 17 January, what is the date 3days after tomorrow?

A day before yesterday is \$17\text{ January}\$.Therefore, today is \$17+2=19\text{ January}\$.\$3\$ days after tomorrow will be\$19+1+3=20 + 3 = 23\text{ January}\$

Q: Find: \$(-13)+32-8-1\$

\$(-13)+32-8-1=-13+32-8-1=10\$

Question 1

Give a positive and a negative integer whose difference is -3

Accepted Answer

Let two integers one negative and other positive whose difference is $-3$ be $-1,\ 2.$Difference$=-1-(2)=-1-2=-3$

Question 2

Fill in the blank.$(-4)+$______$=-12$.

Accepted Answer

Let $x$ be the unknown $(-4)+ x = -12$$x= -12- (-4)$$x = -12+ 4$$x= -8$$(-4)+ (-8)=(-12)$

Question 3

The sum of two integers is -16. If one of them is 53, find the other.

Accepted Answer

By assuming Closure property of addition [a+b=c],Let,$a=53,\ assume\ b=x, c=-16$$=53+x=-16$$= x =-16-53$( By sending 53 from left hand side to the right hand side, it changes to -53)$= x = -69$By the calculation we got another integer is $-69$

Question 4

Find the sum of the first $1000$ positive integers.

Accepted Answer

Sum of n positive integers$=\cfrac{n(n+1)}{2}$For 1000 integers, $n=1000$$=\cfrac{1000(1000+1)}{2}$$=500\times 1001$$=500500$

Question 5

In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack's scores in five successive rounds were $ 25, -5, -10, 15$ and $10$, what was his total at the end?

Accepted Answer

Scores of jack $= 25, -5, -10, 15, 10$$\text{Total at end }= 25 + (-5) + (-10) + 15 + 10$$=25 - 5 - 10 + 15 + 10$$=35$

Question 6

Which of the following statements is CORRECT?
Statement- $1$ : When a positive integer and a negative integer are added, we always get a negative integer.
Statement- $2$ : When two negative integers are added, we get a positive integer.

Accepted Answer

When a positive integer and a negative integer are added, we can get a positive or negative integer.Therefore, statement $1$ is false.Fro example: $-4+3=-1$ or $4+(-3)=1$And when two negative integers are added, we get a negative integer.$\therefore$ Statement $2$ is false.For example: $-3+(-4)=-7$

Question 7

In a class test containing $10$ questions, ' $3$ ' marks are awarded for every correct answer and $(- 1)$ mark is for every incorrect answer and ' $0$ ' for questions not attempted.
(i) Gopi gets $5$ correct and $5$ incorrect answers. What is his score?
(ii) Reshma gets $7$ correct answer and $3$ incorrect answers. What is her score?
(iii) Reshma gets $3$ correct and $4$ incorrect answers out of seven questions she attempts. What is her score?

Accepted Answer

i)  Gopi gets $5$ correct and $5$ incorrect answers      To find his score     Since for every correct answer '$3$ marks are awarded '     For every incorrect answer '$(-1)$ marks are awarded '     Total Score   $ =  5 \times 3  + 5 \times (-1)$                          $ =  15  -  5  $                          $  =  10  $ii)  Reshma gets $7$ correct answer and $3$ incorrect answers     To find his score     Since for every correct answer '$3$ marks are awarded'     For  Every  Incorrect  Answer   ' (-1)   marks   are   awarded '     Total score     $ =  7 \times 3  + 3 \times (-1)$                           $ =  21  -  3  $                           $  =  18  $iii)   Reshma gets $3$ correct answer and $4$ incorrect answers       To find his score      Since for every correct answer '$3$ marks are awarded '       For every incorrect answer '$(-1)$ marks are awarded '       Total score    $ =  3 \times 3  + 4  \times (-1)$                            $ =  9  -  4  $                            $ =  5 $

Question 8

If p: when a positive integer and a negative integer are added we always get a negative integer and q: when two negative integers are added, we get a positive integer, then.

Accepted Answer

When we add positive integer and negative integer then it is not necessary that result would be negative integer. It can be positive integer alsoFor eg- $(+8)+(-6)=2$. Hence the p statement is false.When we add two negative integers, we will always get negative integer.For eg- $(-7)+(-9)=-16$. Hence q statement is also false

Question 9

Taking today as zero on the number line, if the day before yesterday is 17 January, what is the date 3days after tomorrow?

Accepted Answer

A day before yesterday is $17\text{ January}$.Therefore, today is $17+2=19\text{ January}$.$3$ days after tomorrow will be$19+1+3=20 + 3 = 23\text{ January}$

Question 10

Find: $(-13)+32-8-1$

Accepted Answer

$(-13)+32-8-1=-13+32-8-1=10$

Revise with Concepts

Addition of Integers

Subtraction of Integers

Learn with Videos

Quick Summary With Stories

Addition of Integers

Addition of Integers on number line

Subtraction of Integers on Number Line

Give a positive and a negative integer whose difference is -3

Fill in the blank.
$(- 4) +$ ______ $= - 12$ .

The sum of two integers is -16. If one of them is 53, find the other.

Find the sum of the first $1000$ positive integers.

In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack's scores in five successive rounds were $25, - 5, - 10, 15$ and $10$ , what was his total at the end?

Which of the following statements is CORRECT?
Statement- $1$ : When a positive integer and a negative integer are added, we always get a negative integer.
Statement- $2$ : When two negative integers are added, we get a positive integer.

If p: when a positive integer and a negative integer are added we always get a negative integer and q: when two negative integers are added, we get a positive integer, then.

Taking today as zero on the number line, if the day before yesterday is 17 January, what is the date 3days after tomorrow?

Find: $(- 13) + 32 - 8 - 1$

Revise with Concepts

Addition of Integers

Subtraction of Integers

Learn with Videos

Quick Summary With Stories

Addition of Integers

Addition of Integers on number line

Subtraction of Integers on Number Line

Give a positive and a negative integer whose difference is -3

Fill in the blank. (−4)+______=−12.

The sum of two integers is -16. If one of them is 53, find the other.

Find the sum of the first 1000 positive integers.

In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack's scores in five successive rounds were 25,−5,−10,15 and 10, what was his total at the end?

Which of the following statements is CORRECT? Statement-1: When a positive integer and a negative integer are added, we always get a negative integer. Statement-2: When two negative integers are added, we get a positive integer.

If p: when a positive integer and a negative integer are added we always get a negative integer and q: when two negative integers are added, we get a positive integer, then.

Taking today as zero on the number line, if the day before yesterday is 17 January, what is the date 3days after tomorrow?

Find: (−13)+32−8−1

Fill in the blank.
$(- 4) +$ ______ $= - 12$ .

Find the sum of the first $1000$ positive integers.

In a quiz, positive marks are given for correct answers and negative marks are given for incorrect answers. If Jack's scores in five successive rounds were $25, - 5, - 10, 15$ and $10$ , what was his total at the end?

Which of the following statements is CORRECT?
Statement- $1$ : When a positive integer and a negative integer are added, we always get a negative integer.
Statement- $2$ : When two negative integers are added, we get a positive integer.

Find: $(- 13) + 32 - 8 - 1$