Question 12 Marks
Draw a number line and represent each of the following on it: $(-3) + (-5)$
Answer
View full question & answer→If we start from $-3$ and move $5$ units to the left of $-3,$ we will obtain $-8,$ as shown on the number line.
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Question 22 Marks
If $\Delta$ is an operation on integers such that $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$ for all integers a, b. Find the value of: $4\ \Delta\ 3$
Answer
View full question & answer→Given, $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$$4\ \Delta\ 3=-4 + 3 - (-2)$
$=-4+3+2$
$=5-4$
$=1$
$=-4+3+2$
$=5-4$
$=1$
Question 32 Marks
Find the sum of: $-522$ and $-160$
Answer
View full question & answer→$-522 + (-160) = -522 - 160 = -(522 + 160) = -682$
Question 42 Marks
Find the sum of: $2884$ and $-2884$
Answer
View full question & answer→$2884$ and $-2884 = 2884 + (-2884) = 2884 - 2884 = 0$
Question 52 Marks
Find the sum of: $2567$ and $-325$
Answer
View full question & answer→$2567$ and $-325$
$2567 + (-325) = (2567) - (325) = (2567) - (325) = 2567 - 325 = 2242$
$2567 + (-325) = (2567) - (325) = (2567) - (325) = 2567 - 325 = 2242$
Question 62 Marks
Subtract the sum of $-1250$ and $1138$ from the sum of $1136$ and $-1272.$
Answer
View full question & answer→Sum of $-1250$ and $1138 = - 1250 + 1138$
$= 1138 - 1250$
$= -112$
Now, Sum of $1136$ and $-1272 = 1136 - 1272$
$= -136$
$⇒ -136 - (-112) = -136 + 112$
$= -24$
$= 1138 - 1250$
$= -112$
Now, Sum of $1136$ and $-1272 = 1136 - 1272$
$= -136$
$⇒ -136 - (-112) = -136 + 112$
$= -24$
Question 72 Marks
Find the sum of:
$-557$ and $488$
$-557$ and $488$
Answer
View full question & answer→The integers are to be added are of the unlike signs.Therefore to add them we find the difference of their absolute values and assign the sign of the addend having greater absolute value.
$(-557)$ and $488$
$= -[|- 557| - |488|]$
$= -[557 - 488]$
$= -69$
$(-557)$ and $488$
$= -[|- 557| - |488|]$
$= -[557 - 488]$
$= -69$
Question 82 Marks
If $\Delta$ is an operation on integers such that for integers a and b, $\text{a }\Delta\text{ b}=\text{a}-\text{b}-(-5)$. Find the values of: $4\ \Delta\ (-5)$
Answer
View full question & answer→$\because\text{a }\Delta\text{ b}= \text{a}-\text{b}-(-5)$ $\therefore4\ \Delta\ (-5)=4-(-5)-(-5)$ $= 4 +5 + 5$ $= 14$
Question 92 Marks
If $\Delta$ is an operation on integers such that for integers a and b, $\text{a }\Delta\text{ b}=\text{a}-\text{b}-(-5)$. Find the values of: $2\ \Delta\ 5$
Answer
View full question & answer→$\because\text{a }\Delta\text{ b}= \text{a}-\text{b}-(-5)$ $\therefore2\ \Delta\ 5=2-5-(-5)$ $= 2-5 + 5$ $= 2$
Question 102 Marks
Calculate: $1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... + 49 - 50$
Answer
View full question & answer→$1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... + 49 - 50$
$= (1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + ... + (49 - 50)$
$= (-1) + (-1) + (-1) + ... + 25$ terms $= (-1) \times 25 = -25$
Hence, $1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... + 49 - 50 = -25$
$= (1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + ... + (49 - 50)$
$= (-1) + (-1) + (-1) + ... + 25$ terms $= (-1) \times 25 = -25$
Hence, $1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... + 49 - 50 = -25$
Question 112 Marks
The sum of two integers is $84.$ If one of the integers is $44,$ determine the other.
Answer
View full question & answer→Sum of two integers $= 84$
One of the integers $= 44$
Other integer $=$ Sum of two integers $-$ One of the integers
$= 84 - 44 = 40$
Hence, the other integer is $40.$
One of the integers $= 44$
Other integer $=$ Sum of two integers $-$ One of the integers
$= 84 - 44 = 40$
Hence, the other integer is $40.$
Question 122 Marks
Find the value of: $373 + (-245) + (-373) + 145 + 3000$
Answer
View full question & answer→$373 + (-245) + (-373) + 145 + 3000$
$= 373 - 245 - 373 + 3145$
$= 3145 + 373 - 373 - 245$
$= 3145 - 245 = 2900$
$= 373 - 245 - 373 + 3145$
$= 3145 + 373 - 373 - 245$
$= 3145 - 245 = 2900$
Question 132 Marks
Draw a number line and represent each of the following on it: $5 + (-2)$
Answer
View full question & answer→If we start from $5$ and move $2$ units to the left of $5,$ we will obtain $3,$ as shown on the number line. 
Question 142 Marks
Draw a number line and represent each of the following on it: $(-9) + 4$
Answer
View full question & answer→If we start from $-9$ and move $4$ units to the right of $-9,$ we will obtain $-5,$ as shown on the number line. 
Question 152 Marks
If $\Delta$ is an operation on integers such that $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$ for all integers a, b. Find the value of: $6\ \Delta\ (-5)$
Answer
View full question & answer→Given, $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$$6\ \Delta\ (-5)=-6 + (-5) - (-2)$
$=-6-5+2$
$=-11+2$
$=-9$
$=-6-5+2$
$=-11+2$
$=-9$
Question 162 Marks
The sum of two integers is $84.$ If one of the integers is $44,$ determine the other.
Answer
View full question & answer→Sum of two integers $= 84$
One of the integers $= 44$
Other integer $=$ Sum of two integers $-$ One of the integers
$= 84 - 44$
$= 40$
Hence, the other integer is $40.$
One of the integers $= 44$
Other integer $=$ Sum of two integers $-$ One of the integers
$= 84 - 44$
$= 40$
Hence, the other integer is $40.$
Question 172 Marks
Calculate the sum: $5 + (-5) + 5 + (-5) + .............$ If the number of terms is $10.$
Answer
View full question & answer→If the number of term is $10.$
then $5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5)$
$= 5 - 5 + 5 - 5 + 5 - 5 + 5 -5 + 5 -5$
$= 0$
then $5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5)$
$= 5 - 5 + 5 - 5 + 5 - 5 + 5 -5 + 5 -5$
$= 0$
Question 182 Marks
Simplity: $5 + (-5) + 5 + (-5) + .....$ When the number ol terms is $20.$
Answer
View full question & answer→When the number of terms is $20$
$5 + (-5) + 5 + (-5) + ..... = (5 + 5 + 5 + ..... 10$ terms$) + (-5 - 5 - 5 - ..... 10$ terms$) = 10 \times 5 + 10 \times (-5) = 50 - 50 = 0$
$5 + (-5) + 5 + (-5) + ..... = (5 + 5 + 5 + ..... 10$ terms$) + (-5 - 5 - 5 - ..... 10$ terms$) = 10 \times 5 + 10 \times (-5) = 50 - 50 = 0$
Question 192 Marks
Evaluate the following: $-8 - 24 + 31 - 26 - 28 + 7 + 19 - 18 - 8 + 33$
Answer
View full question & answer→$- 8 - 24 + 31- 26 - 28 + 7 + 19 - 18 - 8 + 33$
$= -8 - 24 - 26 - 28 - 18 - 8 + 31+ 7 + 19 + 33$
$= -32 - 26 - 28 - 26 + 38 + 19 + 33$
$= 38 - 32 - 26 - 28 + 33 - 26 + 19$
$= 6 - 26 - 28 + 7 + 19$
$= 6 - 28 - 26 + 26$
$= 6 - 28$
$= -22$
$= -8 - 24 - 26 - 28 - 18 - 8 + 31+ 7 + 19 + 33$
$= -32 - 26 - 28 - 26 + 38 + 19 + 33$
$= 38 - 32 - 26 - 28 + 33 - 26 + 19$
$= 6 - 26 - 28 + 7 + 19$
$= 6 - 28 - 26 + 26$
$= 6 - 28$
$= -22$
Question 202 Marks
Simplity: $5 + (-5) + 5 + (-5) + .....$ When the number of terms is $25$
Answer
View full question & answer→When the number of terms is $25$
$5 + (-5) + 5 + (-5) + ..... = (5 + 5 + 5 + ..... 13$ terms$) + (-5 - 5 - 5 - ..... 12$ terms$) = 13 \times 5 + 12 \times (-5) = 65 - 60 = 5$
$5 + (-5) + 5 + (-5) + ..... = (5 + 5 + 5 + ..... 13$ terms$) + (-5 - 5 - 5 - ..... 12$ terms$) = 13 \times 5 + 12 \times (-5) = 65 - 60 = 5$
Question 212 Marks
Find the sum of: $-10025$ and $139$
Answer
View full question & answer→$-10025$ and $139 -10025 + 139 = -(10025 - 139) = -9886$
Question 222 Marks
Evaluate: $7 \times |-15| - |-9| \times 8$
Answer
View full question & answer→$\because |-15| = 15$ and $|-9| = 9$
$\therefore 7 \times |-15| - |-9| \times 8 = 7 \times 15 − 9 \times 8$
$= 105 - 72$
$= 33$
Hence, $7 \times |-15| - |-9| \times 8 = 33$
$\therefore 7 \times |-15| - |-9| \times 8 = 7 \times 15 − 9 \times 8$
$= 105 - 72$
$= 33$
Hence, $7 \times |-15| - |-9| \times 8 = 33$
Question 232 Marks
Draw a number line and represent each of the following on it: $(-2) + 7 + (-9)$
Answer
View full question & answer→If we start from $-2$ and move $7$ units to the right, we will obtain $5;$ and then if we start from $5$ and move $9$ units to the left, we will obtain $-4,$ as shown on the number line.
Question 242 Marks
If $\Delta$ is an operation on integers such that $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$ for all integers a, b. Find the value of: $(-2)\ \Delta\ (-3)$
Answer
View full question & answer→Given, $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$$(-2)\ \Delta\ (-3)=-(-2) + (-3) - (-2)$
$=2-3+2$
$=4-3$
$=1$
$=2-3+2$
$=4-3$
$=1$
Question 252 Marks
The sum of two integers is $238.$ If one of the integers is $-122,$ determine the other.
Answer
View full question & answer→Given that,
Sum of two integer's $= 238$
one of the integer $= -122$
Required integer $= 238 - (-122)$
$= 238 + 122$
$= 360$
Sum of two integer's $= 238$
one of the integer $= -122$
Required integer $= 238 - (-122)$
$= 238 + 122$
$= 360$
Question 262 Marks
Subtract the sum of $-5020$ and $2320$ from $-709.$
Answer
View full question & answer→The sum of $-5020$ and $2320$ is $= -5020 + 2320 = 2320 - 5020 = -2700$
Now, $(-709) - (-2700) = -709 + 2700 = 1991$
Now, $(-709) - (-2700) = -709 + 2700 = 1991$
Question 272 Marks
If $\Delta$ is an operation on integers such that $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$ for all integers $a, b.$ Find the value of:
$(-5)\ \Delta\ 6$
$(-5)\ \Delta\ 6$
Answer
View full question & answer→Given, $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$$(-5)\ \Delta\ 6=5 + 6- (-2)$
$=5+6+2$
$=13$
$=5+6+2$
$=13$
Question 282 Marks
If $\Delta$ is an operation on integers such that for integers a and b, $\text{a }\Delta\text{ b}=\text{a}-\text{b}-(-5)$. Find the values of: $(-9)\ \Delta\ (-4)$
Answer
View full question & answer→$\because\text{a }\Delta\text{ b}= \text{a}-\text{b}-(-5)$ $\therefore(-9)\ \Delta\ (-4)=(-9)-(-4)-(-5)$ $= -9 +4 + 5$ $= 0$
Question 292 Marks
If $a$ and $b$ are two integers such that a is predecessor of $b.$ Find the value of $a - b.$
Answer
View full question & answer→$a$ and $b$ are two integers such that a is the predecessor of $b,$ that is, $a = b - 1.$
Value $= a - b$
$= b - 1 - b$
$= -1$
Value $= a - b$
$= b - 1 - b$
$= -1$
Question 302 Marks
Calculate: $1 - 2 + 3 - 4 + 5 - 6 + .................. + 15 - 16$
Answer
View full question & answer→$1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + 9 - 10 + 11 - 12 + 13 - 14 + 15 - 16$
$= (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15) − (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16)$
$= 64 - 72$
$= -8$
$= (1 + 3 + 5 + 7 + 9 + 11 + 13 + 15) − (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16)$
$= 64 - 72$
$= -8$
Question 312 Marks
Draw a number line and represent each of the following on it: $6 + (-6)$
Answer
View full question & answer→If we start from $6$ and move $6$ units to the left of $6,$ we will obtain $0,$ as shown on the number line.
Question 322 Marks
Find the sum of: $2547$ and $-2548$
Answer
View full question & answer→$2547$ and $-2548 = 2547 + (-2548) = -(-2547 + 2548) = -1$
Question 332 Marks
If $a$ and $b$ are two integers such that a is the successor of $b.$ Find the value of $a - b.$
Answer
View full question & answer→$a$ and $b$ are two integers such that a is the successor of $b,$ that is, $a = b + 1.$
Value of $a - b = b + 1 - b$
$= 1$
Value of $a - b = b + 1 - b$
$= 1$
Question 342 Marks
If $\Delta$ is an operation on integers such that for integers a and b, $\text{a }\Delta\text{ b}=\text{a}-\text{b}-(-5)$. Find the values of: $(-7)\ \Delta\ 3$
Answer
View full question & answer→$\because\text{a }\Delta\text{ b}= \text{a}-\text{b}-(-5)$ $\therefore(-7)\ \Delta\ 3=(-7)-3-(-5)$ $= -7 - 3 + 5$ $= -(7 + 3) + 5$ $= -10 + 5$ $= -(10 - 5)$ $= -5$
Question 352 Marks
Simplify: $9 \times (-16) + (-17) \times (-16)$
Answer
View full question & answer→$9 \times (-16) + (-17) \times (-16)$
$= -(9 \times 16) + (17 \times 16)$
$= -144 + 272 = 272 - 144 = 128$
Hence, $9 \times (-16) + (-17) \times (-16) = 128$
$= -(9 \times 16) + (17 \times 16)$
$= -144 + 272 = 272 - 144 = 128$
Hence, $9 \times (-16) + (-17) \times (-16) = 128$
Question 362 Marks
Evaluate the following: $-26 - 20 + 33 - (-33) + 21 + 24 - (-25) - 26 - 14 - 34$
Answer
View full question & answer→$-26 - 20 + 33 - (-33) + 21 + 24 - (-25) - 26 - 14 - 34$
$= -46 + 33 + 33 + 21 + 24 + 25 - 26 - 14 - 34$
$= -46 + 66 + 21 + 24 + 25 - 74$
$= -46 + 66 + 70 - 74$
$= -46 - 4 + 66$
$= -50 + 66$
$= 66 - 50$
$= 16$
$= -46 + 33 + 33 + 21 + 24 + 25 - 26 - 14 - 34$
$= -46 + 66 + 21 + 24 + 25 - 74$
$= -46 + 66 + 70 - 74$
$= -46 - 4 + 66$
$= -50 + 66$
$= 66 - 50$
$= 16$
Question 372 Marks
Calculate the sum: $5 + (-5) + 5 + (-5) + .............$ If the number of terms is $11.$
Answer
View full question & answer→If the number of term is $10.$
then $5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 $
$= 5 - 5 + 5 - 5 + 5 - 5 + 5 -5 + 5 -5 + 5$
$= 5$
then $5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 + (-5) + 5 $
$= 5 - 5 + 5 - 5 + 5 - 5 + 5 -5 + 5 -5 + 5$
$= 5$
Question 382 Marks
From the sum of $233$ and $-147,$ subtract $-284.$
Answer
View full question & answer→Sum of $233$ and $-147 = 233 - 147$
$= 86$
$\Rightarrow 86 - (-284) = 86 + 284$
$= 370$
$= 86$
$\Rightarrow 86 - (-284) = 86 + 284$
$= 370$
Question 392 Marks
Draw a number line and represent each of the following on it: $(-1) + (-2) + 2$
Answer
View full question & answer→If we start from $-1$ and move $2$ units to the left of $-1,$
we will obtain $-3;$ and then if we start from $-3$ and move $2$ units to the left,
we will obtain $-1,$ as shown on the number line
we will obtain $-3;$ and then if we start from $-3$ and move $2$ units to the left,
we will obtain $-1,$ as shown on the number line