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:
$4\ \Delta\ 3$
$4\ \Delta\ 3$
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
-522 and -160
Answer
View full question & answer→-522 + (-160)
= -522 - 160
= -(522 + 160)
= -682
= -522 - 160
= -(522 + 160)
= -682
Question 42 Marks
Find the sum of:
2884 and -2884
2884 and -2884
Answer
View full question & answer→2884 and -2884
= 2884 + (-2884)
= 2884 - 2884
= 0
= 2884 + (-2884)
= 2884 - 2884
= 0
Question 52 Marks
Find the sum of:
2567 and -325
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)$
$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$
$\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$
$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$
$\therefore2\ \Delta\ 5=2-5-(-5)$
$= 2-5 + 5$
$= 2$
Question 102 Marks
Calculate:
1 - 2 + 3 - 4 + 5 - 6 + 7 - 8 + ... + 49 - 50
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) × 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) × 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
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
= 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)$
$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.
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
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.
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 × 5 + 10 × (-5)
= 50 - 50
= 0
5 + (-5) + 5 + (-5) + ..... = (5 + 5 + 5 + ..... 10 terms) + (-5 - 5 - 5 - ..... 10 terms)
= 10 × 5 + 10 × (-5)
= 50 - 50
= 0
Question 192 Marks
Evaluate the following:
-8 - 24 + 31 - 26 - 28 + 7 + 19 - 18 - 8 + 33
-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
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 × 5 + 12 × (-5)
= 65 - 60
= 5
5 + (-5) + 5 + (-5) + ..... = (5 + 5 + 5 + ..... 13 terms) + (-5 - 5 - 5 - ..... 12 terms)
= 13 × 5 + 12 × (-5)
= 65 - 60
= 5
Question 212 Marks
Find the sum of:
-10025 and 139
-10025 and 139
Answer
View full question & answer→-10025 and 139
-10025 + 139
= -(10025 - 139)
= -9886
-10025 + 139
= -(10025 - 139)
= -9886
Question 222 Marks
Evaluate:
7 ×|-15| - |-9| × 8
7 ×|-15| - |-9| × 8
Answer
View full question & answer→$\because$ |-15| = 15 and |-9| = 9$\therefore$ 7 × |-15| - |-9| × 8 = 7 × 15 − 9 × 8
= 105 - 72
= 33
Hence, 7 × |-15| - |-9| × 8 = 33
= 105 - 72
= 33
Hence, 7 × |-15| - |-9| × 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:
$(-2)\ \Delta\ (-3)$
$(-2)\ \Delta\ (-3)$
Answer
View full question & answer→Given, $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$$(-2)\ \Delta\ (-3)=-(-2) + (-3) - (-2)$
$=2-3+2$
$=4-3$
$=1$
$=2-3+2$
$=4-3$
$=1$
Question 252 Marks
The sum of two integers is 238. If one of the integers is -122, determine the other.
Answer
View full question & answer→Given that,
Sum of two integer's = 238
one of the integer = -122
Required integer = 238 - (-122)
= 238 + 122
= 360
Sum of two integer's = 238
one of the integer = -122
Required integer = 238 - (-122)
= 238 + 122
= 360
Question 262 Marks
Subtract the sum of -5020 and 2320 from -709.
Answer
View full question & answer→The sum of -5020 and 2320 is = -5020 + 2320
= 2320 - 5020
= -2700
Now, (-709) - (-2700)
= -709 + 2700
= 1991
= 2320 - 5020
= -2700
Now, (-709) - (-2700)
= -709 + 2700
= 1991
Question 272 Marks
If $\Delta$ is an operation on integers such that $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$ for all integers a, b. Find the value of:
$(-5)\ \Delta\ 6$
$(-5)\ \Delta\ 6$
Answer
View full question & answer→Given, $\text{a }\Delta\text{ b}=-\text{a}+\text{b}-(-2)$$(-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:
$(-9)\ \Delta\ (-4)$
$(-9)\ \Delta\ (-4)$
Answer
View full question & answer→$\because\text{a }\Delta\text{ b}= \text{a}-\text{b}-(-5)$
$\therefore(-9)\ \Delta\ (-4)=(-9)-(-4)-(-5)$
$= -9 +4 + 5$
$= 0$
$\therefore(-9)\ \Delta\ (-4)=(-9)-(-4)-(-5)$
$= -9 +4 + 5$
$= 0$
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
= b - 1 - b
= -1
Question 302 Marks
Calculate:
1 - 2 + 3 - 4 + 5 - 6 + .................. + 15 - 16
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
2547 and -2548
Answer
View full question & answer→2547 and -2548
= 2547 + (-2548)
= -(-2547 + 2548)
= -1
= 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:
$(-7)\ \Delta\ 3$
$(-7)\ \Delta\ 3$
Answer
View full question & answer→$\because\text{a }\Delta\text{ b}= \text{a}-\text{b}-(-5)$
$\therefore(-7)\ \Delta\ 3=(-7)-3-(-5)$
$= -7 - 3 + 5$
$= -(7 + 3) + 5$
$= -10 + 5$
$= -(10 - 5)$
$= -5$
$\therefore(-7)\ \Delta\ 3=(-7)-3-(-5)$
$= -7 - 3 + 5$
$= -(7 + 3) + 5$
$= -10 + 5$
$= -(10 - 5)$
$= -5$
Question 352 Marks
Simplify:
9 × (-16) + (-17) × (-16)
9 × (-16) + (-17) × (-16)
Answer
View full question & answer→9 × (-16) + (-17) × (-16) = -(9 × 16) + (17 × 16)
= -144 + 272
= 272 - 144
= 128
Hence, 9 × (-16) + (-17) × (-16) = 128
= -144 + 272
= 272 - 144
= 128
Hence, 9 × (-16) + (-17) × (-16) = 128
Question 362 Marks
Evaluate the following:
-26 - 20 + 33 - (-33) + 21 + 24 - (-25) - 26 - 14 - 34
-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.
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
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
⇒ 86 - (-284) = 86 + 284
= 370
= 86
⇒ 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