Question 12 Marks
Find each of the following products: $(-1) \times (-1) \times (-1) \times … 171$ times
AnswerSince the number of negative integers in the product is odd. The product will be negative. $(-1)^{171}=-1$
View full question & answer→Question 22 Marks
Fill in the blanks: $(-19) \times (-25) + (-19) \times (-15)$
Answer$(-19) \times (-25) + (-19) \times (-15) = (-19) \times [(-25) + (-15)] [$Associative property$] = (-19) \times (-40) = 760$
View full question & answer→Question 32 Marks
Fill in the blanks: $0 ÷ (-34)$
Answer$0 ÷ (-34) = 0 ($zero$).$
Dividing 0 by any integer gives $0.$
View full question & answer→Question 42 Marks
Simplify: $(-26) \times 72 + (-26) \times 28$
Answer$(-26) \times (72 + 28) [$using the distributive law$] = (-26) \times 100 = -2600$
View full question & answer→Question 52 Marks
Subtract the sum of $-1032$ and $878$ from $-34.$
AnswerSum of $-1032$ and $878 = -1032 + 878 = -154$
Subtracting the sum from $-34,$
we get $-34 - (-154) = (-34) + 154 = 120$
View full question & answer→Question 62 Marks
Find $36 - (-64)$ and $(-64) -36.$ Are they equal$?$
Answer$36 - (-64) = 36 + 64 = 100$
Now, $(-64) - 36 = (-64) + (-36) = -100$
Here, $100$ is not equal $-100$
Thus, they are not equal.
View full question & answer→Question 72 Marks
Simplify: $(-8) \times 9 + (- 8) \times 7$
Answer$(-8) \times (9 + 7) [$using the distributive law$] = (-8) \times 16 = -128$
View full question & answer→Question 82 Marks
Fill in the blanks: $37 ÷ 0$
Answer$37 ÷ 0$ Not defined. Dividing any integer by zero is not defined.
View full question & answer→Question 92 Marks
Simplify: $20 \times (-16) + 20 \times 14$
Answer$20 \times (-16 + 14) [$using the distributive law$] = 20 \times (-2) = -40$
View full question & answer→Question 102 Marks
If $a = -8, b = -7, c = 6,$ verify that $(a + b) + c = a + (b + c).$
Answer$(a + b) + c = (-8 + (-7)) + 6$
$= -15 + 6 = -9 a + (b + c)$
$= -8 + (-7 + 6)$
$= -13 + (-1)$
$= -9$
Hence, $(a + b) + c = a + (b + c) [$i.e., Property of Associativity$]$
View full question & answer→Question 112 Marks
Find each of the following products: $(-4) \times (-5) \times (-8) \times (-10)$
AnswerSince the number of negative integers in the product is even. The product will be positive. $(4) \times (5) \times (8) \times (10) = 1600$
View full question & answer→Question 122 Marks
$(-1) \times (-1) \times (-1) \times … 200$ times
AnswerSince the number of negative integers in the product is even the product will be positive. $(-1)^{200}=1$
View full question & answer→Question 132 Marks
The difference of an integer $p$ and $-8$ is $3.$ Find the value of $p.$
Answer$P - (-8) = 3$
$\Rightarrow P = 3 + (-8)$
$\Rightarrow P = -5$
Hence, the value of $P$ is $-5.$
View full question & answer→Question 142 Marks
Simplify:
$(-16) \times (- 8) + (- 4) \times (-8)$
Answer$(-16 + (-4)) \times (-8) [$using the distributive law$]$
$= (-20) \times (-8) = 160$
View full question & answer→Question 152 Marks
Find each of the following products: $(-6) \times (- 5) \times (-7) \times (-2) \times (-3)$
AnswerSince the number of negative integers in the product is odd. the product will be negative. $-(6) \times (5) \times (7) \times (2) \times (3) = -1260$
View full question & answer→Question 162 Marks
$(-5) \times (-5) \times (-5) \times … 5$ times
AnswerSince the number of negative integers in the product is odd. The product will be negative. $(-5)^5=-3125$
View full question & answer→Question 172 Marks
Simplify: $10 \times (-12) + 5 \times (-12)$
Answer$(-12) \times (10 + 5) [$using the distributive law$] = (-12) \times 15 = -180$
View full question & answer→Question 182 Marks
Fill in the blanks: $(-168) ÷ (-14)$
Answer$(-168) ÷ (-14) = 12$
View full question & answer→Question 192 Marks
By what number should $(-240)$ be divided to obtain $16?$
AnswerSuppose that a divides $-240$ to obtain $16.$
Then, we have: $(-240) ÷ a = 16$
$\Rightarrow a = (-240) ÷ 16$
$= -15$
Hence, $-15$ should divide $-240$ to obtain $16.$
View full question & answer→Question 202 Marks
Add the product of $(-16)$ and $(-9)$ to the quotient of $(-132)$ by $6.$
AnswerProduct of $(-16)$ and $(-9) = (-16) \times (-9) = 144$
Now, $(-132) ÷ 6$ gives the quotient $-22 144 + (-22) = 122$
View full question & answer→Question 212 Marks
Simplify: $(-16) \times (-15) + (-16) \times (-5)$
Answer$(-16) \times (-15 + (-5)) [$using the distributive law$] = (-16) \times (-20) = 320$
View full question & answer→Question 222 Marks
The sum of two integers is $-12.$ If one of them is $43$, find the other.
AnswerLet the other integer be $a.$
Then, we have; $a + (-12) = 43 $
$\Rightarrow a = 43 - (-12) $
$= 55$
Hence, the other integer is $55.$
View full question & answer→Question 232 Marks
Simplify: $9 \times (-13) + 9 \times (-7)$
Answer$9 \times (-13 + (-7)) [$using the distributive law$] = 9 \times (-20) = -180$
View full question & answer→Question 242 Marks
Fill in the blanks: $(-105) ÷ 21$
Answer$(-105) ÷ 21 (-105) ÷ 21 = -5$
View full question & answer→Question 252 Marks
The sum of two integers is $-16.$ If one of them is $53.$ Find the other.
AnswerLet the other integer be $a.$
Then, we have: $53 + a = -16 $
$\Rightarrow a = -16 - 53 $
$= -69$
The other integer is $-69.$
View full question & answer→Question 262 Marks
Simplify: $(-11) \times (-15) + (-11) \times (-25)$
Answer$(-11) \times (-15 + (-25)) [$using the distributive law$] = (-11) \times (-40) = 440$
View full question & answer→Question 272 Marks
$(-60) \times (-10) \times (-5) \times (-1)$
AnswerSince the number of negative integers in the product is even, the product will be positive.
$(60) \times (10) \times (5) \times (1) = 3000$
View full question & answer→Question 282 Marks
$(-30) \times (-20) \times (-5)$
AnswerSince the number of negative integers in the product is odd. the product will be negative. $-(30) \times (20) \times (5) = -3000$
View full question & answer→Question 292 Marks
$(-3) \times (-3) \times (-3) \times … 6$ times.
AnswerSince the number of negative integers in the product is even. The product will be positive. $(-3)^6=729$
View full question & answer→Question 302 Marks
If $a = -9$ and $b = -6,$ show that $(a - b)$ Not Equal To $(b - a).$
AnswerHere, $(a - b) = -9 - (-6) = -3$
Similarly, $(b - a) = -6 - (-9) = 3 (a - b)$
not equal to $(b - a)$
View full question & answer→Question 312 Marks
What should be divided by $(-7)$ to obtain $12?$
AnswerLet $a$ be divided by $(-7)$ to obtain $12$.
Then, we have: $a ÷ (-7) = 12$
$\text{a}=-\frac{7}{12}$
Hence, $-\frac{7}{12}$ should be divided by $-7$ to obtain $12.$
View full question & answer→Question 322 Marks
Evaluate:
$25 \times (-33) + 25 \times (-17)$
Answer$25 \times (-33) + 25 \times (-17)$
$= 25 \times [(-33) + (-17)] [$Associative property$]$
$= 25 \times (-50)$
$= -1250$
View full question & answer→Question 332 Marks
What will be the sign of the product, if we multiply $103$ negative integers and $65$ positive Integers$?$
AnswerMultiplying $103$ negative integers will yield a negative integer, whereas $65$ positive integers will give a positive integer. The product of a negative integer and a positive integer is a negative integer.
View full question & answer→Question 342 Marks
Subtract $-134$ from the sum of $38$ and $-87.$
AnswerFirst, we will calculate the sum of $38$ and $-87.$
$38 + (-87) = -49$
Now, subtracting $-134$ from the sum,
we get: $-49 - (-134) = (-49) + 134 = 85$
View full question & answer→Question 352 Marks
The difference of an integer a and $(-6)$ is $4.$ Find the value of $a.$
AnswerWe have:
$a – (-6) = 4$
$\Rightarrow a = 4 + (-6) = -2$
$a = -2$
View full question & answer→Question 362 Marks
Evaluate: $(-16) \times 12 + (-16) \times 8$
Answer$(-16) \times 12 + (-16) \times 8 = (-16) \times (12 + 8) [$Associative property$] = (-16) \times 20 = -320$
View full question & answer→Question 372 Marks
The sum of two integers is $65.$ If one of them is $-31,$ find the other.
AnswerLet the other integer be $a.$
Then, $-31 + a = 65$
$\Rightarrow a = 65 - (-31) = 96$
The other integer is $96.$
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