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MATHS [3 marks sum]

Integers · ICSE STD 7 (ICSE - English Medium). 36 questions.

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36 questions · timed · auto-graded

Question 13 Marks
If $x \times(-1)=36$, is $\times$ positive or negative?
Answer
$
\begin{aligned}
& x \times(-1)=36 \\
& -1 x=36 \\
& x=\frac{36}{-1} \\
& x=-36
\end{aligned}
$
$
\because x=-36
$
$\therefore$ It is a negative integer.
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Question 23 Marks
If $x \times(-1)=-36$, is $\times$ positive or negative?
Answer
$
\begin{aligned}
& x \times(-1)=-36 \\
& -1 x=-36 \\
& x=\frac{-36}{-1} \\
& x=36
\end{aligned}
$
$
\because x=36
$
$\therefore$ It is a positive integer.
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Question 33 Marks
The difference between an integer x and (-9) is 6. Find all possible values of x.
Answer
The difference between an integer x – (- 9) = 6 or - 9 – x = 6
∴ Value of x
⇒ x – (-9) = 6 or ⇒ -9 – x = 6
⇒ x + 9 = 6 or Answer-x = 6 + 9
⇒ x = 6 – 9 or ⇒ -x = 15
⇒ x = -3 or ⇒ x = -15
Hence, possible values ofx are -3 and -15.
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Question 43 Marks
The sum of two integers is -56. If one integer is -42, find the other.
Answer
Sum of two integers = -56
One integer = -42
∴Second integer = -56 – (-42)
= -56 + 42
= - 14
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Question 53 Marks
The sum of two integers is 28. If one integer is -45, find the other
Answer
Sum of two integers = 28
One integer = - 45
∴ Second integer = 28 – (-45)
= 28 + 45
= 73
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Question 63 Marks
The difference between an integer and -6 is -5. Find the values of x.
Answer
The difference between an integer
= x-(-6) = -5
∴ Value of
⇒ x – (-6) = -5
⇒ x + 6 = -5
x = -5 – 6
x = -11
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Question 73 Marks
Find the result of subtracting the sum of all integers between 20 and 30 from the sum of all integers from 20 to 30.
Answer
Required number
= (Sum of all integers between 20 and 30 – Integers between 20 and 30)
(20 + 21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30) – (21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 )
⇒ 20 + 30 = 50
∴ Required number = 50
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Question 83 Marks
Evaluate: $(24 \div \overline{12-9}-12)-(3 \times 8=4+1)$
Answer

$\begin{aligned} & (24 \div \overline{12-9}-12)-(3 \times 8=4+1) \\ & \Rightarrow(24 \div 3-12)-(3 \times 2+1) \\ & \Rightarrow(8-12)-(6+1) \\ & \Rightarrow-4-7 \\ & =-11\end{aligned}$
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Question 93 Marks
Evaluate: -8 – {- 6 (9 – 11) + 18 ÷ -3}
Answer
- 8 – {- 6 (9 – 11) + 18 ÷ -3}
⇒ - 8 – {- 6 (- 2) – 6}
⇒ - 8 - {12 - 6}
⇒ - 8 – {6}
⇒ - 8 - 6
= - 14
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Question 103 Marks
Evaluate: $48-[18-\{16-(5-\overline{4+1})\}]$
Answer

$\begin{aligned} & 48-[18-\{16-(5-\overline{4+1})\}] \\ & \Rightarrow 48-[18-\{16-(5-5)\}] \\ & \Rightarrow 48-[18-\{16-0)\}] \\ & \Rightarrow 48-[18-16] \\ & \Rightarrow 48-2 \\ & =46\end{aligned}$
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Question 113 Marks
Evaluate: 27 – [5 + {28 – (29 – 7)}]
Answer
27 – [5 + {28 – (29 – 7)}]
⇒ 27 – [5 + {28 – 22}]
⇒ 27 – [5 + 6]
⇒ 27 - 11
= 16
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Question 133 Marks
Evaluate: 16 + 8 ÷ 4 – 2 × 3
Answer
16 + 8 ÷ 4 – 2 × 3
⇒ 16 + 2 – 2 x 3
⇒16 + 2 – 6
⇒ 18 - 6
= 12
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Question 143 Marks
Evaluate: (-5) – (-48) ÷ (-16) + (-2) × 6
Answer
(- 5) – (-48) ÷ (-16) + (- 2) × 6
⇒ (- 5) – 3 + (- 2) × 6
⇒ - 5 – 3 – 12
⇒ - 8 - 12
= - 20
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Question 163 Marks
The sum of two integers is -15. If one of them is 9, find the other.
Answer
Sum of two integers = -15
One integer = 9
∴ Second integer = -15 - 9
= -(15 + 9)
= -24
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Question 173 Marks
$2550-[510-\{270-(90-\overline{80+7})\}]$
Answer

$\begin{aligned} & 2550-[510-\{270-(90-\overline{80+7})\}] \\ & =2550-[510-\{270-(90-87)\}] \\ & =2550-[510-\{270-3\}] \\ & =2550-[510-267] \\ & =2550-243 \\ & =2307\end{aligned}$
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Question 183 Marks
$17-[17-\{17-(17-\overline{17-17})\}]$
Answer

$\begin{aligned} & 17-[17-\{17-(17-\overline{17-17})\}] \\ & =17-[17-\{17-(17-0)\}] \\ & =17-[17-\{17-17\}] \\ & =17-[17-0] \\ & =17-17 \\ & =0\end{aligned}$
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Question 193 Marks
46 - [26 - {14 - (15 - 4 ÷ 2 x 2)}]
Answer
46 - [26 - {14 - (15 - 4 ÷ 2 x 2)}]
= 46 - [26 - {14 - (15 - 2 x 2)}]
= 46 - [26 - {14 - (15 - 4)}]
= 46 - [26 - {14 - 11}]
= 46 – [26 – 3]
= 46 – 23
= 23
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Question 203 Marks
$32-[43-\{51-(20-\overline{18-7})\}]$
Answer

$\begin{aligned} & 32-[43-\{51-(20-\overline{18-7})\}] \\ & =32-[43-\{51-(20-11)\}] \\ & =32-[43-\{51-9\}] \\ & =32-[43-42] \\ & =32-1 \\ & =31\end{aligned}$
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Question 223 Marks
$2-[3-\{6-(5-\overline{4-3})\}]$
Answer

$\begin{aligned} & 2-[3-\{6-(5-\overline{4-3})\}] \\ & \Rightarrow 2-[3-\{6-(5-1)\}] \\ & \Rightarrow 2-[3-\{6-4\}] \\ & \Rightarrow 2-(3-2) \\ & \Rightarrow 2-1=1\end{aligned}$
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Question 233 Marks
$9 \times(8-\overline{3+2})-2(2+\overline{3+3})$
Answer

$\begin{aligned} & 9 \times(8-\overline{3+2})-2(2+\overline{3+3}) \\ & =9 \times(8-5)-2(2+6) \\ & =9 \times 3-2 \times 8 \\ & =27-16 \\ & =11\end{aligned}$
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Question 243 Marks
88 - {5 - (- 48) ÷ (- 16)}
Answer

$\begin{aligned} & 88-\{5-(-48) \div(-16)\} \\ & =88-\left\{5-\frac{-48}{-16}\right\} \\ & =88-\{5-3\} \\ & =88-2 \\ & =86\end{aligned}$
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Question 253 Marks
$30+[\{-2 \times(25-\overline{13-3})\}]$
Answer

$\begin{aligned} & 30+[\{-2 \times(25-\overline{13-3})\}] \\ & =30+[\{-2 \times(25-10)\}] \\ & =30+[\{-2 \times 15\}] \\ & =30+[-30] \\ & =30-30 \\ & =0\end{aligned}$
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Question 263 Marks
Evaluate: (-20) x (-1) + 14 ÷ 7
Answer

$\begin{aligned} & (-20) \times(-1)+14 \div 7 \\ & =(-20) \times(-1)+\frac{14}{7} \\ & =(-20) \times(-1)+2 \\ & =20+2=22\end{aligned}$
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Question 273 Marks
Evaluate: (- 18) + 6 ÷ 3 + 5
Answer

$\begin{aligned} & (-18)+6 \div 3+5 \\ & =(-18)+\frac{6}{3}+5 \\ & =(-18)+2+5 \\ & =-18+7=-11\end{aligned}$
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Question 283 Marks
Evaluate: (-4) + (-12) ÷ (-6)
Answer

$\begin{aligned} & (-4)+(-12) \div(-6) \\ & =(-4)+\left(\frac{-12}{-6}\right) \\ & =(-4)+2 \\ & =-4+2=-2\end{aligned}$
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Question 293 Marks
Evaluate: 16 – 8 + 4 ÷ 2 x 3
Answer

$\begin{aligned} & 16-8+4 \div 2 \times 3 \\ & =16-8+\frac{4}{2} \times 3 \\ & =16-8+2 \times 3 \\ & =16-8+6 \\ & =16+6-8 \\ & =22-8=14\end{aligned}$
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Question 303 Marks
Evaluate: 16 ÷ 8 + 4 – 2 x 3
Answer

$\begin{aligned} & 16 \div 8+4-2 \times 3 \\ & =\frac{16}{8}+4-2 \times 3 \\ & =2+4-6 \\ & =6-6=0\end{aligned}$
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Question 313 Marks
Evaluate: 16 + 8 ÷ 4 - 2 x 3
Answer

$\begin{aligned} & 16+8 \div 4-2 \times 3 \\ & =16+\frac{8}{4}-2 \times 3 \\ & =16+2-2 \times 3 \\ & =16+2-6 \\ & =18-6=12\end{aligned}$
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Question 323 Marks
Evaluate: 13 -12 ÷ 4 × 2
Answer

$\begin{aligned} & 13-12 \div 4 \times 2 \\ & =13-\frac{12}{4} \times 2 \\ & =13-3 \times 2 \\ & =13-6=7\end{aligned}$
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Question 333 Marks
Evaluate: 6 – 8 – (- 6) ÷ 2
Answer

$\begin{aligned} & 6-8-(-6) \div 2 \\ & =6-8+\frac{6}{2} \\ & =6-8+3 \\ & =6-5 \\ & =1\end{aligned}$
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Question 343 Marks
Evaluate: 16 - 5 × 3 + 4
Answer
By using the BODMAS rule,
16 - 5 × 3 + 4
We have an operation for multiplication,
= 16 - 15 + 4
Now will go for an addition
= 16 + 4 - 15
= 20 - 15
= 5
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Question 353 Marks
Divide (- 798) by (- 21)
Answer

$\begin{aligned} & (-798) \text { by }(-21) \\ & =\frac{-798}{-21} \\ & =\frac{798}{21} \\ & =\frac{38 \times 21}{21} \\ & =38\end{aligned}$
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Question 363 Marks
Find which is greater.
{(-3) - 4} × (-5) or (-3) - 4 × (-5)
Answer
{(-3) - 4} × (-5)(-3) - 4 × (-5)
{-3 - 4} × (-5)
= (-7) × (-5)
= 35		(-3) + 20
= -3 + 20
= 17
35 > 17
∴ {(-3) - 4} × (-5) is greater.
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[3 marks sum] - MATHS STD 7 Questions - Vidyadip