3 Marks Question

Question 13 Marks

Simplify the following: $23-\Big[23-\big\{23-(23-\overline{23-23})\big\}\Big]$

Answer

$23-\Big[23-\big\{23-(23-\overline{23-23})\big\}\Big]$$=23-\big[23-\big\{23-(23-0)\big\}\big]$
$=23-\big[23-(23-23)\big]$
$=23-[23-0]$
$=23-23$
$=0$
$\therefore\ 23-\Big[23-\big\{23-(23-\overline{23-23})\big\}\Big]=0$

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Question 23 Marks

Simplify the following: $36-\big[18-\{14-(15-4\div2\times2)\}\big]$

Answer

$36-\big[18-\{14-(15-4\div2\times2)\}\big]$ $=36-\big[18-\{14-(11\div2\times2)\}\big]$ $=36-\Big[18-\Big\{14-\Big(\frac{11}{2}\times2\Big)\Big\}\Big]$ $=36-\big[18-\big\{14-11\big\}\big]$ $=36-\big[18-3\big]$ $=36-15$ $=21$ $\therefore\ 36-\big[18-\{14-(15-4\div2\times2)\}\big]=21$

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Question 33 Marks

Simplify the following: $2550-\Big[510-\big\{270-(90-\overline{80+70})\big\}\Big]$

Answer

$2550-\big[510-\big\{270-(90-\overline{80+70})\big\}$ $=2550-\Big[510-\big\{270-(90-150)\big\}\Big]$ $=2550-\big[510-\{270-(-60)\}\big]$ $=2550-\big[510-330\big]$ $=2550-\big[180\big]$ $=2550-180$ $=2370$ $\therefore\ 2550-\big[510-\big\{270-(90-\overline{80+70})\big\}=2370$

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Question 43 Marks

Simplify the following: $\big[29-(-2)\big\{6-(7-3)\big\}\big]\div\big[3\times\big\{5+(-3)\times(-2)\big\}\big]$

Answer

$\big[29-(-2)\big\{6-(7-3)\big\}\big]\div\big[3\times\big\{5+(-3)\times(-2)\big\}\big]$ $=\big[29-(-2)(6-4)\big]\div\big[3\times\{5+(3\times2)\}\big]$ $=\big[29-(-2)(2)\big]\div\big[3\times(5+6)\big]$ $=\big[29+4\big]\div\big[3\times11\big]$ $=\big[33\big]\div\big[33\big]$ $=1$ $\therefore\ \big[29-(-2)\big\{6-(7-3)\big\}\big]\div\big[3\times\big\{5+(-3)\times(-2)\big\}\big]=1$

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Question 53 Marks

Simplify the following: $27-\Big[38-\big\{46-(15-\overline{13-2})\big\}\Big]$

Answer

$27-\Big[38-\big\{46-(15-\overline{13-2})\big\}\Big]$ $=27-\big[38-\{46-(15-11)\}\big]$ $=27-\big[38-(46-4)\big]$ $=27-\big[38-42\big]$ $=127-[-4]$ $=27+4$ $=31$ $\therefore27-\Big[38-\big\{46-(15-\overline{13-2})\big\}\Big]=31$

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Question 63 Marks

Verify the following: $(-23)\{(-5) + (+19)\} = (-23) × (-5) + (-23) × (+19)$

Answer

$L.H.S = (-23)[(-5) + (+19)]$
$= (-23)[-5 + 19] = (-23)[14]$
$= -322$
$R.H.S = (-23) \times (-5) + (-23) \times (+19)$
$= 115 - 437 = -322$
Therefore, $L.H.S = R.H.S$

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Question 73 Marks

Simplify the following: $63-\Big[(-3)\big\{-2-\overline{8-3}\big\}\Big]\div\Big[3\big\{5+(-2)(-1)\big\}\Big]$

Answer

$63-\Big[(-3)\big\{-2-\overline{8-3}\big\}\Big]\div\Big[3\big\{5+(-2)(-1)\big\}\Big]$ $=63-\big[(-3)(-2-5)\big]\div\big[3(5+2)\big]$ $=63-\big[(-3)(-7)\big]\div\big[3(7)\big]$ $=63-\big[21\big]\div\big[21\big]$ $=63-1$ $=62$ $\therefore\ 63-\Big[(-3)\big\{-2-\overline{8-3}\big\}\Big]\div\Big[3\big\{5+(-2)(-1)\big\}\Big]=6$

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Question 83 Marks

Simplify the following: $45-\big[38-\{60\div3-(6-9\div3)\div3\}\big]$

Answer

$45-\big[38-\{60\div3-(6-9\div3)\div3\}\big]$
$=45-\big[38-\{20-(6-3)\div3\}\big]$
$=45-\big[38-\{20-3\div3\}]$
$=45-\big[38-(20-1)\big]$
$=45-\big[38-19\big]$
$=45-\big[19\big]$
$=26$
$\therefore\ 45-\big[38-\{60\div3-(6-9\div3)\div3\}\big]=26$

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Question 93 Marks

Simplify the following: $22-\frac{1}{4}\big\{-5-(-48)\div(-16)\big\}$

Answer

$22-\frac{1}{4}\big\{-5-(-48)\div(-16)\big\}$
$=22-\frac{1}{4}\{-5-(-48-16)\}$
$=22-\frac{1}{4}\Big(-5-\frac{48}{16}\Big)$
$=22-\frac{1}{4}\big(-5-3\big)$
$=22-\frac{1}{4}(-8)$
$=22+\frac{8}{4}$
$=22+2$
$=24$
$\therefore\ 22-\frac{1}{4}\big\{-5-(-48)\div(-16)\big\}=24$

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Question 103 Marks

Simplify the following: $25-\frac{1}{2}\big\{5+4-(3+2-\overline{1+3}\big)\big\}$

Answer

$25-\frac{1}{2}\big\{5+4-(3+2-\overline{1+3}\big)\big\}$
$=25-\frac{1}{2}\big[5+4-(5-4)\big]$
$=25-\frac{1}{2}\big[5+4-1\big]$
$=25-\frac{1}{2}[8]$
$=25-4$
$=21$
$\therefore25-\frac{1}{2}\big\{5+4-(3+2-\overline{1+3}\big)\big\}=21$

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Question 113 Marks

On the occasion of 26 January, 4 packs of stamps were distributed in a classroom having 30 students so that each students got the same number of stamps. If each pack contained 120 stamps, how many stamps did each students get?

Answer

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Question 123 Marks

Verify the following
(i) $19 \times\{7+(-3)\}=19 \times 7+19 \times(-3)$
(ii) $(-23) \mid(-5)+(+19)\}=(-23) \times(-5)+(-23) \times(+19)$

Answer

self

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Question 133 Marks

State which is greater:
(i) $(8+9) \times 10$ and $8+9 \times 10$
(ii) $(8-9) \times 10$ and $8-9 \times 10$
(iii) $\{(-2)-5\} \times(-6)$ and $(-2)-5 \times(-6)$

Answer

(i) $(8+9) \times 10$
(ii) $(8-9) \times 10$
(iii) $[(-2)-5] \times(-6)$

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Question 143 Marks

What will be the sign of the product if we multiply together
(i) 8 negative integers and 1 positive integer?
(ii) 21 negative integers and 3 positive integers?
(iii) 199 negative integers and 10 positive integers?

Answer

(i) positive (ii) negative (iii) negative

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Question 153 Marks

Determine the integer whose product with ' $-1^{\prime}$ is
(i) 58 (ii) 0 (iii) -225

Answer

(i) -58 (ii) 0 (iii) 225

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Question 163 Marks

Find the value of:
$28945 \times 99-(-28945)$

Answer

2894500