3 Mark 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) × (-5) + (-23) × (+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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Maths 3 Mark Question

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