Ssc Math Chapter 1 বাস্তব সংখ্যা Solution || Part 2

ssc math chapter 1 বাস্তব সংখ্যা solution || part 2

প্রশ্ন \ ৯ \ গুণ কর :

(ক) $0.\overset.3 × 0.\overset.6$

সমাধান : প্রদত্ত আবৃত্ত দশমিক ভগ্নাংশ গুলোকে সাধারণ ভগ্নাংশে রূপান্তর করি।

$0.\overset.3 = \frac{3}{9} = \frac{1}{3}$

$0.\overset.6 = \frac{6}{9} = \frac{2}{3}$

⸫ $0.\overset.3 × 0.\overset.6$

= $\frac{1}{3} × \frac{2}{3}$

= $0.\overset.2$

নির্ণেয় গুণফল $0.\overset.2$ .

(খ) $2.\overset.4 × 0.\overset.6$

$2.\overset.4 = \frac{24 - 2}{9} = \frac{22}{9}$

$0.\overset.8 \overset.1= \frac{81 - 0}{99} = \frac{81}{99} = \frac{9}{11}$

⸫ $2.\overset.4 × 0.\overset.6$

= $\frac{22}{9} × \frac{9}{11}$

= 2

নির্ণেয় গুণফল ২

(গ) $0.6\overset.2 × 0.\overset.3$

$0.6\overset.2 = \frac{62 - 6}{90} = \frac{56}{90} = \frac{28}{45}$

$0.\overset.3 = \frac{3}{9} = \frac{1}{3}$

⸫ $0.6\overset.2 × 0.\overset.3$

= $\frac{28}{45} × \frac{1}{3}$

= 0.207407407 ……………. = $0.2\overset.07\overset.4$

নির্ণেয় গুণফল $0.2\overset.07\overset.4$

(ঘ) $42.\overset.1\overset.8 × 0.2\overset.8$

$42.\overset.1\overset.8 = \frac{4218 - 42}{99} = \frac{4176}{99}$

$0.2\overset.8 = \frac{28 - 2}{90} = \frac{26}{90}$

⸫ $42.\overset.1\overset.8 × 0.2\overset.8$

= $\frac{4176}{99} × \frac{26}{90}$

= $\frac{6032}{495}$

= 12.18585858 ……..

= $12.1\overset.8\overset.5$

নির্ণেয় গুণফল $12.1\overset.8\overset.5$

প্রশ্ন \ ১০ \ ভাগ কর :

(ক) $0.\overset.3 ÷ 0.\overset.6$

$0.\overset.3 = \frac{3}{9} = \frac{1}{3}$

$0.\overset.6 = \frac{6}{9} = \frac{2}{3}$

∴ $0.\overset.3 ÷ 0.\overset.6$

= $\frac{1}{3} ÷ \frac{2}{3}$

= $\frac{1}{2}$

= 0.5

নির্ণেয় ভাগফল 0.5

(খ) $0.3\overset.5 ÷ 1.\overset.7$

$0.3\overset.5 = \frac{35 - 3}{90} = \frac{32}{90} = \frac{16}{45}$

$1.\overset.7 = \frac{17 - 1}{9} = \frac{16}{9}$

$0.3\overset.5 ÷ 1.\overset.7$

= $\frac{16}{45} ÷ \frac{16}{9}$

= $\frac{16}{45} × \frac{9}{16}$

= $\frac{1}{5}$

= 0.2

নির্ণেয় ভাগফল 0.2

(গ) $2.3\overset.7 ÷ 0.4\overset.5$

$2.3\overset.7 = \frac{237 - 23}{90} = \frac{214}{90}$

$0.4\overset.5 = \frac{45 - 4}{90} = \frac{41}{90}$

$2.3\overset.7 ÷ 0.4\overset.5$

= $\frac{214}{90} ÷ \frac{41}{90}$

= $\frac{214}{90} × \frac{90}{41}$

= $\frac{214}{41}$

= 5.2195121951 ……………

= $5.\overset.2195\overset.1$

নির্ণেয় ভাগফল $5.\overset.2195\overset.1$

(ঘ) $1.\overset.18\overset.5 ÷ 0. \overset.2\overset.4$

$1.\overset.18\overset.5 = \frac{1185 - 1}{999} = \frac{1184}{999}$

$0. \overset.2\overset.4 = \frac{24}{99}$

∴ $1.\overset.18\overset.5 ÷ 0. \overset.2\overset.4$

= $\frac{1184}{999} ÷ \frac{24}{99}$

= $\frac{1184}{999} × \frac{99}{24}$

= $\frac{1628}{333}$

= 4.8888 ………….

= $4.\overset.8$

নির্ণেয় ভাগফল $4.\overset.8$

প্রশ্ন \ ১২ \ নিচের কোন সংখ্যাগুলো মূলদ এবং কোন সংখ্যাগুলো অমূলদ লেখ :

(ক) $0.\overset.4$

সমাধান : $0.\overset.4 = \frac{4}{9}$

∴ $0.\overset.4$ সংখ্যাটি মূলদ

(খ) $\sqrt{9}$

সমাধান : $\sqrt{9} = \sqrt{3^2} = 3$

∴ $\sqrt{9}$ সংখ্যাটি মূলদ

(গ) $\sqrt{11}$

সমাধান : $\sqrt{11}$

∴ $\sqrt{11}$ সংখ্যাটি অমূলদ

(ঘ) $\frac{\sqrt{6}}{3}$

সমাধান :

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\frac{\sqrt{6}}{3}= \frac{\sqrt{3} × \sqrt{2}}{\sqrt{3} × \sqrt{3}} = \frac{\sqrt{2}}{\sqrt{3}  

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http://wordpress.org/extend/plugins/core-control/
http://wordpress.org/support/topic/an-unexpected-http-error-occurred-during-the-api-request-on-wordpress-3?replies=37

∴ $\frac{\sqrt{6}}{3}$ সংখ্যাটি অমূলদ

(ঙ) $\frac{\sqrt{8}}{\sqrt{7}}$

সমাধান : $\frac{\sqrt{8}}{\sqrt{7}} = \frac{\sqrt{2} × \sqrt{4}}{\sqrt{7}} = \frac{\sqrt{2} × 2}{\sqrt{7}} = \frac{2\sqrt{2}}{\sqrt{7}}$

∴ $\frac{\sqrt{8}}{\sqrt{7}}$ সংখ্যাটি অমূলদ

(চ) $\frac{\sqrt{27}}{\sqrt{48}}$

সমাধান : $\frac{\sqrt{27}}{\sqrt{48}} = \frac{\sqrt{3} × \sqrt{9}}{\sqrt{3} × \sqrt{16}} = \frac{\sqrt{9}}{\sqrt{16}} = \frac{3}{4}$

∴ $\frac{\sqrt{27}}{\sqrt{48}}$ সংখ্যাটি মূলদ

(ছ) $\frac{\frac23}{\frac37}$

সমাধান : $\frac{\frac23}{\frac37} = \frac23 ÷ \frac37 = \frac23 × \frac73 = \frac{14}9$

∴ $\frac{\frac23}{\frac37}$ সংখ্যাটি মূলদ

(জ) $5.\overset.63\overset.9$

সমাধান : $5.\overset.63\overset.9 = \frac{5639 - 5}{999} = \frac{5634}{999}$

∴ $5.\overset.63\overset.9$ সংখ্যাটি মূলদ

প্রশ্ন \ ১৩ \ সরল কর :

(ক) $\left(0.\overset.3\times0.8\overset.3\right)\div\left(0.5\times0.\overset.1\right) + 0.3\overset.5\div0.0\overset.8$

সমাধান : $\left(0.\overset.3\times0.8\overset.3\right)\div\left(0.5\times0.\overset.1\right)+0.3\overset.5\div0.0\overset.8\\\\=\left(\frac39\times\frac{83-8}{90}\right)\div\left(\frac5{10}\times\frac19\right)+\frac{35-3}{90}\div\frac{8-0}{90}\\\\=\left(\frac{\cancel3^1}{{\cancel9}_{{\cancel3}_1}}\times\frac{\cancel{75}^{25}}{90}\right)\div\frac5{90}+\frac{32}{90}\div\frac8{90}\\\\=\frac{25}{90}\div\frac5{90}+\frac{32}{90}\div\frac8{90}\\\\=\frac{\cancel{25}^5}{{\cancel{90}}_1}\times\frac{\cancel{90}^1}{{\cancel5}_1}+\frac{\cancel{32}^4}{{\cancel{90}}_1}\times\frac{\cancel{90}^1}{{\cancel8}_1}\\\\=5\;+\;4\\\\=9$