Question

98 - resolva as expressões
99 - associe cada expressão ao seu valor

Answer 1

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⠀⠀☞ Resolvendo as expressões encontramos 98.a) 13/96; b) 204/161; 99.a) 5/√30; b) 23/10; c) 17/4; d) 32/15. ✅

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⠀⠀Lembrando que:

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• ⠀⠀Para uma soma ou subtração de frações os denominadores devem ser iguais;

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• ⠀⠀Para a divisão entre duas frações mantemos a primeira e multiplicamos pelo inverso da segunda;

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⠀Vamos resolver cada um dos itens:

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$\LARGE\blue{\text{ \sf~a)~~\dfrac{\dfrac{1}{\sqrt{64}} + \dfrac{1}{\sqrt{25}}}{1 + \dfrac{\sqrt{49}}{\sqrt{25}}} }}$

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$\LARGE\blue{\text{ \sf= \dfrac{\dfrac{1}{8} + \dfrac{1}{5}}{1 + \dfrac{7}{5}} }}$

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$\LARGE\blue{\text{ \sf= \dfrac{\dfrac{5}{40} + \dfrac{8}{40}}{\dfrac{5}{5} + \dfrac{7}{5}} }}$

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$\LARGE\blue{\text{ \sf= \dfrac{\dfrac{13}{40}}{\dfrac{12}{5}} }}$

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$\LARGE\blue{\sf= \dfrac{13}{40} \cdot \dfrac{5}{12}}$

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$\LARGE\blue{\sf= \dfrac{13}{8 \cdot 12}}$

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$\LARGE\blue{\sf= \dfrac{13}{96}}$ ✅

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$\LARGE\blue{\text{ \sf~b)~~\dfrac{\sqrt{\dfrac{9}{25}} + \sqrt{\dfrac{36}{49}}}{\sqrt{\dfrac{25}{16}} - \sqrt{\dfrac{1}{100}}} }}$

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$\LARGE\blue{\text{ \sf= \dfrac{\dfrac{3}{5} + \dfrac{6}{7}}{\dfrac{5}{4} - \dfrac{1}{10}} }}$

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$\LARGE\blue{\text{ \sf= \dfrac{\dfrac{21}{35} + \dfrac{30}{35}}{\dfrac{25}{20} - \dfrac{2}{20}} }}$

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$\LARGE\blue{\text{ \sf= \dfrac{\dfrac{51}{35}}{\dfrac{23}{20}} }}$

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$\LARGE\blue{\sf= \dfrac{51 \cdot 20}{35 \cdot 23}}$

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$\LARGE\blue{\sf= \dfrac{51}{7} \cdot \dfrac{4}{23}}$

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$\LARGE\blue{\sf= \dfrac{204}{161}}$ ✅

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$\LARGE\blue{\text{ \sf~a)~~\sqrt{\dfrac{3}{10} + \dfrac{8}{15}} }}$

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$\LARGE\blue{\text{ \sf= \sqrt{\dfrac{9}{30} + \dfrac{16}{30}} }}$

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$\LARGE\blue{\text{ \sf= \sqrt{\dfrac{25}{30}} }}$

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$\LARGE\blue{\text{ \sf= \dfrac{5}{\sqrt{30}} }}$ ✅

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$\LARGE\blue{\text{ \sf~b)~~\sqrt{\dfrac{36}{400}} + \sqrt{\dfrac{625}{900}} + \sqrt{\dfrac{441}{324}} }}$

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$\LARGE\blue{\sf= \dfrac{6}{20} + \dfrac{25}{30} + \dfrac{21}{18}}$

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$\LARGE\blue{\sf= \dfrac{3}{10} + \dfrac{5}{6} + \dfrac{7}{6}}$

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$\LARGE\blue{\sf= \dfrac{9}{30} + \dfrac{25}{30} + \dfrac{35}{30}}$

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$\LARGE\blue{\sf= \dfrac{69}{30}}$

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$\LARGE\blue{\sf= \dfrac{23}{10}}$ ✅

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$\LARGE\blue{\text{ \sf~c)~~\sqrt{\dfrac{729}{81}} \cdot \sqrt{\dfrac{289}{144}} }}$

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$\LARGE\blue{\sf= \dfrac{27}{9} \cdot \dfrac{17}{12} }$

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$\LARGE\blue{\sf= 3 \cdot \dfrac{17}{12} }$

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$\LARGE\blue{\sf= \dfrac{17}{4} }$ ✅

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$\LARGE\blue{\text{ \sf~d)~~\sqrt{\dfrac{256}{225}} \div \dfrac{1}{2} }}$

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$\LARGE\blue{\sf= \dfrac{16}{15} \cdot 2}$

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$\LARGE\blue{\sf= \dfrac{32}{15}}$✅

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

⠀⠀☀️ Leia mais sobre operações entre frações:

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✈ https://brainly.com.br/tarefa/38138588

✈ https://brainly.com.br/tarefa/38325011

$\bf\large\red{\underline{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

⠀⠀⠀⠀☕ $\Large\blue{\text{\bf Bons~estudos.}}$

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($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\gray{"Absque~sudore~et~labore~nullum~opus~perfectum~est."}$

Answer 2

Explicação passo-a-passo:

Boa tarde,

.

$98)a) \dfrac{ \dfrac{1}{ \sqrt{64} } + \dfrac{1}{ \sqrt{25} } }{1 + \dfrac{ \sqrt{49} }{ \sqrt{25} } }$

$\dfrac{ \dfrac{1}{8} + \dfrac{1}{5} } {1 + \dfrac{7}{5} }$

$\dfrac{ \dfrac{5 + 8}{40} }{ \dfrac{5 + 7}{5} }$

$\dfrac{ \dfrac{13}{40} }{ \dfrac{12}{5} }$

$\dfrac{13}{40} \times \dfrac{5}{12}$

$\dfrac{65}{480}$

$\dfrac{65 {}^{ \div 5} }{480 {}^{ \div 5} }$

$\dfrac{13}{96}$

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$b) \dfrac{ \sqrt{ \dfrac{9}{25} } + \sqrt{ \dfrac{36}{49} } }{ \sqrt{ \dfrac{25}{16} } - \sqrt{ \dfrac{1}{100} } }$

$\dfrac{ \dfrac{3}{5} + \dfrac{6}{7} }{ \dfrac{5}{4} - \dfrac{1}{10} }$

$\dfrac{ \dfrac{21 + 30}{35} }{ \dfrac{25 - 2}{20} }$

$\dfrac{ \dfrac{51}{35} }{ \dfrac{23}{20} }$

$\dfrac{51}{35} \times \dfrac{20}{23}$

$\dfrac{1020}{805}$

$\dfrac{1020 {}^{ \div 5} }{805 {}^{ \div 5} }$

$\dfrac{204}{161}$

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$99)a) \sqrt{ \dfrac{3}{10} \div \dfrac{8}{15} }$

$\sqrt{ \dfrac{3}{10} \times \dfrac{15}{8} }$

$\sqrt{ \dfrac{45}{80} }$

$\sqrt{ \dfrac{45 {}^{ \div 5} }{80 {}^{ \div 5} } }$

$\sqrt{ \dfrac{9}{16} }$

$\dfrac{3}{4}$

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$b) \sqrt{ \dfrac{36}{400} } + \sqrt{ \dfrac{625}{900} } + \sqrt{ \dfrac{441}{324} }$

$\sqrt{ \dfrac{36 {}^{ \div 4} }{400 {}^{ \div 4} } } + \sqrt{ \dfrac{625 {}^{ \div 25} }{900 {}^{ \div 25} } } + \sqrt{ \dfrac{441 {}^{ \div 9} }{324 {}^{ \div 9} } }$

$\sqrt{ \dfrac{9}{100} } + \sqrt{ \dfrac{25}{36} } + \sqrt{ \dfrac{49}{36} }$

$\dfrac{3}{10} + \dfrac{5}{6} + \dfrac{7}{6}$

$\dfrac{3}{10} + \dfrac{12}{6}$

$\dfrac{3}{10} + 2$

$\dfrac{3 + 20}{10}$

$\dfrac{23}{10}$

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$c) \sqrt{ \dfrac{729}{81} } \times \sqrt{ \dfrac{289}{144} }$

$\sqrt{9} \times \dfrac{17}{12}$

$3 \times \dfrac{17}{12}$

$\dfrac{51}{12}$

$\dfrac{51 {}^{ \div 3} }{12 {}^{ \div 3} }$

$\dfrac{17}{4}$

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$d) \sqrt{ \dfrac{256}{225} } \div \dfrac{1}{2}$

$\dfrac{16}{15} \times \dfrac{2}{1}$

$\dfrac{32}{15}$