calcule
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Anexos:

Respostas

respondido por: Buckethead1

✅ A soma das frações correspondem respectivamente a

$\large\begin{array}{lr}\rm a)~ 1 \\\\\rm b)~ \dfrac{13}{12} \\\\\rm c)~ 1 \\\\\rm d)~ \dfrac{5}{3}\end{array}$

☁️ Para somar frações, primeiro devemos deixar os denominadores iguais e aí somarmos os numeradores.

$\Large \underline{\boxed{\boxed{ \rm\qquad \dfrac{a}{b} + \dfrac{c}{d} = \dfrac{a}{b} \cdot \dfrac{d}{d} + \dfrac{c}{d}\cdot \dfrac{b}{b} = \dfrac{ad + bc}{bd} \qquad}}}$

✍️ Solução:

❐ a)

$\large\begin{array}{lr}\begin{aligned}\rm \dfrac{5}{7} + \dfrac{2}{7} &=\rm \dfrac{5+2}{7} \\\\&=\rm \dfrac{7}{7} \end{aligned}\\\\\red{\underline{\boxed{\boxed{\rm \therefore\: \dfrac{5}{7} + \dfrac{2}{7} = 1 }}}}\end{array}$

❐ b)

$\large\begin{array}{lr}\begin{aligned}\rm \dfrac{7}{12} + \dfrac{3}{6} &=\rm \dfrac{7}{12} + \dfrac{3}{6} \cdot \dfrac{2}{2} \\\\&=\rm \dfrac{7}{12} + \dfrac{6}{12} \\\\&=\rm \dfrac{7+6}{12} \\\\&=\rm \dfrac{13}{12} \end{aligned}\\\\\red{\underline{\boxed{\boxed{\rm \therefore\: \dfrac{7}{12} + \dfrac{3}{6} = \dfrac{13}{12} }}}}\end{array}$

❐ c)

$\large\begin{array}{lr}\begin{aligned}\rm \dfrac{3}{5} + \dfrac{2}{6} &=\rm \dfrac{3}{5} \cdot \dfrac{6}{6} + \dfrac{3}{6} \cdot \dfrac{5}{5} \\\\&=\rm \dfrac{18}{30} + \dfrac{12}{30} \\\\&=\rm \dfrac{18+12}{30} \\\\&=\rm \dfrac{30}{30} \end{aligned}\\\\\red{\underline{\boxed{\boxed{\rm \therefore\: \dfrac{3}{5} + \dfrac{2}{6} = 1 }}}}\end{array}$

❐ d)

$\large\begin{array}{lr}\begin{aligned}\rm \dfrac{4}{6} + 1 &=\rm \dfrac{4}{6} + \dfrac{6}{6} \\\\&=\rm \dfrac{4 + 6}{6} \\\\&=\rm \dfrac{10^{\div 2} }{6^{\div 2} } \end{aligned}\\\\\red{\underline{\boxed{\boxed{\rm \therefore\: \dfrac{4}{6} + 1 = \dfrac{5}{3} }}}} \\\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\blacksquare\!\blacksquare\end{array}$