Question

7) Efetue as multiplicaçoes e simplifique o resultado, quando possivel:

a) 2 . 5/9

b) 3 . 1/6

c) 4 . 2/7

d) 2 . 7/8

e) 2/3 . 7/9

f) 3/5 . 10/21

g) 6/7 . 7/18

h) 1/8 . 4/9

i) 33/10 . 5/22

8) Qual é a forma mais simples de se escrever cada uma das seguintes expressoes:

a) 1/6 + 3 . 4/9

b) 1 1/2 - 5/16 . 2/5

c) (5/8 5/6) . (1 - 1/7)

d) 1/2 . [1/2(1/2 + 1/4)] - 1/8

e) [6/5 . (2/3 - 1/4) - 1/8] . 4/9

f) (2 - 1/2) . (2 + 2/7) + 5 . (3/5 - 1/2)

PORFAVOR RESPONDEM TUDO :c

Answer 1

Explicação passo-a-passo:

7)

a)

$\sf 2\cdot\dfrac{5}{9}=\red{\dfrac{10}{9}}$

b)

$\sf 3\cdot\dfrac{1}{6}=\dfrac{3}{6}=\dfrac{3\div3}{6\div3}=\red{\dfrac{1}{2}}$

c)

$\sf 4\cdot\dfrac{2}{7}=\red{\dfrac{8}{7}}$

d)

$\sf 2\cdot\dfrac{7}{8}=\dfrac{14}{8}=\dfrac{14\div2}{8\div2}=\red{\dfrac{7}{4}}$

e)

$\sf \dfrac{2}{3}\cdot\dfrac{7}{9}=\red{\dfrac{14}{27}}$

f)

$\sf \dfrac{3}{5}\cdot\dfrac{10}{21}=\dfrac{30}{105}=\dfrac{30\div15}{105\div15}=\red{\dfrac{2}{7}}$

g)

$\sf \dfrac{6}{7}\cdot\dfrac{7}{18}=\dfrac{42}{126}=\dfrac{42\div42}{126\div42}=\red{\dfrac{1}{3}}$

h)

$\sf \dfrac{1}{8}\cdot\dfrac{4}{9}=\dfrac{4}{72}=\dfrac{4\div4}{72\div4}=\red{\dfrac{1}{18}}$

i)

$\sf \dfrac{33}{10}\cdot\dfrac{5}{22}=\dfrac{165}{220}=\dfrac{165\div55}{220\div55}=\red{\dfrac{3}{4}}$

8)

a)

$\sf \dfrac{1}{6}+3\cdot\dfrac{4}{9}$

$\sf =\dfrac{1}{6}+\dfrac{12}{9}$

$\sf =\dfrac{1}{6}+\dfrac{4}{3}$

$\sf =\dfrac{1+8}{6}$

$\sf =\dfrac{9}{6}$

$\sf =\red{\dfrac{3}{2}}$

b)

$\sf 1~\dfrac{1}{2}-\dfrac{5}{16}\cdot\dfrac{2}{5}$

$\sf =\dfrac{2+1}{2}-\dfrac{10}{80}$

$\sf =\dfrac{3}{2}-\dfrac{1}{8}$

$\sf =\dfrac{12-1}{8}$

$\sf =\red{\dfrac{11}{8}}$

c)

$\sf \left(\dfrac{5}{8}+\dfrac{5}{6}\right)\cdot\left(1-\dfrac{1}{7}\right)$

$\sf =\left(\dfrac{15+20}{24}\right)\cdot\left(\dfrac{7-1}{7}\right)$

$\sf =\dfrac{35}{24}\cdot\dfrac{6}{7}$

$\sf =\dfrac{210}{168}$

$\sf =\red{\dfrac{5}{4}}$

d)

$\sf \dfrac{1}{2}\cdot\left[\dfrac{1}{2}\cdot\left(\dfrac{1}{2}+\dfrac{1}{4}\right)\right]-\dfrac{1}{8}$

$\sf =\dfrac{1}{2}\cdot\left[\dfrac{1}{2}\cdot\left(\dfrac{2+1}{4}\right)\right]-\dfrac{1}{8}$

$\sf =\dfrac{1}{2}\cdot\left[\dfrac{1}{2}\cdot\dfrac{3}{4}\right]-\dfrac{1}{8}$

$\sf =\dfrac{1}{2}\cdot\dfrac{3}{8}-\dfrac{1}{8}$

$\sf =\dfrac{3}{16}-\dfrac{1}{8}$

$\sf =\dfrac{3-2}{16}$

$\sf =\red{\dfrac{1}{16}}$

e)

$\sf \left[\dfrac{6}{5}\cdot\left(\dfrac{2}{3}-\dfrac{1}{4}\right)-\dfrac{1}{8}\right]\cdot\dfrac{4}{9}$

$\sf =\left[\dfrac{6}{5}\cdot\left(\dfrac{8-3}{12}\right)-\dfrac{1}{8}\right]\cdot\dfrac{4}{9}$

$\sf =\left[\dfrac{6}{5}\cdot\dfrac{5}{12}-\dfrac{1}{8}\right]\cdot\dfrac{4}{9}$

$\sf =\left[\dfrac{30}{60}-\dfrac{1}{8}\right]\cdot\dfrac{4}{9}$

$\sf =\left[\dfrac{1}{2}-\dfrac{1}{8}\right]\cdot\dfrac{4}{9}$

$\sf =\left[\dfrac{4-1}{8}\right]\cdot\dfrac{4}{9}$

$\sf =\dfrac{3}{8}\cdot\dfrac{4}{9}$

$\sf =\dfrac{12}{72}$

$\sf =\red{\dfrac{1}{6}}$

f)

$\sf \left(2-\dfrac{1}{2}\right)\cdot\left(2+\dfrac{2}{7}\right)+5\cdot\left(\dfrac{3}{5}-\dfrac{1}{2}\right)$

$\sf =\left(\dfrac{4-1}{2}\right)\cdot\left(\dfrac{14+2}{7}\right)+5\cdot\left(\dfrac{6-5}{10}\right)$

$\sf =\dfrac{3}{2}\cdot\dfrac{16}{7}+5\cdot\dfrac{1}{10}$

$\sf =\dfrac{3}{2}\cdot\dfrac{16}{7}+\dfrac{5}{10}$

$\sf =\dfrac{3}{2}\cdot\dfrac{16}{7}+\dfrac{1}{2}$

$\sf =\dfrac{21-32+7}{14}$

$\sf =\dfrac{-4}{14}$

$\sf =\red{\dfrac{-2}{7}}$