Question

Calcule .



a) 2/3 . 2/5

b) 4/5 . 2/7

c) 25/3 . 6/25

d) 11/12 . 4/5

e) 4/9 . 3/8

f) 5/7 . 14/25

Answer 1

Resposta:

Explicação passo-a-passo:

a) 2/3 . 2/5

$\frac{2}{3}\cdot \frac{2}{5}=\frac{2\cdot \:2}{3\cdot \:5}= \frac{4}{3\cdot \:5}=\frac{4}{15}$

b) 4/5 . 2/7

$\frac{4}{5}\cdot \frac{2}{7}=\frac{4\cdot \:2}{5\cdot \:7}=\frac{8}{5\cdot \:7}= \frac{8}{35}$

c) 25/3 . 6/25

$\frac{25}{3}\cdot \frac{6}{25}= \\\mathrm{Faca\:o\:cancelamento\:cruzado\:do\:fator\:comum:}\:25\\=\frac{6}\\{3}=2\\\ ou seja\\\frac{25}{3}\cdot \frac{6}{25}= \frac{6}{3}=2$

d) 11/12 . 4/5

$\frac{11}{12}\cdot \frac{4}{5}=\\\mathrm{Fatorar\:o\:numero:\:}\:12=4\cdot \:3\\=\frac{11}{4\cdot \:3}\cdot \frac{4}{5}\\\mathrm{Faca\:o\:cancelamento\:cruzado\:do\:fator\:comum:}\:4\\=\frac{11}{3}\cdot \frac{1}{5}\\\mathrm{Aplicar\:as\:propriedades\:das\:fracoes}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}\\\frac{11}{3}\cdot \frac{1}{5}=\frac{11\cdot \:1}{3\cdot \:5}\\\mathrm{Multiplicar\:os\:números:}\:11\cdot \:1=11\\=\frac{11}{3\cdot \:5}$

$\mathrm{Multiplicar\:os\:numeros:}\:3\cdot \:5=15\\=\frac{11}{15}\\\\Ou seja$$\frac{11}{12}\cdot \frac{4}{5}=\frac{11}{4\cdot \:3}\cdot \frac{4}{5}=\frac{11}{3}\cdot \frac{1}{5}=\frac{11\cdot \:1}{3\cdot \:5}=\frac{11}{3\cdot \:5}=\frac{11}{15}$

e) 4/9 . 3/8

$\frac{4}{9}\cdot \frac{3}{8}=\\\\\mathrm{Fatorar\:o\:numero:\:}\:8=4\cdot \:2\\=\frac{4}{9}\cdot \frac{3}{4\cdot \:2}\\\mathrm{Faca\:o\:cancelamento\:cruzado\:do\:fator\:comum:}\:4\\=\frac{1}{9}\cdot \frac{3}{2}\\\mathrm{Fatorar\:o\:numero:\:}\:9=3\cdot \:3\\=\frac{1}{3\cdot \:3}\cdot \frac{3}{2}\\\mathrm{Faca\:o\:cancelamento\:cruzado\:do\:fator\:comum:}\:3\\=\frac{1}{3}\cdot \frac{1}{2}$$\mathrm{Aplicar\:as\:propriedades\:das\:fracoes}:\quad \frac{a}{b}\cdot \frac{c}{d}=\frac{a\:\cdot \:c}{b\:\cdot \:d}\\\frac{1}{3}\cdot \frac{1}{2}=\frac{1\cdot \:1}{3\cdot \:2}\\\mathrm{Multiplicar\:os\:numeros:}\:1\cdot \:1=1\\=\frac{1}{3\cdot \:2}\\\\\mathrm{Multiplicar\:os\:numeros:}\:3\cdot \:2=6\\=\frac{1}{6}\\\\Ou seja$$\frac{4}{9}\cdot \frac{3}{8}=\frac{4}{9}\cdot \frac{3}{4\cdot \:2}=\frac{1}{9}\cdot \frac{3}{2}=\frac{1}{3\cdot \:3}\cdot \frac{3}{2}=\frac{1}{3}\cdot \frac{1}{2}=\frac{1\cdot \:1}{3\cdot \:2}=\frac{1}{3\cdot \:2}=\frac{1}{6}$

f) 5/7 . 14/25

$\frac{5}{7}\cdot \frac{14}{25}=\\\mathrm{Fatorar\:o\:numero:\:}\:14=7\cdot \:2\\\\=\frac{5}{7}\cdot \frac{7\cdot \:2}{25}\\\mathrm{Faca\:o\:cancelamento\:cruzado\:do\:fator\:comum:}\:7\\=\frac{5}{1}\cdot \frac{2}{25}\\\mathrm{Fatorar\:o\:numero:\:}\:25=5\cdot \:5\\=\frac{5}{1}\cdot \frac{2}{5\cdot \:5}\\\mathrm{Faca\:o\:cancelamento\:cruzado\:do\:fator\:comum:}\:5\\=\frac{2}{5}\\\\Ou seja$

$\frac{5}{7}\cdot \frac{14}{25}=\frac{5}{7}\cdot \frac{7\cdot \:2}{25}=\frac{5}{1}\cdot \frac{2}{25}=\frac{5}{1}\cdot \frac{2}{5\cdot \:5}=\frac{2}{5}$