Question

5) Simplifique as frações até torná-las irredutíveis:
a) 12/16
b) 9/18
c) 15/20​

Answer 1

$\sf\: A = \frac{12}{16} \div 4 = \frac{3}{4}$

$\sf\:B = \frac{9}{18} \div 9 = \frac{1}{2}$

$\sf\:C = \frac{15}{20} \div 5 = \frac{3}{4}$

Answer 2

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$\tt{a)}\\\boxed{\begin{array}{c|l}\sf{12,16}&\boxed{\sf{2}}\\\sf{6,8}&\boxed{\sf{2}}\\\sf{3,4}&\sf{2}\\\sf{3,2}&\sf{2}\\\sf{3,1}&\sf{3}\\\sf{1,1}\end{array}}\\\sf{M.D.C(12,16)=2\cdot2=4}\\\sf{\dfrac{12\div4}{16\div4}=\boxed{\boxed{\sf{\dfrac{3}{4}}}}}$

$\tt{b)}\\\boxed{\begin{array}{c|l}\sf{9,18}&\sf{2}\\\sf{9,9}&\boxed{\sf{3}}\\\sf{3,3}&\boxed{\sf{3}}\\\sf{1,1}&\sf{}\end{array}}\\\sf{M.D.C(9,18)=3\cdot3=9}\\\sf{\dfrac{9\div9}{18\div9}=\boxed{\boxed{\sf \dfrac{1}{2}}}}\\\tt{c)}\\\boxed{\begin{array}{c|l}\sf{15,20}&\sf{2}\\\sf{15,10}&\sf{2}\\\sf{15,5}&\sf{3}\\\sf{5,5}&\boxed{\sf{5}}\\\sf{1,1}\end{array}}\\\sf{M.D.C(15,20)=5}\\\sf{\dfrac{15\div5}{20\div5}=\boxed{\boxed{\boxed{\sf{\dfrac{3}{4}}}}}}}$