Najjednoduchší tvar

Vydeľte nasledujúce zlomky a zredukujte ich na najjednoduchší tvar, ak je to možné:

1. 2 3/4 ÷ 3 1/12
2. 3 2/3 ÷ 4 1/2
3. 5 3/7 ÷ 2 3/9
4. 6 2/3 ÷ 1 1/5

Správna odpoveď:

a =  33/37
b =  22/27
c =  2 ¹⁶⁄₄₉ = 114/49
d =  5 ⁵⁄₉ = 50/9

Postup správneho riešenia:

$$\begin{gathered} a_1=2\frac{3}{4}=2+\frac{3}{4}=\frac{2\cdot 4+3}{4}=\frac{8+3}{4}=\frac{11}{4}=2\frac{3}{4}=2,75 \\ {a}_2=3\frac{1}{12}=3+\frac{1}{12}=\frac{3\cdot 12+1}{12}=\frac{36+1}{12}=\frac{37}{12}=3\frac{1}{12}\doteq 3,0833 \\ a=a_1/a_2=\frac{11}{4}/\frac{37}{12}=\frac{11}{4}:\frac{37}{12}=\frac{11}{4}\cdot \frac{12}{37}=\frac{11\cdot 12}{4\cdot 37}=\frac{132}{148}=\frac{33}{37}=0,8919 \end{gathered}$$

$$\begin{gathered} b_1=3\frac{2}{3}=3+\frac{2}{3}=\frac{3\cdot 3+2}{3}=\frac{9+2}{3}=\frac{11}{3}=3\frac{2}{3}\doteq 3,6667 \\ {b}_2=4\frac{1}{2}=4+\frac{1}{2}=\frac{4\cdot 2+1}{2}=\frac{8+1}{2}=\frac{9}{2}=4\frac{1}{2}=4,5 \\ b=b_1/b_2=\frac{11}{3}/\frac{9}{2}=\frac{11}{3}:\frac{9}{2}=\frac{11}{3}\cdot \frac{2}{9}=\frac{11\cdot 2}{3\cdot 9}=\frac{22}{27}=0,8148 \end{gathered}$$

$$\begin{gathered} c_1=5\frac{3}{7}=5+\frac{3}{7}=\frac{5\cdot 7+3}{7}=\frac{35+3}{7}=\frac{38}{7}=5\frac{3}{7}\doteq 5,4286 \\ {c}_2=2\frac{3}{9}=2+\frac{3}{9}=\frac{2\cdot 9+3}{9}=\frac{18+3}{9}=\frac{21}{9}=\frac{7}{3}=2\frac{1}{3}\doteq 2,3333 \\ c=c_1/c_2=\frac{38}{7}/\frac{7}{3}=\frac{38}{7}:\frac{7}{3}=\frac{38}{7}\cdot \frac{3}{7}=\frac{38\cdot 3}{7\cdot 7}=\frac{114}{49}=2\frac{16}{49}=2,3265 \end{gathered}$$

$$\begin{gathered} d_1=6\frac{2}{3}=6+\frac{2}{3}=\frac{6\cdot 3+2}{3}=\frac{18+2}{3}=\frac{20}{3}=6\frac{2}{3}\doteq 6,6667 \\ {d}_2=1\frac{1}{5}=1+\frac{1}{5}=\frac{1\cdot 5+1}{5}=\frac{5+1}{5}=\frac{6}{5}=1\frac{1}{5}=1,2 \\ d=d_1/d_2=\frac{20}{3}/\frac{6}{5}=\frac{20}{3}:\frac{6}{5}=\frac{20}{3}\cdot \frac{5}{6}=\frac{20\cdot 5}{3\cdot 6}=\frac{100}{18}=\frac{50}{9}=5\frac{5}{9}=5,5556 \end{gathered}$$

Skúsiť iný príklad