Operace se zlomky

Vyhodnoťte operace se zlomky:
a=5/6 + 3/4
b = 2 1/2 + 3 2/3
c = 4/8 - 3/8
d = 5/10 - 3/10
e = 11-4/5
f= 6/9 - 3/5
g = 11 2/3 - 7 5/6
h = 3 x 2/7
i= 4/5 x 10/12
j = 1/2 X 9 X 6/12
k= 3 2/5 X 2 1/4
l= 2 2/6 X 5 1/7

Správná odpověď:

a =  1 ⁷⁄₁₂ = 19/12
b =  6 ¹⁄₆ = 37/6
c =  1/8
d =  1/5
e =  10 ¹⁄₅ = 51/5
f =  1/15
g =  3 ⁵⁄₆ = 23/6
h =  6/7
i =  2/3
j =  2 ¹⁄₄ = 9/4
k =  7 ¹³⁄₂₀ = 153/20
l =  12

Postup správného řešení:

$a=\frac{5}{6}+\frac{3}{4}=\frac{10}{12}+\frac{9}{12}=\frac{10+9}{12}=\frac{19}{12}=1\frac{7}{12}=1,5833$

$$\begin{gathered} b_1=2\frac{1}{2}=2+\frac{1}{2}=\frac{2\cdot 2+1}{2}=\frac{4+1}{2}=\frac{5}{2}=2\frac{1}{2}=2,5 \\ {b}_2=3\frac{2}{3}=3+\frac{2}{3}=\frac{3\cdot 3+2}{3}=\frac{9+2}{3}=\frac{11}{3}=3\frac{2}{3}\doteq 3,6667 \\ b=b_1+b_2=\frac{5}{2}+\frac{11}{3}=\frac{15}{6}+\frac{22}{6}=\frac{15+22}{6}=\frac{37}{6}=6\frac{1}{6}=6,1667 \end{gathered}$$

$c=\frac{4}{8}-\frac{3}{8}=\frac{4-3}{8}=\frac{1}{8}=0,125$

$d=\frac{5}{10}-\frac{3}{10}=\frac{5-3}{10}=\frac{2}{10}=\frac{1}{5}=0,2$

$e=11-\frac{4}{5}=\frac{11\cdot 5}{5}-\frac{4}{5}=\frac{55}{5}-\frac{4}{5}=\frac{55-4}{5}=\frac{51}{5}=10\frac{1}{5}=10,2$

$f=\frac{6}{9}-\frac{3}{5}=\frac{30}{45}-\frac{27}{45}=\frac{30-27}{45}=\frac{3}{45}=\frac{1}{15}=0,0667$

$$\begin{gathered} g_1=11\frac{2}{3}=11+\frac{2}{3}=\frac{11\cdot 3+2}{3}=\frac{33+2}{3}=\frac{35}{3}=11\frac{2}{3}\doteq 11,6667 \\ {g}_2=7\frac{5}{6}=7+\frac{5}{6}=\frac{7\cdot 6+5}{6}=\frac{42+5}{6}=\frac{47}{6}=7\frac{5}{6}\doteq 7,8333 \\ g=g_1-g_2=\frac{35}{3}-\frac{47}{6}=\frac{70}{6}-\frac{47}{6}=\frac{70-47}{6}=\frac{23}{6}=3\frac{5}{6}=3,8333 \end{gathered}$$

$h=3\cdot \frac{2}{7}=\frac{3\cdot 2}{7}=\frac{6}{7}=0,8571$

$i=\frac{4}{5}\cdot \frac{10}{12}=\frac{4\cdot 10}{5\cdot 12}=\frac{40}{60}=\frac{2}{3}=0,6667$

$j=\frac{1}{2}\cdot 9\cdot \frac{6}{12}=\frac{9}{4}=2\frac{1}{4}=2,25$

$$\begin{gathered} k_1=3\frac{2}{5}=3+\frac{2}{5}=\frac{3\cdot 5+2}{5}=\frac{15+2}{5}=\frac{17}{5}=3\frac{2}{5}=3,4 \\ {k}_2=2\frac{1}{4}=2+\frac{1}{4}=\frac{2\cdot 4+1}{4}=\frac{8+1}{4}=\frac{9}{4}=2\frac{1}{4}=2,25 \\ k=k_1\cdot k_2=\frac{17}{5}\cdot \frac{9}{4}=\frac{17\cdot 9}{5\cdot 4}=\frac{153}{20}=7\frac{13}{20}=7,65 \end{gathered}$$

$$\begin{gathered} l_1=2\frac{2}{6}=2+\frac{2}{6}=\frac{2\cdot 6+2}{6}=\frac{12+2}{6}=\frac{14}{6}=\frac{7}{3}=2\frac{1}{3}\doteq 2,3333 \\ {l}_2=5\frac{1}{7}=5+\frac{1}{7}=\frac{5\cdot 7+1}{7}=\frac{35+1}{7}=\frac{36}{7}=5\frac{1}{7}\doteq 5,1429 \\ l=l_1\cdot l_2=\frac{7}{3}\cdot \frac{36}{7}=\frac{7\cdot 36}{3\cdot 7}=\frac{252}{21}=12 \end{gathered}$$

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