zad. 4
Oblicz:
a) 3,375 + 4⅙ - 2⅔ =
b) 10⅔ - 4⅞ + ⅚ =
c) 5,25 - 2⅔ = 1⅚ =
d) 4,5 + 6¾ - (12 - 5⅜) =
zad. 9
Oblicz:
e) 3½ · (1⅗ = 2,75) =
f) 1⅔ : (5,5 · 2²/₁₁ - 3⅔) =
zad. 11
Oblicz:
3,75 · ⅘ - ⅘
_____________ =
1⁴/₁₁ : 3 : ¹/₁₂₁
z obliczeniami bedzie naj!
to zad. 11 to ta kreska to jest kreska ulamkowa
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zad 4.
a) 3,375 + 4⅙ - 2⅔ =![3\frac{1}{8}+4\frac{1}{6}-2\frac{2}{3} = \frac{25}{8}+\frac{25}{6}-\frac{8}{3} = \frac{75}{24}+\frac{100}{24}-\frac{64}{24} = \frac{111}{24} = 4\frac{15}{24} = 4\frac{5}{8} 3\frac{1}{8}+4\frac{1}{6}-2\frac{2}{3} = \frac{25}{8}+\frac{25}{6}-\frac{8}{3} = \frac{75}{24}+\frac{100}{24}-\frac{64}{24} = \frac{111}{24} = 4\frac{15}{24} = 4\frac{5}{8}](https://tex.z-dn.net/?f=3%5Cfrac%7B1%7D%7B8%7D%2B4%5Cfrac%7B1%7D%7B6%7D-2%5Cfrac%7B2%7D%7B3%7D+++%3D+%5Cfrac%7B25%7D%7B8%7D%2B%5Cfrac%7B25%7D%7B6%7D-%5Cfrac%7B8%7D%7B3%7D+%3D+++%5Cfrac%7B75%7D%7B24%7D%2B%5Cfrac%7B100%7D%7B24%7D-%5Cfrac%7B64%7D%7B24%7D+%3D+%5Cfrac%7B111%7D%7B24%7D+%3D+++4%5Cfrac%7B15%7D%7B24%7D+%3D+4%5Cfrac%7B5%7D%7B8%7D)
b) 10⅔ - 4⅞ + ⅚ =![10\frac{2}{3}-4\frac{7}{8}+\frac{5}{6} = \frac{32}{3}-\frac{39}{8}+\frac{5}{6} = \frac{256}{24}-\frac{117}{24}+\frac{20}{24} = \frac{159}{24} = 6\frac{15}{24} = 6\frac{5}{8} 10\frac{2}{3}-4\frac{7}{8}+\frac{5}{6} = \frac{32}{3}-\frac{39}{8}+\frac{5}{6} = \frac{256}{24}-\frac{117}{24}+\frac{20}{24} = \frac{159}{24} = 6\frac{15}{24} = 6\frac{5}{8}](https://tex.z-dn.net/?f=10%5Cfrac%7B2%7D%7B3%7D-4%5Cfrac%7B7%7D%7B8%7D%2B%5Cfrac%7B5%7D%7B6%7D+%3D+++%5Cfrac%7B32%7D%7B3%7D-%5Cfrac%7B39%7D%7B8%7D%2B%5Cfrac%7B5%7D%7B6%7D+%3D+++%5Cfrac%7B256%7D%7B24%7D-%5Cfrac%7B117%7D%7B24%7D%2B%5Cfrac%7B20%7D%7B24%7D+%3D+%5Cfrac%7B159%7D%7B24%7D+%3D+++6%5Cfrac%7B15%7D%7B24%7D+%3D+6%5Cfrac%7B5%7D%7B8%7D)
c) 5,25 - 2⅔ + 1⅚ =![5\frac{1}{4}-2\frac{2}{3}+1\frac{5}{6} = \frac{21}{4}-\frac{8}{3}+\frac{11}{6} = \frac{126}{24}-\frac{64}{24}+\frac{44}{24} = \frac{106}{24} = 4\frac{10}{24} = 4\frac{5}{8} 5\frac{1}{4}-2\frac{2}{3}+1\frac{5}{6} = \frac{21}{4}-\frac{8}{3}+\frac{11}{6} = \frac{126}{24}-\frac{64}{24}+\frac{44}{24} = \frac{106}{24} = 4\frac{10}{24} = 4\frac{5}{8}](https://tex.z-dn.net/?f=5%5Cfrac%7B1%7D%7B4%7D-2%5Cfrac%7B2%7D%7B3%7D%2B1%5Cfrac%7B5%7D%7B6%7D+%3D+++%5Cfrac%7B21%7D%7B4%7D-%5Cfrac%7B8%7D%7B3%7D%2B%5Cfrac%7B11%7D%7B6%7D+%3D+++%5Cfrac%7B126%7D%7B24%7D-%5Cfrac%7B64%7D%7B24%7D%2B%5Cfrac%7B44%7D%7B24%7D+%3D+%5Cfrac%7B106%7D%7B24%7D+%3D+++4%5Cfrac%7B10%7D%7B24%7D+%3D+4%5Cfrac%7B5%7D%7B8%7D)
d) 4,5 + 6¾ - (12 - 5⅜) =![4\frac{1}{2}+4\frac{3}{4}-(12-5\frac{3}{8}) = \frac{9}{2}+\frac{19}{4}-(\frac{96}{8}-\frac{43}{8}) = \frac{36}{8}+\frac{36}{8}-\frac{53}{8} = \frac{19}{8} = 2\frac{3}{8} 4\frac{1}{2}+4\frac{3}{4}-(12-5\frac{3}{8}) = \frac{9}{2}+\frac{19}{4}-(\frac{96}{8}-\frac{43}{8}) = \frac{36}{8}+\frac{36}{8}-\frac{53}{8} = \frac{19}{8} = 2\frac{3}{8}](https://tex.z-dn.net/?f=4%5Cfrac%7B1%7D%7B2%7D%2B4%5Cfrac%7B3%7D%7B4%7D-%2812-5%5Cfrac%7B3%7D%7B8%7D%29+++%3D+%5Cfrac%7B9%7D%7B2%7D%2B%5Cfrac%7B19%7D%7B4%7D-%28%5Cfrac%7B96%7D%7B8%7D-%5Cfrac%7B43%7D%7B8%7D%29+%3D+++%5Cfrac%7B36%7D%7B8%7D%2B%5Cfrac%7B36%7D%7B8%7D-%5Cfrac%7B53%7D%7B8%7D+%3D+%5Cfrac%7B19%7D%7B8%7D+%3D+2%5Cfrac%7B3%7D%7B8%7D)
zad. 9
Oblicz:
e) 3½ · (1⅗ + 2,75) =![\frac{7}{2}*(\frac{9}{6}+\frac{11}{4}) = \frac{63}{12}+\frac{77}{8} = \frac{126}{24}+\frac{231}{24} = \frac{357}{24} = 14\frac{21}{24} = 14\frac{7}{8} \frac{7}{2}*(\frac{9}{6}+\frac{11}{4}) = \frac{63}{12}+\frac{77}{8} = \frac{126}{24}+\frac{231}{24} = \frac{357}{24} = 14\frac{21}{24} = 14\frac{7}{8}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B2%7D%2A%28%5Cfrac%7B9%7D%7B6%7D%2B%5Cfrac%7B11%7D%7B4%7D%29+++%3D+%5Cfrac%7B63%7D%7B12%7D%2B%5Cfrac%7B77%7D%7B8%7D+%3D+%5Cfrac%7B126%7D%7B24%7D%2B%5Cfrac%7B231%7D%7B24%7D+%3D+++%5Cfrac%7B357%7D%7B24%7D+%3D+14%5Cfrac%7B21%7D%7B24%7D+%3D+14%5Cfrac%7B7%7D%7B8%7D)
f) 1⅔ : (5,5 · 2²/₁₁ - 3⅔) =![\frac{5}{3}:(\frac{11}{2}*\frac{24}{11}-\frac{11}{3}) = \frac{5}{3}:(\frac{24}{2}-\frac{11}{3}) = \frac{5}{3}:(\frac{72}{6}-\frac{22}{6}) = \frac{5}{3}:(\frac{50}{6}) = \frac{5}{3}*(\frac{6}{50}) = \frac{2}{10} \frac{5}{3}:(\frac{11}{2}*\frac{24}{11}-\frac{11}{3}) = \frac{5}{3}:(\frac{24}{2}-\frac{11}{3}) = \frac{5}{3}:(\frac{72}{6}-\frac{22}{6}) = \frac{5}{3}:(\frac{50}{6}) = \frac{5}{3}*(\frac{6}{50}) = \frac{2}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B3%7D%3A%28%5Cfrac%7B11%7D%7B2%7D%2A%5Cfrac%7B24%7D%7B11%7D-%5Cfrac%7B11%7D%7B3%7D%29+++%3D+%5Cfrac%7B5%7D%7B3%7D%3A%28%5Cfrac%7B24%7D%7B2%7D-%5Cfrac%7B11%7D%7B3%7D%29+%3D+++%5Cfrac%7B5%7D%7B3%7D%3A%28%5Cfrac%7B72%7D%7B6%7D-%5Cfrac%7B22%7D%7B6%7D%29+%3D+%5Cfrac%7B5%7D%7B3%7D%3A%28%5Cfrac%7B50%7D%7B6%7D%29+%3D+++%5Cfrac%7B5%7D%7B3%7D%2A%28%5Cfrac%7B6%7D%7B50%7D%29++%3D+%5Cfrac%7B2%7D%7B10%7D+)
zad. 11
Oblicz:
3,75 · ⅘ - ⅘
_____________ =
1⁴/₁₁ : 3 : ¹/₁₂₁
góra![\frac{15}{4}*\frac{1}{5}-\frac{1}{5} = \frac{5}{4}-\frac{1}{5} = \frac{25}{20}-\frac{4}{20} = \frac{21}{20} \frac{15}{4}*\frac{1}{5}-\frac{1}{5} = \frac{5}{4}-\frac{1}{5} = \frac{25}{20}-\frac{4}{20} = \frac{21}{20}](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B4%7D%2A%5Cfrac%7B1%7D%7B5%7D-%5Cfrac%7B1%7D%7B5%7D+%3D+%5Cfrac%7B5%7D%7B4%7D-%5Cfrac%7B1%7D%7B5%7D+%3D+%5Cfrac%7B25%7D%7B20%7D-%5Cfrac%7B4%7D%7B20%7D+%3D+%5Cfrac%7B21%7D%7B20%7D+)
dół![\frac{15}{11}*\frac{1}{3}*121 = \frac{5}{11}*121 = 55 \frac{15}{11}*\frac{1}{3}*121 = \frac{5}{11}*121 = 55](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B11%7D%2A%5Cfrac%7B1%7D%7B3%7D%2A121+%3D+%5Cfrac%7B5%7D%7B11%7D%2A121+%3D+55)
KOŃCÓWKA![\frac{21}{20}*\frac{1}{55} = \frac{21}{1100} \frac{21}{20}*\frac{1}{55} = \frac{21}{1100}](https://tex.z-dn.net/?f=%5Cfrac%7B21%7D%7B20%7D%2A%5Cfrac%7B1%7D%7B55%7D+%3D+%5Cfrac%7B21%7D%7B1100%7D)