§ 2. Задание 78. «Алгебра. 7 класс. Учебник для общеобразовательных организаций» АЛГЕБРА 7 ГДЗ Задание 78

    Задание 78

    Разложите данные дроби в десятичные с помощью деления уголком:

      • $${\largeа)}\ \frac{7}{5},\ \frac{3}{16},\ \frac{48}{15};$$
      • $${\largeб)}\ \frac{3}{2000},\ \frac{17}{40},\ \frac{28}{140};$$
      • $${\largeв)}\ \frac{3}{12},\ \frac{7}{56},\ \frac{6}{24};$$
      • $${\largeг)}\ \frac{7}{4},\ \frac{3}{2},\ \frac{9}{5};$$
      • $${\largeд)}\ \frac{3}{25},\ \frac{12}{75},\ \frac{17}{200};$$
      • $${\largeе)}\ \frac{123}{20},\ \frac{783}{540},\ \frac{324}{25};$$
      • $${\largeж)}\ \frac{625}{125},\ \frac{860}{400},\ \frac{33}{60};$$
      • $${\largeз)}\ \frac{1024}{256},\ \frac{804}{400},\ \frac{624}{120}.$$

    Источник заимствования: Алгебра. 7 класс. Учебник для общеобразовательных организаций / – Просвещение, 2013. – 19 c. ISBN 978-5-09-027739-6
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    Решение:

      • $${\largeа)}\ \frac{7}{5}=1{,}4$$$$\phantom{\largeа)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}7\phantom{0}\\5\\\hline\end{array}\begin{array}{|l}5\\\hline1{,}4\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}20\\20\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeа)}\ \frac{3}{16}=0{,}1875$$$$\phantom{\largeа)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}3\phantom{0000}\\0\\\hline\end{array}\begin{array}{|l}16\\\hline0{,}1875\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}30\\16\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}140\\128\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}120\\112\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}-\begin{array}{r}80\\80\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeа)}\ \frac{48}{15}=3{,}2$$$$\phantom{\largeа)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}48\phantom{0}\\45\\\hline\end{array}\begin{array}{|l}15\\\hline3{,}2\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}30\\30\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}0\end{array}\end{array}$$

      • $${\largeб)}\ \frac{3}{2000}=0{,}0015$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}3\phantom{0000}\\0\\\hline\end{array}\begin{array}{|l}2000\\\hline0{,}0015\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}30\\0\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}300\\0\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}3000\\2000\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}10000\\10000\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeб)}\ \frac{17}{40}=0{,}425$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}17\phantom{000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}40\\\hline0{,}425\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}170\\160\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}100\\80\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}200\\200\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeб)}\ \frac{28}{140}=0{,}2$$$$\phantom{\largeб)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}28\phantom{0}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}140\\\hline0{,}2\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}280\\280\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}0\end{array}\end{array}$$

      • $${\largeв)}\ \frac{3}{12}=0{,}25$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}3\phantom{00}\\0\\\hline\end{array}\begin{array}{|l}12\\\hline0{,}25\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}30\\24\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}60\\60\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeв)}\ \frac{7}{56}=0{,}125$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}7\phantom{000}\\0\\\hline\end{array}\begin{array}{|l}56\\\hline0{,}125\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}70\\56\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}140\\112\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}280\\280\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeв)}\ \frac{6}{24}=0{,}25$$$$\phantom{\largeв)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}6\phantom{00}\\0\\\hline\end{array}\begin{array}{|l}24\\\hline0{,}25\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}60\\48\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}120\\120\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}0\end{array}\end{array}$$

      • $${\largeг)}\ \frac{7}{4}=1{,}75$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}7\phantom{00}\\4\\\hline\end{array}\begin{array}{|l}4\\\hline1{,}75\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}30\\28\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}20\\20\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeг)}\ \frac{3}{2}=1{,}5$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}3\phantom{0}\\2\\\hline\end{array}\begin{array}{|l}2\\\hline1{,}5\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}10\\10\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeг)}\ \frac{9}{5}=1{,}8$$$$\phantom{\largeг)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}9\phantom{0}\\5\\\hline\end{array}\begin{array}{|l}5\\\hline1{,}8\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}40\\40\\\hline\end{array}\end{array}\\\phantom{000}\begin{array}{r}0\end{array}\end{array}$$

      • $${\largeд)}\ \frac{3}{25}=0{,}12$$$$\phantom{\largeд)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}3\phantom{00}\\0\\\hline\end{array}\begin{array}{|l}25\\\hline0{,}12\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}30\\25\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}50\\50\\\hline\end{array}\end{array}\\\phantom{0000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeд)}\ \frac{12}{75}=0{,}16$$$$\phantom{\largeд)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}12\phantom{00}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}75\\\hline0{,}16\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}120\\75\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}450\\450\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeд)}\ \frac{17}{200}=0{,}085$$$$\phantom{\largeд)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}17\phantom{000}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}200\\\hline0{,}085\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}170\\0\\\hline\end{array}\end{array}\\\begin{array}{r}-\begin{array}{r}1700\\1600\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}1000\\1000\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$

      • $${\largeе)}\ \frac{123}{20}=6{,}15$$$$\phantom{\largeе)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}123\phantom{00}\\120\\\hline\end{array}\begin{array}{|l}20\\\hline6{,}15\end{array}\\\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}30\\20\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}100\\100\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeе)}\ \frac{783}{540}=1{,}45$$$$\phantom{\largeе)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}783\phantom{00}\\540\\\hline\end{array}\begin{array}{|l}540\\\hline1{,}45\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}2430\\2160\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}2700\\2700\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeе)}\ \frac{324}{25}=12{,}96$$$$\phantom{\largeе)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}324\phantom{00}\\25\\\hline\end{array}\begin{array}{|l}25\\\hline12{,}96\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}74\\50\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}240\\225\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}150\\150\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$

      • $${\largeж)}\ \frac{625}{125}=5$$$$\phantom{\largeж)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}625\\625\\\hline\end{array}\begin{array}{|l}125\\\hline5\end{array}\\\end{array}\\\phantom{0000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeж)}\ \frac{860}{400}=2{,}15$$$$\phantom{\largeж)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}860\phantom{00}\\800\\\hline\end{array}\begin{array}{|l}400\\\hline2{,}15\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}600\\400\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}2000\\2000\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeж)}\ \frac{33}{60}=0{,}55$$$$\phantom{\largeж)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}33\phantom{00}\\\phantom{0}0\\\hline\end{array}\begin{array}{|l}60\\\hline0{,}55\end{array}\\\end{array}\\\begin{array}{r}-\begin{array}{r}330\\300\\\hline\end{array}\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}300\\300\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}0\end{array}\end{array}$$

      • $${\largeз)}\ \frac{1024}{256}=4$$$$\phantom{\largeз)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}1024\\1024\\\hline\end{array}\begin{array}{|l}256\\\hline4\end{array}\\\end{array}\\\phantom{00000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeз)}\ \frac{804}{400}=2{,}01$$$$\phantom{\largeз)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}804\phantom{00}\\800\\\hline\end{array}\begin{array}{|l}400\\\hline2{,}01\end{array}\\\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}40\\0\\\hline\end{array}\end{array}\\\phantom{00}\begin{array}{r}-\begin{array}{r}400\\400\\\hline\end{array}\end{array}\\\phantom{000000}\begin{array}{r}0\end{array}\end{array}$$
      • $$\phantom{\largeз)}\ \frac{624}{120}=5{,}2$$$$\phantom{\largeз)}\ \begin{array}{l}\begin{array}{r}-\begin{array}{l}624\phantom{0}\\600\\\hline\end{array}\begin{array}{|l}120\\\hline5{,}2\end{array}\\\end{array}\\\phantom{0}\begin{array}{r}-\begin{array}{r}240\\240\\\hline\end{array}\end{array}\\\phantom{00000}\begin{array}{r}0\end{array}\end{array}$$