Решебник по математике 6 класс Ерина Никольский рабочая тетрадь Часть 1, 2 Часть 1 | Страница 93

\[\mathbf{Страница\ 93.}\]

\[\boxed{\mathbf{1.}}\]

\[a + b = b + a:\]

\[переместительный\ закон\ \]

\[сложения\]

\[(a + b) + c = a + (b + c):\]

\[сочетательный\ закон\ \]

\[сложения\]

\[a \cdot b = b \cdot a:\]

\[переместительный\ закон\ \]

\[умножения\]

\[(a \cdot b) \cdot c = a \cdot (b \cdot c):\]

\[сочетательный\ закон\ \]

\[умножения\]

\[(a + b) \cdot c = a \cdot c + b \cdot c:\]

\[распределительный\ закон\]

\[\boxed{\mathbf{2.}}\]

\[\textbf{а)}\ 800 \cdot 476 \cdot ( - 125) =\]

\[= 476 \cdot ( - 100\ 000) =\]

\[= - 47\ 600\ 000\]

\[\textbf{б)}\ 967 + 858 - 67 =\]

\[= 900 + 858 = 1758\]

\[\textbf{в)}\ 36 \cdot ( - 73) + 64 \cdot ( - 73) =\]

\[= - 73 \cdot (36 + 64) =\]

\[= - 73 \cdot 100 = - 7300\]

\[\textbf{г)}\ 89 \cdot 38 - 39 \cdot 38 =\]

\[= 38 \cdot (89 - 39) =\]

\[= 38 \cdot 50 = 1900\]

\[\textbf{д)}\ 261 \cdot ( - 17) - 11 \cdot ( - 17) =\]

\[= - 17 \cdot (261 - 11) =\]

\[= - 17 \cdot 250 = - 4250\]

\[\textbf{е)}\ ( - 448) \cdot 75 + 48 \cdot 75 =\]

\[= 75 \cdot ( - 448 + 48) =\]

\[= 75 \cdot ( - 400) =\]

\[= - 30\ 000\]

\[\boxed{\mathbf{3.}}\]

\[\textbf{а)}\ \frac{17}{18} - \frac{31}{89} + \frac{1}{18} + \frac{58}{89} =\]

\[= \frac{18}{18} + \frac{27}{89} = 1 + \frac{27}{89} = 1\frac{27}{89}\]

\[\textbf{б)}\ \frac{64}{123} + \frac{74}{119} - \frac{64}{123} = \frac{74}{119}\]

\[\textbf{в)}\ \frac{29}{71} \cdot \frac{218}{305} + \frac{218}{305} \cdot \frac{42}{71} =\]

\[= \frac{218}{305} \cdot \left( \frac{29}{71} + \frac{42}{71} \right) =\]

\[= \frac{218}{305} \cdot \frac{71}{71} = \frac{218}{305}\]

\[\textbf{г)}\ \frac{48}{49} \cdot \frac{29}{51} - \frac{48}{49} \cdot \frac{22}{51} =\]

\[= \frac{48}{49} \cdot \left( \frac{29}{51} - \frac{22}{51} \right) =\]

\[= \frac{48}{49} \cdot \frac{7}{51} = \frac{16}{7 \cdot 17} = \frac{16}{119}\]

\[\boxed{\mathbf{4.}}\]

\[\textbf{а)}\ \frac{42 \cdot 57 + 57 \cdot 39}{66 \cdot 39 + 15 \cdot 39} =\]

\[= \frac{57 \cdot (42 + 39)}{39 \cdot (66 + 15)} =\]

\[= \frac{57 \cdot 81}{39 \cdot 81} = \frac{19}{13} = 1\frac{6}{13}\]

\[\textbf{б)}\ \frac{37 \cdot 88 + 40 \cdot 88}{21 \cdot 165 + 23 \cdot 165} =\]

\[= \frac{88 \cdot (37 + 40)}{165 \cdot (21 + 23)} =\]

\[= \frac{88 \cdot 77}{165 \cdot 44} = \frac{2 \cdot 7}{15} = \frac{14}{15}\]

\[\textbf{в)}\ \frac{42 \cdot 39 + 15 \cdot 39}{60 \cdot 13 + 168 \cdot 13} =\]

\[= \frac{39 \cdot (42 + 15)}{13 \cdot (60 + 168)} =\]

\[= \frac{39 \cdot 57}{13 \cdot 228} = \frac{3}{4}\]

\[\textbf{г)}\ \frac{597 \cdot 734 - 597 \cdot 34}{597 \cdot 861 - 597 \cdot 61} =\]

\[= \frac{597 \cdot (734 - 34)}{597 \cdot (861 - 61)} =\]

\[= \frac{597 \cdot 700}{597 \cdot 800} = \frac{7}{8}\]

\[\textbf{д)}\ \frac{38 \cdot 42 + 42 \cdot 25}{36 \cdot 159 - 36 \cdot 12} =\]

\[= \frac{42 \cdot (38 + 25)}{36 \cdot (159 - 12)} =\]

\[= \frac{42 \cdot 63}{36 \cdot 147} = \frac{7 \cdot 9}{6 \cdot 21} = \frac{1}{2}\]