Решебник по математике 5 класс Ерина Виленкин рабочая тетрадь Часть 1, 2 Часть 1 | Страница 59

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\[15.\ Упрощение\ выражений\]

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

\[\textbf{а)}\ a \cdot b = b \cdot a\]

\[\textbf{б)}\ (a \cdot b) \cdot c = a \cdot (b \cdot c)\]

\[\textbf{в)}\ a \cdot (b + c) = a \cdot b + a \cdot c\]

\[\textbf{г)}\ a \cdot (b - c) = a \cdot b - a \cdot c\]

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

\[\textbf{а)}\ 81 \cdot 5 = (80 + 1) \cdot 5 =\]

\[= 80 \cdot 5 + 1 \cdot 5 = 400 + 5 = 405\]

\[\textbf{б)}\ 408 \cdot 7 = (400 + 8) \cdot 7 =\]

\[= 400 \cdot 7 + 8 \cdot 7 = 2800 + 56 =\]

\[= 2856\]

\[\textbf{в)}\ 397 \cdot 4 = (400 - 3) \cdot 4 =\]

\[= 400 \cdot 4 - 3 \cdot 4 = 1600 - 12 =\]

\[= 1588\]

\[\textbf{г)}\ 298 \cdot 4 = (300 - 2) \cdot 4 =\]

\[= 300 \cdot 4 - 2 \cdot 4 = 1200 - 8 =\]

\[= 1192\]

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

\[\textbf{а)}\ 121 \cdot 5 = (120 + 1) \cdot 5 =\]

\[= 600 + 5 = 605\]

\[\textbf{б)}\ 34 \cdot 101 = (100 + 1) \cdot 34 =\]

\[= 3400 + 34 = 3434\]

\[\textbf{в)}\ 211 \cdot 5 = (200 + 11) \cdot 5 =\]

\[= 1000 + 55 = 1055\]

\[\textbf{г)}\ 79 \cdot 9 = (80 - 1) \cdot 9 =\]

\[= 720 - 9 = 711\]

\[\textbf{д)}\ 89 \cdot 6 = (90 - 1) \cdot 6 =\]

\[= 540 - 6 = 534\]

\[\textbf{е)}\ 312 \cdot 8 = (300 + 12) \cdot 8 =\]

\[= 2400 + 96 = 2496\]

\[\textbf{ж)}\ 59 \cdot 101 = 59 \cdot (100 + 1) =\]

\[= 5900 + 59 = 5959\]

\[\textbf{з)}\ 59 \cdot 99 = 59 \cdot (100 - 1) =\]

\[= 5900 - 59 = 5841\]