Digital Matematika - 4 сынып - Екі таңбалы сандарға бағандап бөлу

Тапсырма

Сандарды бағанға бөлуді орындаңыз:

\(\displaystyle -\)	\(\displaystyle 4\)	\(\displaystyle 3\)	\(\displaystyle 0\)	\(\displaystyle 5\)	\(\displaystyle 35\)
\(\displaystyle -\)
	\(\displaystyle -\)
	\(\displaystyle -\)
	\(\displaystyle -\)
	\(\displaystyle -\)
				\(\displaystyle 0\)

Шешім

\(\displaystyle 1\)-ден \(\displaystyle 9{\small } \)-ға дейінгі сандар үшін \(\displaystyle 35\)-ке көбейту кестесін құрамыз:

\(\displaystyle 35\)-ке көбейту кестесі

Енді \(\displaystyle 4305\)-ті \(\displaystyle 35{\small } \)-ке бөлу процесін қарастырайық.
Алғашқы \(\displaystyle 4\)саны \(\displaystyle 35{\small}\)-тен кем болғандықтан, бірден алғашқы екі санды, яғни \(\displaystyle 43{\small }\)санын бірге аламыз.

1 қадам.

\(\displaystyle \color{orange}{43}\)-ті \(\displaystyle 35\)-ке қалдықпен бөлейік

1. \(\displaystyle 43\)-ті \(\displaystyle 35\)-ке қалдықпен бөлейік.

\(\displaystyle 43{\small}\)-тен максималды қанша \(\displaystyle \color{blue}{35}\)алуға болатынын табайық .

Яғни, \(\displaystyle 43\)-ті \(\displaystyle \color{blue}{35}\)-ке қалдықпен бөлгендегі толымсыз бөліндіні табамыз.

\(\displaystyle 43=\color{green}{1} \cdot \color{blue}{35}+8{\small }\) болғандықтан,

онда \(\displaystyle 35\)-ті \(\displaystyle \color{green}{1}\) рет алуға болады.

Сондықтан \(\displaystyle \color{green}{1}\)-ді бөліндіге жазамыз:

\(\displaystyle -\)	\(\displaystyle \small 4\)	\(\displaystyle \small 3\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)	\(\displaystyle \small 35\)
\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)			\(\displaystyle \small \color{green}{1}\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
				\(\displaystyle \small 0\)

2. Әрі қарай, бағанда \(\displaystyle 43\)-тен көбейтінді \(\displaystyle \color{blue}{35}\cdot \color{green}{1}=\color{green}{35}{\small }\) азайтамыз:

\(\displaystyle -\)	\(\displaystyle \small \color{orange}{4}\)	\(\displaystyle \small \color{orange}{3}\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)	\(\displaystyle \small 35\)
\(\displaystyle -\)	\(\displaystyle \small \color{green}{ 3}\)	\(\displaystyle \small \color{green}{ 5}\)			\(\displaystyle \small \color{green}{ 1}\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small 8\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
				\(\displaystyle \small 0\)

3. \(\displaystyle 43{\underline 0}5{\small }\) ондықтар разрядынан санды аламыз:

\(\displaystyle -\)	\(\displaystyle \small 4\)	\(\displaystyle \small 3\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)	\(\displaystyle \small 35\)
\(\displaystyle -\)	\(\displaystyle \small 3\)	\(\displaystyle \small 5\)			\(\displaystyle \small 1\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small 8\)	\(\displaystyle \small \bf 0\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
				\(\displaystyle \small 0\)

\(\displaystyle 80{\small }\) санын алдық.

2 қадам.

\(\displaystyle \color{cyan}{80}\)-ді на \(\displaystyle 35\)-ке қалдықпен бөлейік

1. \(\displaystyle 80\) -ді \(\displaystyle 35{\small }\)-ке бөлейік.

\(\displaystyle 80{\small }\)-нен максималды қанша \(\displaystyle \color{blue}{35}\) алуға болатынын табайық.

Яғни, \(\displaystyle 80\)-ді \(\displaystyle \color{blue}{35}{\small }\)-ке бөлгендегі толымсыз бөліндіні табамыз.

\(\displaystyle 80=\color{green}{2} \cdot \color{blue}{35} +10{\small }\) болғандықтан,

онда \(\displaystyle 35 \)-ті \(\displaystyle \color{green}{2}\) рет алуға болады.
Сондықтан \(\displaystyle \color{green}{2}\)-ні келесі санмен бөліндіге жазамыз:

\(\displaystyle -\)	\(\displaystyle \small 4\)	\(\displaystyle \small 3\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)	\(\displaystyle \small 35\)
\(\displaystyle -\)	\(\displaystyle \small 3\)	\(\displaystyle \small 5\)			\(\displaystyle \small 1\)	\(\displaystyle \small \color{green}{ 2}\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small 8\)	\(\displaystyle \small 0\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
				\(\displaystyle \small 0\)

2. Әрі қарай, бағанда \(\displaystyle 80\)-нен көбейтінді \(\displaystyle \color{blue}{35}\cdot \color{green}{2}=\color{green}{70}{\small }\) азайтамыз:

\(\displaystyle -\)	\(\displaystyle \small 4\)	\(\displaystyle \small 3\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)	\(\displaystyle \small 35\)
\(\displaystyle -\)	\(\displaystyle \small 3\)	\(\displaystyle \small 5\)			\(\displaystyle \small 1\)	\(\displaystyle \small \color{green}{ 2}\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small \color{cyan}{8}\)	\(\displaystyle \small \color{cyan}{0}\)
	\(\displaystyle -\)	\(\displaystyle \small \color{green}{ 7}\)	\(\displaystyle \small \color{green}{ 0}\)
	\(\displaystyle -\)	\(\displaystyle \small 1\)	\(\displaystyle \small 0\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
				\(\displaystyle \small 0\)

3. \(\displaystyle 430{\underline 5}{\small : }\) бірліктер разрядынан санды аламыз:

\(\displaystyle -\)	\(\displaystyle \small 4\)	\(\displaystyle \small 3\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)	\(\displaystyle \small 35\)
\(\displaystyle -\)	\(\displaystyle \small 3\)	\(\displaystyle \small 5\)			\(\displaystyle \small 1\)	\(\displaystyle \small 2\)	\(\displaystyle \small ?\)
	\(\displaystyle -\)	\(\displaystyle \small 8\)	\(\displaystyle \small 0\)
	\(\displaystyle -\)	\(\displaystyle \small 7\)	\(\displaystyle \small 0\)
	\(\displaystyle -\)	\(\displaystyle \small 1\)	\(\displaystyle \small 0\)	\(\displaystyle \small \bf 5\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
				\(\displaystyle \small 0\)

\(\displaystyle 105{\small }\) санын алдық.

3 қадам.

Делим \(\displaystyle \color{red}{105}\)-ті на \(\displaystyle 35\)-ке қалдықпен бөлейік

1.\(\displaystyle 105\)-ті \(\displaystyle 35{\small }\)-ке бөлейік.

\(\displaystyle 105{\small }\)-тен максималды қанша \(\displaystyle \color{blue}{35}\) алуға болатынын табайық.

Яғни, \(\displaystyle 105\)-ті \(\displaystyle \color{blue}{35}{\small }\)-ке бөлгендегі бөліндіні табамыз.

\(\displaystyle 105=\color{green}{3} \cdot \color{blue}{35}{\small }\) болғандықтан,

онда \(\displaystyle 35\)-ті \(\displaystyle \color{green}{3}\) рет алуға болады.

Сондықтан \(\displaystyle \color{green}{3}\)-ті келесі санмен бөліндіге жазамыз:

\(\displaystyle -\)	\(\displaystyle \small 4\)	\(\displaystyle \small 3\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)	\(\displaystyle \small 35\)
\(\displaystyle -\)	\(\displaystyle \small 3\)	\(\displaystyle \small 5\)			\(\displaystyle \small 1\)	\(\displaystyle \small 2\)	\(\displaystyle \small \color{green}{ 3}\)
	\(\displaystyle -\)	\(\displaystyle \small 8\)	\(\displaystyle \small 0\)
	\(\displaystyle -\)	\(\displaystyle \small 7\)	\(\displaystyle \small 0\)
	\(\displaystyle -\)	\(\displaystyle \small 1\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)
	\(\displaystyle -\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)	\(\displaystyle \small ?\)
				\(\displaystyle \small 0\)

2. Әрі қарай, бағанда \(\displaystyle 105\)-тен көбейтінді \(\displaystyle \color{blue}{35}\cdot \color{green}{3}=\color{green}{105}{\small :}\) азайтамыз :

\(\displaystyle -\)	\(\displaystyle \small 4\)	\(\displaystyle \small 3\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)	\(\displaystyle \small 35\)
\(\displaystyle -\)	\(\displaystyle \small 3\)	\(\displaystyle \small 5\)			\(\displaystyle \small 1\)	\(\displaystyle \small 2\)	\(\displaystyle \small \color{green}{ 3}\)
	\(\displaystyle -\)	\(\displaystyle \small 8\)	\(\displaystyle \small 0\)
	\(\displaystyle -\)	\(\displaystyle \small 7\)	\(\displaystyle \small 0\)
	\(\displaystyle -\)	\(\displaystyle \small \color{red}{ 1}\)	\(\displaystyle \small \color{red}{ 0}\)	\(\displaystyle \small \color{red}{ 5}\)
	\(\displaystyle -\)	\(\displaystyle \small \color{green}{ 1}\)	\(\displaystyle \small \color{green}{ 0}\)	\(\displaystyle \small \color{green}{ 5}\)
				\(\displaystyle \small 0\)

\(\displaystyle 0{\small }\) алдық, бөлу процесі аяқталды.

Осылайша,

\(\displaystyle -\)	\(\displaystyle \small \color{orange}{4}\)	\(\displaystyle \small \color{orange}{3}\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)	\(\displaystyle \small 35\)
\(\displaystyle -\)	\(\displaystyle \small 3\)	\(\displaystyle \small 5\)			\(\displaystyle \small 1\)	\(\displaystyle \small 2\)	\(\displaystyle \small 3\)
	\(\displaystyle -\)	\(\displaystyle \small \color{cyan}{8}\)	\(\displaystyle \small \color{cyan}{0}\)
	\(\displaystyle -\)	\(\displaystyle \small 7\)	\(\displaystyle \small 0\)
	\(\displaystyle -\)	\(\displaystyle \small \color{red}{ 1}\)	\(\displaystyle \small \color{red}{ 0}\)	\(\displaystyle \small \color{red}{ 5}\)
	\(\displaystyle -\)	\(\displaystyle \small 1\)	\(\displaystyle \small 0\)	\(\displaystyle \small 5\)
				\(\displaystyle \small 0\)

	\(\displaystyle 1\)	\(\displaystyle 2\)	\(\displaystyle 3\)	\(\displaystyle 4\)	\(\displaystyle 5\)	\(\displaystyle 6\)	\(\displaystyle 7\)	\(\displaystyle 8\)	\(\displaystyle 9\)
\(\displaystyle \color{blue}{35}\)	\(\displaystyle 35\)	\(\displaystyle 70\)	\(\displaystyle 105\)	\(\displaystyle 140\)	\(\displaystyle 175\)	\(\displaystyle 210\)	\(\displaystyle 245\)	\(\displaystyle 280\)	\(\displaystyle 315\)

Теориясы: Екі таңбалы сандарға бағандап бөлу