Математика 5 класс Никольский, Потапов, Решетников

Учебник по математике 5 класс Никольский

авторы: , , .
издательство: Просвещение 2017 год

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Номер №766

Сократите дроби по образцу:
а)
$\frac{24}{36} = \frac{\overset{1}{\bcancel{2}} * 12}{\underset{1}{\bcancel{2}} * 18} = \frac{2 * \overset{1}{\bcancel{6}}}{3 * \underset{1}{\bcancel{6}}} = \frac{2}{3}$
, короче:
$\frac{\overset{2}{\bcancel{24}}}{\underset{3}{\bcancel{36}}} = \frac{2}{3}$
;
б)
$\frac{4}{8}, \frac{9}{36}, \frac{7}{28}, \frac{5}{35}$
;
в)
$\frac{2}{8}, \frac{8}{24}, \frac{12}{28}, \frac{45}{100}$
;
г)
$\frac{25}{35}, \frac{45}{54}, \frac{8}{400}, \frac{32}{256}$
;
д)
$\frac{12}{18}, \frac{18}{20}, \frac{20}{24}, \frac{24}{30}$
;
е)
$\frac{56}{49}, \frac{40}{32}, \frac{48}{36}, \frac{28}{21}$
;
ж)
$\frac{21}{56}, \frac{144}{120}, \frac{156}{128}, \frac{396}{240}$
.

Решение б

$\frac{4}{8} = \frac{\overset{1}{\bcancel{2}} * 2}{\underset{1}{\bcancel{2}} * 4} = \frac{1 * \overset{1}{\bcancel{2}}}{2 * \underset{1}{\bcancel{2}}} = \frac{1}{2}$
,
короче:
$\frac{\overset{1}{\bcancel{4}}}{\underset{2}{\bcancel{8}}} = \frac{1}{2}$
.
 
$\frac{9}{36} = \frac{\overset{1}{\bcancel{3}} * 3}{\underset{1}{\bcancel{3}} * 12} = \frac{1 * \overset{1}{\bcancel{3}}}{4 * \underset{1}{\bcancel{3}}} = \frac{1}{4}$
,
короче:
$\frac{\overset{1}{\bcancel{9}}}{\underset{4}{\bcancel{36}}} = \frac{1}{4}$
.
 
$\frac{7}{28} = \frac{\overset{1}{\bcancel{7}} * 1}{\underset{1}{\bcancel{7}} * 4} = \frac{1}{4}$
,
короче:
$\frac{\overset{1}{\bcancel{7}}}{\underset{4}{\bcancel{28}}} = \frac{1}{4}$
.
 
$\frac{5}{35} = \frac{\overset{1}{\bcancel{5}} * 1}{\underset{1}{\bcancel{5}} * 7} = \frac{1}{7}$
,
короче:
$\frac{\overset{1}{\bcancel{5}}}{\underset{7}{\bcancel{35}}} = \frac{1}{7}$
.

Решение в

$\frac{2}{8} = \frac{\overset{1}{\bcancel{2}} * 1}{\underset{1}{\bcancel{2}} * 4} = \frac{1}{4}$
,
короче:
$\frac{\overset{1}{\bcancel{2}}}{\underset{4}{\bcancel{8}}} = \frac{1}{4}$
.
 
$\frac{8}{24} = \frac{\overset{1}{\bcancel{2}} * 4}{\underset{1}{\bcancel{2}} * 12} = \frac{1 * \overset{1}{\bcancel{4}}}{3 * \underset{1}{\bcancel{4}}} = \frac{1}{3}$
,
короче:
$\frac{\overset{1}{\bcancel{8}}}{\underset{3}{\bcancel{24}}} = \frac{1}{3}$
.
 
$\frac{12}{28} = \frac{\overset{1}{\bcancel{2}} * 6}{\underset{1}{\bcancel{2}} * 14} = \frac{3 * \overset{1}{\bcancel{2}}}{7 * \underset{1}{\bcancel{2}}} = \frac{3}{7}$
,
короче:
$\frac{\overset{3}{\bcancel{12}}}{\underset{7}{\bcancel{28}}} = \frac{3}{7}$
.
 
$\frac{45}{100} = \frac{\overset{1}{\bcancel{5}} * 9}{\underset{1}{\bcancel{5}} * 20} = \frac{9}{2}$
,
короче:
$\frac{\overset{9}{\bcancel{45}}}{\underset{20}{\bcancel{100}}} = \frac{9}{20}$
.

Решение г

$\frac{25}{35} = \frac{\overset{1}{\bcancel{5}} * 5}{\underset{1}{\bcancel{5}} * 7} = \frac{5}{7}$
,
короче:
$\frac{\overset{5}{\bcancel{25}}}{\underset{7}{\bcancel{35}}} = \frac{5}{7}$
.
 
$\frac{45}{54} = \frac{\overset{1}{\bcancel{3}} * 15}{\underset{1}{\bcancel{3}} * 18} = \frac{5 * \overset{1}{\bcancel{3}}}{6 * \underset{1}{\bcancel{3}}} = \frac{5}{6}$
,
короче:
$\frac{\overset{5}{\bcancel{45}}}{\underset{6}{\bcancel{54}}} = \frac{5}{6}$

 
$\frac{8}{400} = \frac{\overset{1}{\bcancel{2}} * 4}{\underset{1}{\bcancel{2}} * 200} = \frac{1 * \overset{1}{\bcancel{4}}}{50 * \underset{1}{\bcancel{4}}} = \frac{1}{50}$
,
короче:
$\frac{\overset{1}{\bcancel{8}}}{\underset{50}{\bcancel{400}}} = \frac{1}{50}$
.
 
$\frac{32}{256} = \frac{\overset{1}{\bcancel{2}} * 16}{\underset{1}{\bcancel{2}} * 128} = \frac{1 * \overset{1}{\bcancel{16}}}{8 * \underset{1}{\bcancel{16}}} = \frac{1}{8}$
,
короче:
$\frac{\overset{1}{\bcancel{32}}}{\underset{8}{\bcancel{256}}} = \frac{1}{8}$
.

Решение д

$\frac{12}{18} = \frac{\overset{1}{\bcancel{2}} * 6}{\underset{1}{\bcancel{2}} * 9} = \frac{2 * \overset{1}{\bcancel{3}}}{3 * \underset{1}{\bcancel{3}}} = \frac{2}{3}$
,
короче:
$\frac{\overset{2}{\bcancel{12}}}{\underset{3}{\bcancel{18}}} = \frac{2}{3}$

 
$\frac{18}{20} = \frac{\overset{1}{\bcancel{2}} * 9}{\underset{1}{\bcancel{2}} * 10} = \frac{9}{10}$
,
короче:
$\frac{\overset{9}{\bcancel{18}}}{\underset{10}{\bcancel{20}}} = \frac{9}{10}$
.
 
$\frac{20}{24} = \frac{\overset{1}{\bcancel{2}} * 10}{\underset{1}{\bcancel{2}} * 12} = \frac{5 * \overset{1}{\bcancel{2}}}{6 * \underset{1}{\bcancel{2}}} = \frac{5}{6}$
,
короче:
$\frac{\overset{5}{\bcancel{20}}}{\underset{6}{\bcancel{24}}} = \frac{5}{6}$
.
 
$\frac{24}{30} = \frac{\overset{1}{\bcancel{2}} * 12}{\underset{1}{\bcancel{2}} * 15} = \frac{4 * \overset{1}{\bcancel{3}}}{5 * \underset{1}{\bcancel{3}}} = \frac{4}{5}$
,
короче:
$\frac{\overset{4}{\bcancel{24}}}{\underset{5}{\bcancel{30}}} = \frac{4}{5}$
.

Решение е

$\frac{56}{49} = \frac{\overset{1}{\bcancel{7}} * 8}{\underset{1}{\bcancel{7}} * 7} = \frac{8}{7}$
,
короче:
$\frac{\overset{8}{\bcancel{56}}}{\underset{7}{\bcancel{49}}} = \frac{8}{7}$
.
 
$\frac{40}{32} = \frac{\overset{1}{\bcancel{2}} * 20}{\underset{1}{\bcancel{2}} * 16} = \frac{5 * \overset{1}{\bcancel{4}}}{4 * \underset{1}{\bcancel{4}}} = \frac{5}{4}$
,
короче:
$\frac{\overset{5}{\bcancel{40}}}{\underset{4}{\bcancel{32}}} = \frac{5}{4}$
.
 
$\frac{48}{36} = \frac{\overset{1}{\bcancel{2}} * 24}{\underset{1}{\bcancel{2}} * 18} = \frac{4 * \overset{1}{\bcancel{6}}}{3 * \underset{1}{\bcancel{6}}} = \frac{4}{3}$
,
короче:
$\frac{\overset{4}{\bcancel{48}}}{\underset{3}{\bcancel{36}}} = \frac{4}{3}$
.
 
$\frac{28}{21} = \frac{\overset{1}{\bcancel{7}} * 4}{\underset{1}{\bcancel{7}} * 3} = \frac{4}{3}$
,
короче:
$\frac{\overset{1}{\bcancel{28}}}{\underset{3}{\bcancel{21}}} = \frac{4}{3}$
.

Решение ж

$\frac{21}{56} = \frac{\overset{1}{\bcancel{7}} * 3}{\underset{1}{\bcancel{7}} * 8} = \frac{3}{8}$
,
короче:
$\frac{\overset{3}{\bcancel{21}}}{\underset{8}{\bcancel{56}}} = \frac{3}{8}$
.
 
$\frac{144}{120} = \frac{\overset{1}{\bcancel{2}} * 72}{\underset{1}{\bcancel{2}} * 60} = \frac{6 * \overset{1}{\bcancel{12}}}{5 * \underset{5}{\bcancel{12}}} = \frac{6}{5}$
,
короче:
$\frac{\overset{6}{\bcancel{144}}}{\underset{5}{\bcancel{120}}} = \frac{6}{5}$

 
$\frac{156}{128} = \frac{\overset{1}{\bcancel{2}} * 78}{\underset{1}{\bcancel{2}} * 64} = \frac{39 * \overset{1}{\bcancel{2}}}{32 * \underset{1}{\bcancel{2}}} = \frac{39}{32}$
,
короче:
$\frac{\overset{39}{\bcancel{156}}}{\underset{32}{\bcancel{128}}} = \frac{156}{128}$
.
 
$\frac{396}{240} = \frac{\overset{1}{\bcancel{2}} * 198}{\underset{1}{\bcancel{2}} * 120} = \frac{33 * \overset{1}{\bcancel{6}}}{20 * \underset{1}{\bcancel{6}}} = \frac{33}{20}$
,
короче:
$\frac{\overset{33}{\bcancel{396}}}{\underset{20}{\bcancel{240}}} = \frac{33}{20}$
.
Посмотреть глоссарийДругие варианты решения