Задание № 832
Сложите дроби:
а) 1/2+1/3;
б) 1/2+1/5;
в) 1/3+1/4;
г) 1/4+1/5;
д) 1/2+1/4;
е) 1/3+1/6;
ж) 1/2+1/6;
з) 1/4+1/8.
Решение
а) $\frac12+\frac13=\frac{1\ast3+1\ast2}{2\ast3}=\frac{3+2}6=\frac56$
б) $\frac12+\frac15=\frac{1\ast5+1\ast2}{2\ast5}=\frac{5+2}{10}=\frac7{10}$
в) $\frac13+\frac14=\frac{1\ast4+1\ast3}{3\ast4}=\frac{4+3}{12}=\frac7{12}$
г) $\frac14+\frac15=\frac{1\ast5+1\ast4}{4\ast5}=\frac{5+4}{20}=\frac9{20}$
д) $\frac12+\frac14=\frac{1\ast2+1}{2\ast2}=\frac{2+1}4=\frac34$
е) $\frac13+\frac16=\frac{1\ast2+1}{2\ast3}=\frac{2+1}6=\frac36=\frac{1\ast3}{2\ast3}=\frac12$
ж) $\frac12+\frac16=\frac{1\ast3+1}{2\ast3}=\frac{3+1}6=\frac46=\frac{2\ast2}{3\ast2}=\frac23$
з) $\frac14+\frac18=\frac{1\ast2+1}{4\ast2}=\frac{2+1}8=\frac38$
Задание № 833
Вычислите:
а) $\frac1{10}+\frac7{100}=\frac{1\ast10}{10\ast10}+\frac7{100}=\frac{10+7}{100}=\frac{17}{100}$
б) $\frac{21}{100}+\frac1{10}=\frac{21}{100}+\frac{1\ast10}{10\ast10}=\frac{21+10}{100}=\frac{31}{100}$
в) $\frac35+\frac9{10}=\frac{3\ast2}{5\ast2}+\frac9{10}=\frac{6+9}{10}=\frac{15}{10}=\frac{3\ast5}{2\ast5}=\frac32$
г) $\frac23+\frac56=\frac{2\ast2}{3\ast2}+\frac56=\frac{4+5}6=\frac96=\frac{3\ast3}{2\ast3}=\frac32$
д) $\frac{15}{24}+\frac38=\frac{15}{24}+\frac{3\ast3}{8\ast3}=\frac{15+9}{24}=\frac{24}{24}=1$
е) $\frac76+\frac{16}{18}=\frac{7\ast3}{6\ast3}+\frac{16}{18}=\frac{7\ast3+16}{18}=\frac{21+16}{18}=\frac{37}{18}$
ж) $\frac1{12}+\frac16=\frac1{12}+\frac{1\ast2}{6\ast2}=\frac{1+2}{12}=\frac3{12}=\frac{1\ast3}{4\ast3}=\frac14$
з) $\frac12+\frac3{10}=\frac{1\ast5}{2\ast5}+\frac3{10}=\frac{5+3}{10}=\frac8{10}=\frac{4\ast2}{5\ast2}=\frac45$
Задание № 834
Вычислите:
а) $\frac3{36}+\frac79=\frac3{36}+\frac{7\ast4}{9\ast4}=\frac{3+28}{36}=\frac{31}{36}$
б) $\frac25+\frac3{20}=\frac{2\ast4}{5\ast4}+\frac3{20}=\frac{8+3}{20}=\frac{11}{20}$
в) $\frac16+\frac5{12}=\frac{1\ast2}{6\ast2}+\frac5{12}=\frac{2+5}{12}=\frac7{12}$
г) $\frac{11}{49}+\frac67=\frac{11}{49}+\frac{6\ast7}{7\ast7}=\frac{11+42}{49}=\frac{53}{49}$
д) $\frac{13}{24}+\frac58=\frac{13}{24}+\frac{5\ast3}{8\ast3}=\frac{13+15}{24}=\frac{28}{24}$
е) $\frac38+\frac6{32}=\frac{3\ast4}{8\ast4}+\frac6{32}=\frac{12+6}{32}=\frac{18}{32}$
ж) $\frac6{120}+\frac3{20}=\frac6{120}+\frac{3\ast6}{20\ast6}=\frac{6+18}{120}=\frac{24}{120}=\frac{1\ast24}{5\ast24}=\frac15$
з) $\frac9{16}+\frac{50}{100}=\frac9{16}+\frac{1\ast50}{2\ast50}=\frac9{16}+\frac12=\frac9{16}+\frac{1\ast8}{2\ast8}=\frac{9+8}{16}=\frac{17}{16}$
Задание № 835
Вычислите:
а) $\frac16+\frac19=\frac{1\ast3}{6\ast3}+\frac{1\ast2}{9\ast2}=\frac{3+2}{18}=\frac5{18}$
б) $\frac29+\frac56=\frac{2\ast2}{9\ast2}+\frac{5\ast3}{6\ast3}=\frac{4+15}{18}=\frac{19}{18}$
в) $\frac29+\frac38=\frac{2\ast8}{9\ast8}+\frac{3\ast9}{8\ast9}=\frac{16+27}{72}=\frac{43}{72}$
г) $\frac2{10}+\frac6{15}=\frac{2\ast3}{10\ast3}+\frac{6\ast2}{15\ast2}=\frac{6+12}{30}=\frac{18}{30}$
д) $\frac3{10}+\frac2{12}=\frac{3\ast6}{10\ast6}+\frac{2\ast5}{12\ast5}=\frac{18+10}{60}=\frac{28}{60}=\frac{7\ast4}{15\ast4}=\frac7{15}$
е) $\frac5{12}+\frac4{15}=\frac{5\ast5}{12\ast5}+\frac{4\ast4}{15\ast4}=\frac{25+16}{60}=\frac{41}{60}$
ж) $\frac34+\frac5{18}=\frac{3\ast9}{4\ast9}+\frac{5\ast2}{18\ast2}=\frac{27+10}{36}=\frac{37}{36}$
з) $\frac2{26}+\frac3{39}=\frac{1\ast2}{13\ast2}+\frac{1\ast3}{13\ast3}=\frac{1+1}{13}=\frac2{13}$
и) $\frac7{34}+\frac5{51}=\frac{7\ast6}{34\ast6}+\frac{5\ast4}{51\ast4}=\frac{42+20}{204}=\frac{31\ast2}{102\ast2}=\frac{31}{102}$
к) $\frac4{210}+\frac5{140}=\frac{4\ast2}{210\ast2}+\frac{5\ast3}{140\ast3}=\frac{8+15}{420}=\frac{23}{420}$
л) $\frac7{450}+\frac8{180}=\frac{7\ast2}{450\ast2}+\frac{8\ast5}{180\ast5}=\frac{14+40}{900}=\frac{54}{900}=\frac{3\ast18}{50\ast18}=\frac3{50}$
м) $\frac9{180}+\frac7{120}=\frac{9\ast2}{180\ast2}+\frac{7\ast3}{120\ast3}=\frac{18+21}{360}=\frac{39}{360}=\frac{13\ast3}{120\ast3}=\frac{13}{120}$
Задание № 836
Вычислите:
а) $\frac14+\frac47+\frac9{28}=\frac{1\ast7}{4\ast7}+\frac{4\ast4}{7\ast4}+\frac9{28}=\frac{7+16+9}{28}=\frac{32}{28}=\frac{8\ast4}{7\ast4}=\frac87$
б) $\frac15+\frac3{10}+\frac7{20}=\frac{1\ast4}{5\ast4}+\frac{3\ast2}{10\ast2}+\frac7{20}=\frac{4+6+7}{20}=\frac{17}{20}$
в) $\frac3{20}+\frac7{30}+\frac2{40}=\frac{3\ast6}{20\ast6}+\frac{7\ast4}{30\ast4}+\frac{2\ast3}{40\ast3}=\frac{18+28+6}{120}=\frac{52}{120}=\frac{13\ast4}{30\ast4}=\frac{13}{30}$
г) $\frac{17}{20}+\frac{23}{30}+\frac{11}{60}=\frac{17\ast3}{20\ast3}+\frac{23\ast2}{30\ast2}+\frac{11}{60}=\frac{51+46+11}{60}=\frac{108}{60}=\frac{12\ast9}{12\ast5}=\frac95$
д) $\frac3{20}+\frac7{30}+\frac9{50}=\frac{3\ast15}{20\ast15}+\frac{7\ast10}{3\ast10}+\frac{9\ast6}{50\ast6}=\frac{45+70+54}{300}=\frac{169}{300}$
е) $\frac7{40}+\frac{11}{70}+\frac{13}{30}=\frac{7\ast21}{40\ast21}+\frac{11\ast12}{70\ast12}+\frac{13\ast28}{30\ast28}=\frac{147+132+364}{840}=\frac{643}{840}$
Задание № 837
Запишите дробь в виде суммы двух дробей:
а) 3/5;
б) 7/9;
в) 5/7;
г) 3/10.
Решение
а) $\frac35=\frac15+\frac25$
б) $\frac79=\frac19+\frac89$
$\frac79=\frac29+\frac59$
$\frac79=\frac39+\frac49$
в) $\frac57=\frac17+\frac47$
$\frac57=\frac27+\frac37$
г) $\frac3{10}=\frac1{10}+\frac2{10}$
Задание № 838
Подберите дробь, которая в сумме с данной дробью дает 1.
а) 1/3;
б) 2/7;
в) 5/9;
г) 8/13;
д) 5/41;
е) 13/27.
Решение
а) $\frac13+\frac23=\frac33=1$
б) $\frac27+\frac57=\frac77=1$
в) $\frac59+\frac49=\frac99=1$
г) $\frac8{13}+\frac5{13}=\frac{13}{13}=1$
д) $\frac5{41}+\frac{36}{41}=\frac{41}{41}=1$
е) $\frac{13}{27}+\frac{14}{27}=\frac{27}{27}=1$
Задание № 839
Сложите дроби, предварительно сократив их:
а) $\frac6{15}+\frac5{25}=\frac{3\ast2}{5\ast3}+\frac{5\ast1}{5\ast5}=\frac25+\frac15=\frac35$
б) $\frac{10}{16}+\frac3{24}=\frac{5\ast2}{8\ast2}+\frac{3\ast1}{3\ast8}=\frac58+\frac18=\frac68=\frac{3\ast2}{4\ast2}=\frac34$
в) $\frac{30}{45}+\frac8{36}=\frac{6\ast5}{9\ast5}+\frac{2\ast4}{9\ast4}=\frac69+\frac29=\frac89$
г) $\frac{60}{120}+\frac{75}{150}=\frac{1\ast60}{2\ast60}+\frac{1\ast75}{2\ast75}=\frac12+\frac12=\frac22=1$
д) $\frac{24}{360}+\frac{16}{480}=\frac{12\ast2}{12\ast30}+\frac{16\ast1}{16\ast30}=\frac2{30}+\frac1{30}=\frac3{30}=\frac1{10}$
