Задание 6. Действия с обыкновенными и десятичными дробями

{"questions":[{"content":"$$\\dfrac{1}{10} + \\dfrac{29}{20}$$[[fill_choice_big-1]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$1,55$","$2,55$","$1,2$","$0,5$"],"placeholder":0,"answer":0}},"step":1,"hints":["Чтобы сложить дроби, необходимо привести их к общему знаменателю. Наименьший общий знаменатель для чисел $10$ и $20$ равен $20.$","Преобразуем первую дробь:<br />$$\\dfrac{1}{10} = \\dfrac{1 \\cdot 2}{10 \\cdot 2} = \\dfrac{2}{20}$$","Теперь сложим дроби с одинаковыми знаменателями:<br />$$\\dfrac{2}{20} + \\dfrac{29}{20} = \\dfrac{2 + 29}{20} = \\dfrac{31}{20}$$","Дробь $\\frac{31}{20}$ можно представить в виде десятичной дроби. Для этого умножим числитель и знаменатель на $5{:}$<br />$$\\dfrac{31}{20} = \\dfrac{31 \\cdot 5}{20 \\cdot 5} = \\dfrac{155}{100} = 1.55$$"]}]}

{"questions":[{"content":"$$\\dfrac{3}{8}+\\dfrac{1}{4}$$[[fill_choice_big-1]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$0,63$","$0,50$","$0,75$","$0,58$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю: $$\\dfrac{1}{4}=\\dfrac{2}{8}$$","Сложите дроби: $$\\dfrac{3}{8}+\\dfrac{2}{8}=\\dfrac{5}{8}$$","Переведите в десятичную дробь: $$\\dfrac{5}{8}=0{,}625\\approx 0{,}63$$"]},{"content":"$$\\dfrac{7}{10}-\\dfrac{1}{5}$$[[fill_choice_big-2]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$0,50$","$0,40$","$0,60$","$0,30$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю: $$\\dfrac{1}{5}=\\dfrac{2}{10}$$","Вычтите дроби: $$\\dfrac{7}{10}-\\dfrac{2}{10}=\\dfrac{5}{10}=\\dfrac{1}{2}$$","Переведите в десятичную дробь: $$\\dfrac{1}{2}=0{,}50$$"]},{"content":"$$\\dfrac{5}{16}+\\dfrac{3}{8}$$[[fill_choice_big-3]]","widgets":{"fill_choice_big-3":{"type":"fill_choice_big","options":["$0,69$","$0,63$","$0,56$","$0,75$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $16$: $$\\dfrac{3}{8}=\\dfrac{6}{16}$$","Сложите дроби: $$\\dfrac{5}{16}+\\dfrac{6}{16}=\\dfrac{11}{16}$$","Переведите в десятичную дробь: $$\\dfrac{11}{16}=0{,}6875\\approx 0{,}69$$"]},{"content":"$$\\dfrac{9}{20}+\\dfrac{1}{4}$$[[fill_choice_big-4]]","widgets":{"fill_choice_big-4":{"type":"fill_choice_big","options":["$0,70$","$0,65$","$0,75$","$0,60$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $20$: $$\\dfrac{1}{4}=\\dfrac{5}{20}$$","Сложите дроби: $$\\dfrac{9}{20}+\\dfrac{5}{20}=\\dfrac{14}{20}=\\dfrac{7}{10}$$","Переведите в десятичную дробь: $$\\dfrac{7}{10}=0{,}70$$"]},{"content":"$$\\dfrac{13}{25}-\\dfrac{3}{10}$$[[fill_choice_big-5]]","widgets":{"fill_choice_big-5":{"type":"fill_choice_big","options":["$0,22$","$0,18$","$0,20$","$0,24$"],"placeholder":0,"answer":0}},"step":1,"hints":["Найдите общий знаменатель: $\\text{НОК}(25,10)=50$.","Приведите к знаменателю $50$: $$\\dfrac{13}{25}=\\dfrac{26}{50},\\quad \\dfrac{3}{10}=\\dfrac{15}{50}$$","Вычтите: $$\\dfrac{26}{50}-\\dfrac{15}{50}=\\dfrac{11}{50}$$","Переведите в десятичную дробь: $$\\dfrac{11}{50}=0{,}22$$"]},{"content":"$$\\dfrac{7}{8}-\\dfrac{1}{16}$$[[fill_choice_big-6]]","widgets":{"fill_choice_big-6":{"type":"fill_choice_big","options":["$0,81$","$0,75$","$0,88$","$0,85$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к знаменателю $16$: $$\\dfrac{7}{8}=\\dfrac{14}{16}$$","Вычтите: $$\\dfrac{14}{16}-\\dfrac{1}{16}=\\dfrac{13}{16}$$","Переведите в десятичную дробь: $$\\dfrac{13}{16}=0{,}8125\\approx 0{,}81$$"]},{"content":"$$\\dfrac{3}{5}+\\dfrac{7}{20}$$[[fill_choice_big-7]]","widgets":{"fill_choice_big-7":{"type":"fill_choice_big","options":["$0,95$","$0,85$","$0,90$","$1,05$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $20$: $$\\dfrac{3}{5}=\\dfrac{12}{20}$$","Сложите: $$\\dfrac{12}{20}+\\dfrac{7}{20}=\\dfrac{19}{20}$$","Переведите в десятичную дробь: $$\\dfrac{19}{20}=0{,}95$$"]},{"content":"$$\\dfrac{11}{40}+\\dfrac{1}{8}$$[[fill_choice_big-8]]","widgets":{"fill_choice_big-8":{"type":"fill_choice_big","options":["$0,40$","$0,38$","$0,42$","$0,35$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $40$: $$\\dfrac{1}{8}=\\dfrac{5}{40}$$","Сложите: $$\\dfrac{11}{40}+\\dfrac{5}{40}=\\dfrac{16}{40}=\\dfrac{2}{5}$$","Переведите в десятичную дробь: $$\\dfrac{2}{5}=0{,}40$$"]},{"content":"$$\\dfrac{9}{25}-\\dfrac{1}{5}$$[[fill_choice_big-9]]","widgets":{"fill_choice_big-9":{"type":"fill_choice_big","options":["$0,16$","$0,18$","$0,20$","$0,12$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $25$: $$\\dfrac{1}{5}=\\dfrac{5}{25}$$","Вычтите: $$\\dfrac{9}{25}-\\dfrac{5}{25}=\\dfrac{4}{25}$$","Переведите в десятичную дробь: $$\\dfrac{4}{25}=0{,}16$$"]},{"content":"$$\\dfrac{5}{12}+\\dfrac{1}{6}$$[[fill_choice_big-10]]","widgets":{"fill_choice_big-10":{"type":"fill_choice_big","options":["$0,58$","$0,57$","$0,60$","$0,55$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $12$: $$\\dfrac{1}{6}=\\dfrac{2}{12}$$","Сложите: $$\\dfrac{5}{12}+\\dfrac{2}{12}=\\dfrac{7}{12}$$","Переведите в десятичную дробь: $$\\dfrac{7}{12}=0{,}5833\\ldots\\approx 0{,}58$$"]},{"content":"$$\\dfrac{7}{16}+\\dfrac{5}{32}$$[[fill_choice_big-11]]","widgets":{"fill_choice_big-11":{"type":"fill_choice_big","options":["$0,59$","$0,57$","$0,62$","$0,55$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $32$: $$\\dfrac{7}{16}=\\dfrac{14}{32}$$","Сложите: $$\\dfrac{14}{32}+\\dfrac{5}{32}=\\dfrac{19}{32}$$","Переведите в десятичную дробь: $$\\dfrac{19}{32}=0{,}59375\\approx 0{,}59$$"]},{"content":"$$\\dfrac{3}{4}-\\dfrac{7}{20}$$[[fill_choice_big-12]]","widgets":{"fill_choice_big-12":{"type":"fill_choice_big","options":["$0,40$","$0,35$","$0,45$","$0,50$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $20$: $$\\dfrac{3}{4}=\\dfrac{15}{20}$$","Вычтите: $$\\dfrac{15}{20}-\\dfrac{7}{20}=\\dfrac{8}{20}=\\dfrac{2}{5}$$","Переведите в десятичную дробь: $$\\dfrac{2}{5}=0{,}40$$"]},{"content":"$$\\dfrac{11}{25}+\\dfrac{3}{10}$$[[fill_choice_big-13]]","widgets":{"fill_choice_big-13":{"type":"fill_choice_big","options":["$0,74$","$0,70$","$0,78$","$0,72$"],"placeholder":0,"answer":0}},"step":1,"hints":["Найдите общий знаменатель: $\\text{НОК}(25,10)=50$.","Приведите к знаменателю $50$: $$\\dfrac{11}{25}=\\dfrac{22}{50},\\quad \\dfrac{3}{10}=\\dfrac{15}{50}$$","Сложите: $$\\dfrac{22}{50}+\\dfrac{15}{50}=\\dfrac{37}{50}$$","Переведите в десятичную дробь: $$\\dfrac{37}{50}=0{,}74$$"]},{"content":"$$\\dfrac{9}{50}+\\dfrac{1}{5}$$[[fill_choice_big-14]]","widgets":{"fill_choice_big-14":{"type":"fill_choice_big","options":["$0,38$","$0,36$","$0,40$","$0,34$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $50$: $$\\dfrac{1}{5}=\\dfrac{10}{50}$$","Сложите: $$\\dfrac{9}{50}+\\dfrac{10}{50}=\\dfrac{19}{50}$$","Переведите в десятичную дробь: $$\\dfrac{19}{50}=0{,}38$$"]},{"content":"$$\\dfrac{13}{40}-\\dfrac{1}{8}$$[[fill_choice_big-15]]","widgets":{"fill_choice_big-15":{"type":"fill_choice_big","options":["$0,20$","$0,18$","$0,25$","$0,22$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $40$: $$\\dfrac{1}{8}=\\dfrac{5}{40}$$","Вычтите: $$\\dfrac{13}{40}-\\dfrac{5}{40}=\\dfrac{8}{40}=\\dfrac{1}{5}$$","Переведите в десятичную дробь: $$\\dfrac{1}{5}=0{,}20$$"]},{"content":"$$\\dfrac{7}{25}+\\dfrac{3}{20}$$[[fill_choice_big-16]]","widgets":{"fill_choice_big-16":{"type":"fill_choice_big","options":["$0,43$","$0,41$","$0,45$","$0,39$"],"placeholder":0,"answer":0}},"step":1,"hints":["Найдите общий знаменатель: $\\text{НОК}(25,20)=100$.","Приведите к знаменателю $100$: $$\\dfrac{7}{25}=\\dfrac{28}{100},\\quad \\dfrac{3}{20}=\\dfrac{15}{100}$$","Сложите: $$\\dfrac{28}{100}+\\dfrac{15}{100}=\\dfrac{43}{100}$$","Переведите в десятичную дробь: $$\\dfrac{43}{100}=0{,}43$$"]},{"content":"$$\\dfrac{5}{8}-\\dfrac{3}{20}$$[[fill_choice_big-17]]","widgets":{"fill_choice_big-17":{"type":"fill_choice_big","options":["$0,48$","$0,50$","$0,45$","$0,52$"],"placeholder":0,"answer":0}},"step":1,"hints":["Найдите общий знаменатель: $\\text{НОК}(8,20)=40$.","Приведите к знаменателю $40$: $$\\dfrac{5}{8}=\\dfrac{25}{40},\\quad \\dfrac{3}{20}=\\dfrac{6}{40}$$","Вычтите: $$\\dfrac{25}{40}-\\dfrac{6}{40}=\\dfrac{19}{40}$$","Переведите в десятичную дробь: $$\\dfrac{19}{40}=0{,}475\\approx 0{,}48$$"]},{"content":"$$\\dfrac{11}{16}-\\dfrac{1}{32}$$[[fill_choice_big-18]]","widgets":{"fill_choice_big-18":{"type":"fill_choice_big","options":["$0,66$","$0,65$","$0,68$","$0,63$"],"placeholder":0,"answer":0}},"step":1,"hints":["Приведите дроби к общему знаменателю $32$: $$\\dfrac{11}{16}=\\dfrac{22}{32}$$","Вычтите: $$\\dfrac{22}{32}-\\dfrac{1}{32}=\\dfrac{21}{32}$$","Переведите в десятичную дробь: $$\\dfrac{21}{32}=0{,}65625\\approx 0{,}66$$"]},{"content":"$$\\dfrac{9}{10}+\\dfrac{3}{25}$$[[fill_choice_big-19]]","widgets":{"fill_choice_big-19":{"type":"fill_choice_big","options":["$1,02$","$1,05$","$0,98$","$1,12$"],"placeholder":0,"answer":0}},"step":1,"hints":["Найдите общий знаменатель: $\\text{НОК}(10,25)=50$.","Приведите к знаменателю $50$: $$\\dfrac{9}{10}=\\dfrac{45}{50},\\quad \\dfrac{3}{25}=\\dfrac{6}{50}$$","Сложите: $$\\dfrac{45}{50}+\\dfrac{6}{50}=\\dfrac{51}{50}=1\\dfrac{1}{50}$$","Переведите в десятичную дробь: $$\\dfrac{51}{50}=1{,}02$$"]},{"content":"$$\\dfrac{17}{20}-\\dfrac{3}{8}$$[[fill_choice_big-20]]","widgets":{"fill_choice_big-20":{"type":"fill_choice_big","options":["$0,48$","$0,50$","$0,45$","$0,52$"],"placeholder":0,"answer":0}},"step":1,"hints":["Найдите общий знаменатель: $\\text{НОК}(20,8)=40$.","Приведите к знаменателю $40$: $$\\dfrac{17}{20}=\\dfrac{34}{40},\\quad \\dfrac{3}{8}=\\dfrac{15}{40}$$","Вычтите: $$\\dfrac{34}{40}-\\dfrac{15}{40}=\\dfrac{19}{40}$$","Переведите в десятичную дробь: $$\\dfrac{19}{40}=0{,}475\\approx 0{,}48$$"]}]}

{"questions":[{"content":"$$\\dfrac{3}{8}\\cdot \\dfrac{4}{5}$$[[fill_choice_big-1]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$0,30$","$0,32$","$0,28$","$0,25$"],"placeholder":0,"answer":0}},"step":1,"hints":["Перемножьте числители и знаменатели: $$\\dfrac{3}{8}\\cdot \\dfrac{4}{5}=\\dfrac{3\\cdot 4}{8\\cdot 5}$$","Сократите дробь: $$\\dfrac{12}{40}=\\dfrac{3}{10}$$","Переведите в десятичную дробь: $$\\dfrac{3}{10}=0{,}30$$"]},{"content":"$$\\dfrac{7}{10}\\cdot \\dfrac{3}{5}$$[[fill_choice_big-2]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$0,42$","$0,35$","$0,28$","$0,48$"],"placeholder":0,"answer":0}},"step":1,"hints":["Перемножьте числители и знаменатели: $$\\dfrac{7}{10}\\cdot \\dfrac{3}{5}=\\dfrac{21}{50}$$","Проверьте, можно ли сократить дробь: $$\\dfrac{21}{50}$$ не сокращается.","Переведите в десятичную дробь: $$\\dfrac{21}{50}=0{,}42$$"]},{"content":"$$\\dfrac{9}{16}\\cdot \\dfrac{8}{15}$$[[fill_choice_big-3]]","widgets":{"fill_choice_big-3":{"type":"fill_choice_big","options":["$0,30$","$0,24$","$0,36$","$0,28$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сначала удобно сократить дроби до умножения: $$\\dfrac{9}{16}\\cdot \\dfrac{8}{15}$$","Сократите $8$ и $16$: $$\\dfrac{9}{\\color{#000}16}\\cdot \\dfrac{\\color{#000}8}{15}=\\dfrac{9}{2}\\cdot \\dfrac{1}{15}$$","Перемножьте: $$\\dfrac{9}{2}\\cdot \\dfrac{1}{15}=\\dfrac{9}{30}=\\dfrac{3}{10}$$","Переведите в десятичную дробь: $$\\dfrac{3}{10}=0{,}30$$"]},{"content":"$$\\dfrac{5}{12}\\cdot \\dfrac{9}{10}$$[[fill_choice_big-4]]","widgets":{"fill_choice_big-4":{"type":"fill_choice_big","options":["$0,38$","$0,35$","$0,41$","$0,45$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сократите дроби до умножения: $$\\dfrac{5}{12}\\cdot \\dfrac{9}{10}$$","Сократите $5$ и $10$: $$\\dfrac{1}{12}\\cdot \\dfrac{9}{2}$$","Перемножьте: $$\\dfrac{1\\cdot 9}{12\\cdot 2}=\\dfrac{9}{24}=\\dfrac{3}{8}$$","Переведите в десятичную дробь: $$\\dfrac{3}{8}=0{,}375\\approx 0{,}38$$"]},{"content":"$$\\dfrac{11}{20}\\cdot \\dfrac{4}{11}$$[[fill_choice_big-5]]","widgets":{"fill_choice_big-5":{"type":"fill_choice_big","options":["$0,20$","$0,22$","$0,25$","$0,18$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сократите одинаковые множители: $$\\dfrac{11}{20}\\cdot \\dfrac{4}{11}$$","Сократите $11$ в числителе и знаменателе: $$\\dfrac{1}{20}\\cdot 4=\\dfrac{4}{20}=\\dfrac{1}{5}$$","Переведите в десятичную дробь: $$\\dfrac{1}{5}=0{,}20$$"]},{"content":"$$\\dfrac{13}{25}\\cdot \\dfrac{5}{26}$$[[fill_choice_big-6]]","widgets":{"fill_choice_big-6":{"type":"fill_choice_big","options":["$0,10$","$0,12$","$0,08$","$0,15$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сократите дроби до умножения: $$\\dfrac{13}{25}\\cdot \\dfrac{5}{26}$$","Сократите $13$ и $26$: $$\\dfrac{1}{25}\\cdot \\dfrac{5}{2}$$","Перемножьте: $$\\dfrac{5}{50}=\\dfrac{1}{10}$$","Переведите в десятичную дробь: $$\\dfrac{1}{10}=0{,}10$$"]},{"content":"$$\\dfrac{3}{4}:\\dfrac{5}{8}$$[[fill_choice_big-7]]","widgets":{"fill_choice_big-7":{"type":"fill_choice_big","options":["$1,20$","$0,60$","$1,50$","$1,10$"],"placeholder":0,"answer":0}},"step":1,"hints":["Деление замените умножением на обратную дробь: $$\\dfrac{3}{4}:\\dfrac{5}{8}=\\dfrac{3}{4}\\cdot \\dfrac{8}{5}$$","Сократите $8$ и $4$: $$\\dfrac{3}{1}\\cdot \\dfrac{2}{5}=\\dfrac{6}{5}$$","Переведите в десятичную дробь: $$\\dfrac{6}{5}=1{,}2=1{,}20$$"]},{"content":"$$\\dfrac{7}{10}:\\dfrac{7}{25}$$[[fill_choice_big-8]]","widgets":{"fill_choice_big-8":{"type":"fill_choice_big","options":["$1,75$","$2,50$","$0,70$","$1,25$"],"placeholder":0,"answer":0}},"step":1,"hints":["Деление замените умножением на обратную дробь: $$\\dfrac{7}{10}:\\dfrac{7}{25}=\\dfrac{7}{10}\\cdot \\dfrac{25}{7}$$","Сократите $7$ в числителе и знаменателе: $$\\dfrac{25}{10}=\\dfrac{5}{2}$$","Переведите в десятичную дробь: $$\\dfrac{5}{2}=2{,}5=2{,}50$$","Сравните с вариантами и выберите эквивалентную запись: $$2{,}50=2{,}5$$"]},{"content":"$$\\dfrac{9}{20}:\\dfrac{3}{5}$$[[fill_choice_big-9]]","widgets":{"fill_choice_big-9":{"type":"fill_choice_big","options":["$0,75$","$0,45$","$0,60$","$0,90$"],"placeholder":0,"answer":0}},"step":1,"hints":["Замените деление умножением на обратную дробь: $$\\dfrac{9}{20}\\cdot \\dfrac{5}{3}$$","Сократите $9$ и $3$: $$\\dfrac{3}{20}\\cdot 5=\\dfrac{15}{20}=\\dfrac{3}{4}$$","Переведите в десятичную дробь: $$\\dfrac{3}{4}=0{,}75$$"]},{"content":"$$\\dfrac{5}{8}:\\dfrac{1}{4}$$[[fill_choice_big-10]]","widgets":{"fill_choice_big-10":{"type":"fill_choice_big","options":["$2,50$","$1,25$","$2,00$","$3,00$"],"placeholder":0,"answer":0}},"step":1,"hints":["Замените деление умножением на обратную дробь: $$\\dfrac{5}{8}:\\dfrac{1}{4}=\\dfrac{5}{8}\\cdot 4$$","Выполните умножение: $$\\dfrac{5\\cdot 4}{8}=\\dfrac{20}{8}=\\dfrac{5}{2}$$","Переведите в десятичную дробь: $$\\dfrac{5}{2}=2{,}5=2{,}50$$"]},{"content":"$$\\dfrac{6}{25}\\cdot \\dfrac{5}{12}$$[[fill_choice_big-11]]","widgets":{"fill_choice_big-11":{"type":"fill_choice_big","options":["$0,10$","$0,12$","$0,08$","$0,15$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сократите дроби до умножения: $$\\dfrac{6}{25}\\cdot \\dfrac{5}{12}$$","Сократите $6$ и $12$: $$\\dfrac{1}{25}\\cdot \\dfrac{5}{2}$$","Перемножьте: $$\\dfrac{5}{50}=\\dfrac{1}{10}$$","Переведите в десятичную дробь: $$\\dfrac{1}{10}=0{,}10$$"]},{"content":"$$\\dfrac{7}{16}\\cdot \\dfrac{8}{35}$$[[fill_choice_big-12]]","widgets":{"fill_choice_big-12":{"type":"fill_choice_big","options":["$0,10$","$0,12$","$0,08$","$0,14$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сократите дроби до умножения: $$\\dfrac{7}{16}\\cdot \\dfrac{8}{35}$$","Сократите $8$ и $16$: $$\\dfrac{7}{2}\\cdot \\dfrac{1}{35}$$","Сократите $7$ и $35$: $$\\dfrac{1}{2}\\cdot \\dfrac{1}{5}=\\dfrac{1}{10}$$","Переведите в десятичную дробь: $$\\dfrac{1}{10}=0{,}10$$"]},{"content":"$$\\dfrac{3}{5}:\\dfrac{6}{25}$$[[fill_choice_big-13]]","widgets":{"fill_choice_big-13":{"type":"fill_choice_big","options":["$2,50$","$1,50$","$2,00$","$3,20$"],"placeholder":0,"answer":0}},"step":1,"hints":["Замените деление умножением на обратную дробь: $$\\dfrac{3}{5}\\cdot \\dfrac{25}{6}$$","Сократите $25$ и $5$: $$3\\cdot \\dfrac{5}{6}=\\dfrac{15}{6}=\\dfrac{5}{2}$$","Переведите в десятичную дробь: $$\\dfrac{5}{2}=2{,}5=2{,}50$$"]},{"content":"$$\\dfrac{21}{40}:\\dfrac{7}{10}$$[[fill_choice_big-14]]","widgets":{"fill_choice_big-14":{"type":"fill_choice_big","options":["$0,75$","$0,60$","$0,80$","$0,70$"],"placeholder":0,"answer":0}},"step":1,"hints":["Замените деление умножением на обратную дробь: $$\\dfrac{21}{40}\\cdot \\dfrac{10}{7}$$","Сократите $21$ и $7$: $$\\dfrac{3}{40}\\cdot 10=\\dfrac{30}{40}=\\dfrac{3}{4}$$","Переведите в десятичную дробь: $$\\dfrac{3}{4}=0{,}75$$"]},{"content":"$$\\dfrac{9}{25}\\cdot \\dfrac{5}{6}$$[[fill_choice_big-15]]","widgets":{"fill_choice_big-15":{"type":"fill_choice_big","options":["$0,30$","$0,27$","$0,36$","$0,24$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сократите дроби до умножения: $$\\dfrac{9}{25}\\cdot \\dfrac{5}{6}$$","Сократите $5$ и $25$: $$\\dfrac{9}{5\\cdot 5}\\cdot \\dfrac{1}{6}=\\dfrac{9}{150}$$","Сократите: $$\\dfrac{9}{150}=\\dfrac{3}{50}$$","Переведите в десятичную дробь: $$\\dfrac{3}{50}=0{,}06$$"]},{"content":"$$\\dfrac{15}{16}\\cdot \\dfrac{8}{25}$$[[fill_choice_big-16]]","widgets":{"fill_choice_big-16":{"type":"fill_choice_big","options":["$0,30$","$0,28$","$0,32$","$0,25$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сократите дроби до умножения: $$\\dfrac{15}{16}\\cdot \\dfrac{8}{25}$$","Сократите $8$ и $16$: $$\\dfrac{15}{2}\\cdot \\dfrac{1}{25}$$","Перемножьте: $$\\dfrac{15}{50}=\\dfrac{3}{10}$$","Переведите в десятичную дробь: $$\\dfrac{3}{10}=0{,}30$$"]},{"content":"$$\\dfrac{7}{20}:\\dfrac{7}{16}$$[[fill_choice_big-17]]","widgets":{"fill_choice_big-17":{"type":"fill_choice_big","options":["$0,80$","$1,25$","$0,70$","$0,75$"],"placeholder":0,"answer":0}},"step":1,"hints":["Замените деление умножением на обратную дробь: $$\\dfrac{7}{20}\\cdot \\dfrac{16}{7}$$","Сократите $7$ в числителе и знаменателе: $$\\dfrac{16}{20}$$","Сократите дробь: $$\\dfrac{16}{20}=\\dfrac{4}{5}$$","Переведите в десятичную дробь: $$\\dfrac{4}{5}=0{,}8=0{,}80$$"]},{"content":"$$\\dfrac{4}{15}\\cdot \\dfrac{9}{8}$$[[fill_choice_big-18]]","widgets":{"fill_choice_big-18":{"type":"fill_choice_big","options":["$0,30$","$0,25$","$0,35$","$0,40$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сократите дроби до умножения: $$\\dfrac{4}{15}\\cdot \\dfrac{9}{8}$$","Сократите $4$ и $8$: $$\\dfrac{1}{15}\\cdot \\dfrac{9}{2}$$","Перемножьте: $$\\dfrac{9}{30}=\\dfrac{3}{10}$$","Переведите в десятичную дробь: $$\\dfrac{3}{10}=0{,}30$$"]},{"content":"$$\\dfrac{3}{25}:\\dfrac{6}{5}$$[[fill_choice_big-19]]","widgets":{"fill_choice_big-19":{"type":"fill_choice_big","options":["$0,10$","$0,08$","$0,12$","$0,15$"],"placeholder":0,"answer":0}},"step":1,"hints":["Замените деление умножением на обратную дробь: $$\\dfrac{3}{25}\\cdot \\dfrac{5}{6}$$","Сократите $3$ и $6$: $$\\dfrac{1}{25}\\cdot \\dfrac{5}{2}$$","Перемножьте: $$\\dfrac{5}{50}=\\dfrac{1}{10}$$","Переведите в десятичную дробь: $$\\dfrac{1}{10}=0{,}10$$"]},{"content":"$$\\dfrac{27}{50}:\\dfrac{9}{10}$$[[fill_choice_big-20]]","widgets":{"fill_choice_big-20":{"type":"fill_choice_big","options":["$0,60$","$0,54$","$0,75$","$0,45$"],"placeholder":0,"answer":0}},"step":1,"hints":["Замените деление умножением на обратную дробь: $$\\dfrac{27}{50}\\cdot \\dfrac{10}{9}$$","Сократите $27$ и $9$: $$\\dfrac{3}{50}\\cdot 10=\\dfrac{30}{50}=\\dfrac{3}{5}$$","Переведите в десятичную дробь: $$\\dfrac{3}{5}=0{,}6=0{,}60$$"]}]}

{"questions":[{"content":"$$3{,}48+1{,}75$$[[fill_choice_big-1]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$5{,}23$","$5{,}13$","$4{,}23$","$5{,}32$"],"placeholder":0,"answer":0}},"step":1,"hints":["Запишите числа одно под другим так, чтобы запятые оказались друг под другом: $3{,}48$ и $1{,}75$.","Сложите поразрядно: сотые $8+5=13$ (пишем $3$, $1$ переносим в десятые), десятые $4+7+1=12$ (пишем $2$, $1$ переносим в единицы).","Единицы и целая часть: $3+1+1=5$, получаем $5{,}23$."]},{"content":"$$6{,}2-3{,}78$$[[fill_choice_big-2]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$2{,}42$","$3{,}42$","$2{,}52$","$2{,}32$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте количество знаков после запятой: $6{,}2=6{,}20$.","Вычтите поразрядно: $20-78$ нельзя, поэтому займем 1 из десятых: $20+100=120$, а десятые уменьшим на 1.","Получаем: $6{,}20-3{,}78=2{,}42$."]},{"content":"$$0{,}56+2{,}9$$[[fill_choice_big-3]]","widgets":{"fill_choice_big-3":{"type":"fill_choice_big","options":["$3{,}46$","$3{,}56$","$2{,}46$","$3{,}36$"],"placeholder":0,"answer":0}},"step":1,"hints":["Представьте $2{,}9$ как $2{,}90$, чтобы удобнее складывать с $0{,}56$.","Сложите сотые и десятые: $56+90=146$ сотых, это $1{,}46$.","Добавьте целую часть: $2+1{,}46=3{,}46$."]},{"content":"$$12{,}05-4{,}8$$[[fill_choice_big-4]]","widgets":{"fill_choice_big-4":{"type":"fill_choice_big","options":["$7{,}25$","$8{,}25$","$7{,}35$","$6{,}25$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте разряды: $4{,}8=4{,}80$.","Вычтите поразрядно: сотые $5-0=5$, десятые $0-8$ нельзя, поэтому займем 1 из единиц: $10-8=2$.","Целые: $11-4=7$, получаем $7{,}25$."]},{"content":"$$7{,}39+0{,}61$$[[fill_choice_big-5]]","widgets":{"fill_choice_big-5":{"type":"fill_choice_big","options":["$8{,}00$","$7{,}90$","$8{,}10$","$7{,}99$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сложите сотые: $9+1=10$ (пишем $0$, $1$ переносим в десятые).","Сложите десятые: $3+6+1=10$ (пишем $0$, $1$ переносим в единицы).","Сложите целые: $7+0+1=8$, получаем $8{,}00$."]},{"content":"$$5{,}007-2{,}58$$[[fill_choice_big-6]]","widgets":{"fill_choice_big-6":{"type":"fill_choice_big","options":["$2{,}427$","$2{,}527$","$3{,}427$","$2{,}47$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте разряды: $2{,}58=2{,}580$.","Вычтите поразрядно: $5{,}007-2{,}580$ (в тысячных нужно занимать через разряды).","Получается $2{,}427$."]},{"content":"$$0{,}84+0{,}167$$[[fill_choice_big-7]]","widgets":{"fill_choice_big-7":{"type":"fill_choice_big","options":["$1{,}007$","$0{,}907$","$1{,}017$","$0{,}997$"],"placeholder":0,"answer":0}},"step":1,"hints":["Запишите $0{,}84$ как $0{,}840$, чтобы было три знака после запятой.","Сложите поразрядно: $840+167=1007$ тысячных.","Это $1{,}007$."]},{"content":"$$9{,}5-0{,}76$$[[fill_choice_big-8]]","widgets":{"fill_choice_big-8":{"type":"fill_choice_big","options":["$8{,}74$","$8{,}84$","$9{,}24$","$8{,}64$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте: $9{,}5=9{,}50$.","Вычтите десятые и сотые: $50-76$ нельзя, займем 1 из единиц: $150-76=74$ сотых.","Целые: $8-0=8$, получаем $8{,}74$."]},{"content":"$$14{,}32+5{,}68$$[[fill_choice_big-9]]","widgets":{"fill_choice_big-9":{"type":"fill_choice_big","options":["$20{,}00$","$19{,}90$","$20{,}10$","$21{,}00$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сложите сотые: $2+8=10$ (пишем $0$, перенос $1$ в десятые).","Сложите десятые: $3+6+1=10$ (пишем $0$, перенос $1$ в единицы).","Сложите целые: $14+5+1=20$, получаем $20{,}00$."]},{"content":"$$2{,}4+0{,}095$$[[fill_choice_big-10]]","widgets":{"fill_choice_big-10":{"type":"fill_choice_big","options":["$2{,}495$","$2{,}405$","$2{,}35$","$2{,}505$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте: $2{,}4=2{,}400$.","Сложите тысячные: $400+95=495$ тысячных.","Получаем $2{,}495$."]},{"content":"$$8{,}01-3{,}999$$[[fill_choice_big-11]]","widgets":{"fill_choice_big-11":{"type":"fill_choice_big","options":["$4{,}011$","$4{,}111$","$5{,}011$","$4{,}001$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте: $8{,}01=8{,}010$.","Вычитая $8{,}010-3{,}999$, выполняйте занимание последовательно в тысячных, сотых и десятых.","Получается $4{,}011$."]},{"content":"$$0{,}375+0{,}625$$[[fill_choice_big-12]]","widgets":{"fill_choice_big-12":{"type":"fill_choice_big","options":["$1{,}000$","$0{,}990$","$1{,}010$","$0{,}950$"],"placeholder":0,"answer":0}},"step":1,"hints":["Сложите тысячные: $375+625=1000$ тысячных.","Это $1{,}000$.","Можно записать как $1{,}0$ или $1$."]},{"content":"$$10{,}6-7{,}35$$[[fill_choice_big-13]]","widgets":{"fill_choice_big-13":{"type":"fill_choice_big","options":["$3{,}25$","$2{,}25$","$3{,}35$","$4{,}25$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте: $10{,}6=10{,}60$.","Вычтите: $60-35=25$ сотых.","Целые: $10-7=3$, получаем $3{,}25$."]},{"content":"$$4{,}08+6{,}913$$[[fill_choice_big-14]]","widgets":{"fill_choice_big-14":{"type":"fill_choice_big","options":["$10{,}993$","$10{,}903$","$11{,}003$","$9{,}993$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте: $4{,}08=4{,}080$.","Сложите дробные части: $0{,}080+0{,}913=0{,}993$.","Добавьте целые: $4+6=10$, получаем $10{,}993$."]},{"content":"$$15{,}00-0{,}125$$[[fill_choice_big-15]]","widgets":{"fill_choice_big-15":{"type":"fill_choice_big","options":["$14{,}875$","$14{,}885$","$14{,}775$","$14{,}925$"],"placeholder":0,"answer":0}},"step":1,"hints":["Запишите $15{,}00$ как $15{,}000$.","Вычтите $15{,}000-0{,}125$, выполняя занимание в тысячных и сотых.","Получается $14{,}875$."]},{"content":"$$0{,}09+0{,}9$$[[fill_choice_big-16]]","widgets":{"fill_choice_big-16":{"type":"fill_choice_big","options":["$0{,}99$","$1{,}09$","$0{,}909$","$0{,}9$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте: $0{,}9=0{,}90$.","Сложите сотые: $9+90=99$ сотых.","Это $0{,}99$."]},{"content":"$$23{,}47-18{,}92$$[[fill_choice_big-17]]","widgets":{"fill_choice_big-17":{"type":"fill_choice_big","options":["$4{,}55$","$5{,}55$","$4{,}45$","$3{,}55$"],"placeholder":0,"answer":0}},"step":1,"hints":["Вычтите сотые: $7-2=5$.","Вычтите десятые: $4-9$ нельзя, займем 1 из единиц: $14-9=5$.","Целые: $22-18=4$, получаем $4{,}55$."]},{"content":"$$1{,}234+9{,}99$$[[fill_choice_big-18]]","widgets":{"fill_choice_big-18":{"type":"fill_choice_big","options":["$11{,}224$","$11{,}214$","$10{,}224$","$11{,}324$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте: $9{,}99=9{,}990$.","Сложите дробные части: $0{,}990+0{,}234=1{,}224$ (есть переход через 1).","Целые: $9+1+1=11$, получаем $11{,}224$."]},{"content":"$$0{,}707-0{,}08$$[[fill_choice_big-19]]","widgets":{"fill_choice_big-19":{"type":"fill_choice_big","options":["$0{,}627$","$0{,}687$","$0{,}607$","$0{,}727$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте: $0{,}08=0{,}080$.","Вычтите тысячные: $707-80=627$ тысячных.","Это $0{,}627$."]},{"content":"$$100{,}5-99{,}95$$[[fill_choice_big-20]]","widgets":{"fill_choice_big-20":{"type":"fill_choice_big","options":["$0{,}55$","$1{,}55$","$0{,}45$","$0{,}65$"],"placeholder":0,"answer":0}},"step":1,"hints":["Выровняйте: $100{,}5=100{,}50$.","Вычтите: $100{,}50-99{,}95$ (в сотых нужно занимать 1 из десятых).","Получается $0{,}55$."]}]}