Задание 14. Действия с дробями

{"questions":[{"content":"Найдите значение выражения: $$6\\frac{3}{5} + 1\\frac{1}{3} \\cdot 1.2$$ [[fill_choice_big-1]][[image-2096]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$8.7$","$-8.5$","$8.2$"],"placeholder":0,"answer":2},"image-2096":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2025/02/test-01.svg","width":"300"}},"explanation":"$2.3$","hints":["Выполним сначала умножение, для этого представим оба множителя в виде неправильных обыкновенных дробей: $$1\\frac{1}{3} \\cdot 1.2 = \\frac{4}{3} \\cdot \\frac{12}{10} = \\frac{4 \\cdot 4}{10} = 1.6$$ Выполним сложение: $$6\\frac{3}{5} + 1.6 = 8.2$$"]},{"content":"Найдите значение выражения: $$2\\frac{4}{5} + \\frac{2}{9} \\cdot 4.5$$[[fill_choice_big-2]][[image-2130]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$3.8$","$3.5$","$3$"],"placeholder":0,"answer":0},"image-2130":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2024/10/magic_box-01.svg","width":"300"}},"hints":["Выполним сначала умножение, для этого представим оба множителя в виде неправильных обыкновенных дробей: $$\\frac{2}{9} \\cdot 4.5 = \\frac{2}{9} \\cdot \\frac{45}{10} = \\frac{2 \\cdot 5}{10} = 1$$ Выполним сложение: $$2\\frac{4}{5} + 1 = 3.8$$"]},{"content":"Найдите значение выражения: $$\\frac{1}{3} \\cdot 0.99 + 2$$ [[fill_choice_big-33]][[image-2167]]","widgets":{"fill_choice_big-33":{"type":"fill_choice_big","options":["$3.89$","$2.36$","$2.33$"],"placeholder":0,"answer":2},"image-2167":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/04/uchitel-doska-globus.svg","width":"300"}},"hints":["Выполним умножение, а затем сложение: $$\\frac{1}{3} \\cdot 0.99 + 2 = \\frac{0.99}{3} + 2 $$ $$ 0.33 + 2 = 2.33$$"]},{"content":"Найдите значение выражения:$$\\frac{12}{7} : \\left( \\frac{6}{7}-\\frac{3}{4} \\right)$$ [[fill_choice_big-71]][[image-2207]]","widgets":{"fill_choice_big-71":{"type":"fill_choice_big","options":["$18$","$14$","$16$"],"placeholder":0,"answer":2},"image-2207":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/02/student-uchenik.svg","width":"300"}},"hints":["$$\\frac{12}{7} : \\left( \\frac{6}{7}-\\frac{3}{4} \\right) = \\frac{12}{7} : \\frac{3}{28} $$ $$ \\frac{12}{7} \\cdot \\frac{28}{3} = 16$$"]},{"content":"Найдите значение выражения:$$\\frac{8}{15} : \\left( \\frac{2}{3}-\\frac{3}{5} \\right)$$[[fill_choice_big-143]][[image-2250]]","widgets":{"fill_choice_big-143":{"type":"fill_choice_big","options":["$8$","$8.4$","$9$"],"placeholder":0,"answer":0},"image-2250":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/02/mudrecz-kolonna-atom.svg","width":"300"}},"hints":["$$\\frac{8}{15} : \\left( \\frac{2}{3}-\\frac{3}{5} \\right)=\\frac{8}{15} : \\frac{1}{15} $$ $$ \\frac{8}{15} \\cdot \\frac{15}{1} = 8$$"]},{"content":"Найдите значение выражения: $4.5 \\cdot 6.6 + 3.4$[[fill_choice_big-238]][[image-2296]]","widgets":{"fill_choice_big-238":{"type":"fill_choice_big","options":["$36.4$","$35.2$","$33.1$"],"placeholder":0,"answer":2},"image-2296":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/08/dumaet-doska-drobi-tsifry2-3.svg","width":"300"}},"hints":["Выполним сначала умножение, а потом сложение:$$4.5 \\cdot 6.6 + 3.4 = 29.7 + 3.4 = 33.1$$"]},{"content":"Найдите значение выражения: $$4.2 \\cdot 7.5 + 0.8$$[[fill_choice_big-328]][[image-2345]]","widgets":{"fill_choice_big-328":{"type":"fill_choice_big","options":["$32.5$","$32.3$","$32.9$"],"placeholder":0,"answer":1},"image-2345":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/05/obrazavr_deyatelnost_dop-04-2.svg","width":"300"}},"hints":["Выполним сначала умножение, а потом сложение:$$4.2 \\cdot 7.5 + 0.8 = 31.5 + 0.8 = 32.3$$"]},{"content":"Найдите значение выражения: $$1\\frac{5}{6}-0.5 \\cdot \\left(-\\frac{10}{3} \\right)$$ [[fill_choice_big-474]][[image-2397]]","widgets":{"fill_choice_big-474":{"type":"fill_choice_big","options":["$4.5$","$3.5$","$5.2$"],"placeholder":0,"answer":1},"image-2397":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/06/teacher.svg","width":"300"}},"hints":["$$1\\frac{5}{6}-0.5 \\cdot \\left(-\\frac{10}{3} \\right)= \\frac{11}{6} + \\frac{5}{10} \\cdot \\frac{10}{3} $$ $$ \\frac{11}{6} + \\frac{5}{3} = 3.5$$"]},{"content":"Найдите значение выражения: $$9.9 : 3.3 + 5.9$$[[fill_choice_big-618]][[image-2452]]","widgets":{"fill_choice_big-618":{"type":"fill_choice_big","options":["$8.9$","$9.9$","$7.8$"],"placeholder":0,"answer":0},"image-2452":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/05/kniga_obrazavr-01.svg","width":"300"}},"hints":["Выполним сначала деление, а потом сложение: $$9.9 : 3.3 + 5.9 = 3 + 5.9 = 8.9$$"]},{"content":"Найдите значение выражения: $$(1.3+2.9)\\cdot5.5$$[[fill_choice_big-788]][[image-2510]]","widgets":{"fill_choice_big-788":{"type":"fill_choice_big","options":["$23.1$","$23.9$","$22.1$"],"placeholder":0,"answer":0},"image-2510":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/08/schety-1.svg","width":"300"}},"hints":["Выполним сначала действие в скобках, а затем умножение:$$(1.3+2.9) \\cdot 5.5 = 4.2 \\cdot 5.5 = 23.1$$"]}]}

{"questions":[{"content":"Найдите значение выражения: $$\\left( \\frac{1}{13}-2\\frac{3}{4} \\right) \\cdot 26$$ [[fill_choice_big-1]][[image-956]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$68.7$","$-69.5$","$-67.8$"],"placeholder":0,"answer":1},"image-956":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/04/uchitel-doska-globus.svg","width":"300"}},"explanation":"$2.3$","hints":["$$\\left( \\frac{1}{13}-2\\frac{3}{4} \\right) \\cdot 26 = \\frac{1}{13} \\cdot 26-2\\frac{3}{4} \\cdot 26$$ $$ \\frac{1}{13} \\cdot 26-2\\frac{3}{4}\\cdot 26= 2-\\frac{11 \\cdot 26}{4}$$ $$2-\\frac{11 \\cdot 26}{4}= 2-\\frac{143}{2} = -69.5$$"]},{"content":"Найдите значение выражения: $$ \\frac{13}{7} : \\left( \\frac{1}{3}+\\frac{2}{7} \\right) $$[[fill_choice_big-2]][[image-990]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$4$","$3.5$","$3$"],"placeholder":0,"answer":2},"image-990":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/06/mama_doch-01.svg","width":"300"}},"hints":["$$\\frac{13}{7} : \\left( \\frac{1}{3} + \\frac{2}{7} \\right) = \\frac{13}{7} : \\left( \\frac{7}{21} + \\frac{6}{21} \\right)$$ $$\\frac{13}{7} : \\left( \\frac{7}{21} + \\frac{6}{21} \\right) = \\frac{13}{7} : \\frac{13}{21}$$ $$\\frac{13}{7} : \\frac{13}{21} = \\frac{13 \\cdot 21}{7 \\cdot 13} = 3$$"]},{"content":"Найдите значение выражения: $4.5\\cdot7.2−0.5.$[[fill_choice_big-33]][[image-1027]]","widgets":{"fill_choice_big-33":{"type":"fill_choice_big","options":["$31.9$","$36.6$","$33.9$"],"placeholder":0,"answer":0},"image-1027":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2024/01/uchit-risovat-01.svg","width":"300"}},"hints":["$$4.5\\cdot7.2−0.5=32.4−0.5=31.9$$"]},{"content":"Найдите значение выражения: $6.4 \\cdot 7.5−3.4.$[[fill_choice_big-71]][[image-1067]]","widgets":{"fill_choice_big-71":{"type":"fill_choice_big","options":["$42.8$","$46.6$","$44.6$"],"placeholder":0,"answer":2},"image-1067":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/01/horoshaya-mama-1.svg","width":"300"}},"hints":["$$6.4 \\cdot 7.5−3.4=48−3.4=44.6$$"]},{"content":"Найдите значение выражения: $(1.2+2.3) \\cdot 5.6.$[[fill_choice_big-143]][[image-1110]]","widgets":{"fill_choice_big-143":{"type":"fill_choice_big","options":["$19.6$","$20.4$","$18$"],"placeholder":0,"answer":0},"image-1110":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2021/12/papa.svg","width":"300"}},"hints":["$$ (1.2+2.3) \\cdot 5.6=3.5 \\cdot 5.6 = 19.6 $$"]},{"content":"Найдите значение выражения: $(3.7+2.8) \\cdot 5.6.$[[fill_choice_big-238]][[image-1156]]","widgets":{"fill_choice_big-238":{"type":"fill_choice_big","options":["$36.4$","$35.2$","$33.8$"],"placeholder":0,"answer":0},"image-1156":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2021/12/roditeli.svg","width":"300"}},"hints":["$$ (3.7+2.8) \\cdot 5.6 = 6.5 \\cdot 5.6 = 36.4 $$"]},{"content":"Найдите значение выражения: $15.2 : 1.9 \\cdot 7.5.$[[fill_choice_big-328]][[image-1205]]","widgets":{"fill_choice_big-328":{"type":"fill_choice_big","options":["$70$","$60$","$50$"],"placeholder":0,"answer":1},"image-1205":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/02/ochki.svg","width":"299"}},"hints":["Выполним сначала деление, а потом умножение: $$15.2 : 1.9 \\cdot 7.5 = 8 \\cdot 7.5 = 60$$"]},{"content":"Найдите значение выражения: $1.2 : 0.6 \\cdot 1.5.$[[fill_choice_big-474]][[image-1257]]","widgets":{"fill_choice_big-474":{"type":"fill_choice_big","options":["$4$","$3$","$5$"],"placeholder":0,"answer":1},"image-1257":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/03/arhitektor-stroitel-doska-chertezh-rulon-bumaga-3.svg","width":"300"}},"hints":["Выполним сначала деление, а потом умножение: $$1.2 : 0.6 \\cdot 1.5=2 \\cdot 1.5 = 3$$"]},{"content":"Найдите значение выражения: $$0.32 : \\frac{8}{9} + 5.$$[[fill_choice_big-618]][[image-1312]]","widgets":{"fill_choice_big-618":{"type":"fill_choice_big","options":["$5.36$","$3.33$","$2.85$"],"placeholder":0,"answer":0},"image-1312":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/02/mudrecz-kolonna-atom.svg","width":"300"},"image-1351":{"type":"image","url":""}},"hints":["Заменим деление на дробь умножением на обратную ей дробь: $$0.32 : \\frac{8}{9} + 5 = 0.32 \\cdot \\frac{9}{8} + 5 $$ $$ 0.36 + 5 = 5.36$$"]},{"content":"Найдите значение выражения: $$0.24 : \\frac{2}{3} + 2.$$[[fill_choice_big-788]][[image-1432]]","widgets":{"fill_choice_big-788":{"type":"fill_choice_big","options":["$2.36$","$2.96$","$2.66$"],"placeholder":0,"answer":0},"image-1432":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/08/v-ochkah-s-knigoi-kniga-tetrad-pishet-01-1.svg","width":"300"}},"hints":["Заменим деление на дробь умножением на обратную ей дробь: $$0.24 : \\frac{2}{3} + 2 = 0.24 \\cdot \\frac{3}{2} + 2 $$ $$ 0.24 \\cdot 1.5 + 2 = 2.36$$"]}]}

{"questions":[{"content":"Найдите значение выражения:$$\\frac{1}{1+\\frac{1}{7} }$$[[fill_choice_big-2]][[image-41]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$0.875$","$0.777$","$0.675$"],"placeholder":0,"answer":0},"image-41":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/11/obrazavr_angl_3_klass_papa_uchitel.svg","width":"300"}},"hints":["$$\\frac{1}{1+\\frac{1}{7} }=1:\\Big(1+\\frac{1}{7}\\Big)$$ $$1:\\Big(1+\\frac{1}{7}\\Big)=1:\\frac{8}{7}$$ $$1:\\frac{8}{7}=\\frac{7}{8}=0.875$$"]},{"content":"Найдите значение выражения:$$\\frac{7}{2}\\cdot\\frac{5}{4}-\\frac{3}{8}$$[[fill_choice_big-16]][[image-75]]","widgets":{"fill_choice_big-16":{"type":"fill_choice_big","options":["$5.5$","$4$","$8$"],"placeholder":0,"answer":1},"image-75":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/10/obrazavr_skuchayushhij.svg","width":"300"}},"hints":["$$\\frac{7}{2}\\cdot\\frac{5}{4}-\\frac{3}{8}=\\frac{35}{8}-\\frac{3}{8}$$$$\\frac{35}{8}-\\frac{3}{8}=\\frac{32}{8}=4$$"]},{"content":"Найдите значение выражения:$$\\frac{5}{4}+\\frac{7}{6}:\\frac{2}{3}$$[[fill_choice_big-59]][[image-112]]","widgets":{"fill_choice_big-59":{"type":"fill_choice_big","options":["$2.5$","$3$","$5$"],"placeholder":0,"answer":1},"image-112":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/10/obrazavr_ozadachennyj.svg","width":"300"}},"hints":["$$\\frac{5}{4}+\\frac{7}{6}:\\frac{2}{3}=\\frac{5}{4}+\\frac{7}{6}\\cdot\\frac{3}{2}$$ $$\\frac{5}{4}+\\frac{7}{{}^{2}\\cancel{6}}\\cdot\\frac{{}^{1}\\cancel{3}}{2}=\\frac{5}{4}+\\frac{7}{4}=\\frac{12}{4}=3$$"]},{"content":"Найдите значение выражения:$$\\frac{12}{7}:\\Big(\\frac{6}{7}-\\frac{3}{4}\\Big)$$[[fill_choice_big-154]][[image-152]]","widgets":{"fill_choice_big-154":{"type":"fill_choice_big","options":["$16$","$14$","$26$"],"placeholder":0,"answer":0},"image-152":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/05/sidyat-za-partoj-ruchka.svg","width":"300"}},"hints":["$$\\frac{12}{7}:\\Big(\\frac{6}{7}-\\frac{3}{4}\\Big)=\\frac{12}{7}:\\Big(\\frac{24}{28}-\\frac{21}{28}\\Big)$$$$\\frac{12}{7}:\\Big(\\frac{24}{28}-\\frac{21}{28}\\Big)=\\frac{12}{7}:\\frac{3}{28}$$$$\\frac{12}{7}:\\frac{3}{28}=\\frac{{}^{4}\\cancel{12}}{7}\\cdot\\frac{28}{{}^{1}\\cancel{3}}=16$$"]},{"content":"Найдите значение выражения:$$4.2\\cdot3.5:0.7$$[[fill_choice_big-265]][[image-195]]","widgets":{"fill_choice_big-265":{"type":"fill_choice_big","options":["$28$","$21$","$35$"],"placeholder":0,"answer":1},"image-195":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/04/sidit-chasy.svg","width":"300"}},"hints":["Первым действием нужно разделить один из множителей на $0.7$, а затем получившееся частное умножить на второй множитель:$$4.2\\cdot3.5:0.7=4.2\\cdot5=21$$"]},{"content":"Найдите значение выражения:$$1.56:1.3-0.4$$[[fill_choice_big-370]][[image-241]]","widgets":{"fill_choice_big-370":{"type":"fill_choice_big","options":["$0.65$","$0.95$","$0.8$"],"placeholder":0,"answer":2},"image-241":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/11/dumaet-primer-doska2-v2.svg","width":"300"}},"hints":["Первым действием выполним деление, а потом вычитание:$$1.56:1.3-0.4=1.2-0.4=0.8$$"]},{"content":"Найдите значение выражения:$$\\frac{1.7+3.8}{2.2}$$[[fill_choice_big-589]][[image-290]]","widgets":{"fill_choice_big-589":{"type":"fill_choice_big","options":["$2.5$","$3.5$","$6.25$"],"placeholder":0,"answer":0},"image-290":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/12/kipling-01.svg","width":"300"}},"hints":["Первым действием делаем сложение:$$\\frac{1.7+3.8}{2.2}=\\frac{5.5}{2.2}$$<br />Далее полученный результат можно разделить на $1.1$ для получения целых чисел: $$\\frac{5.5}{2.2}=\\frac{5}{2}=2.5$$"]},{"content":"Найдите значение выражения:$$1-\\frac{1}{3}\\cdot1.2$$[[fill_choice_big-829]][[image-342]]","widgets":{"fill_choice_big-829":{"type":"fill_choice_big","options":["$-0.8$","$0.8$","$0.6$"],"placeholder":0,"answer":2},"image-342":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/12/lawyer-01.svg","width":"299"}},"hints":["Переведём десятичную дробь в обыкновенную:$$1.2=\\frac{12}{10}=\\frac{6}{5}$$<br />Выполним умножение, а затем вычитание:$$1-\\frac{1}{{}^{1}\\cancel{3}}\\cdot\\frac{{}^{2}\\cancel{6}}{5}=1-\\frac{2}{5}$$$$1-\\frac{2}{5}=\\frac{3}{5}=0.6$$"]},{"content":"Найдите значение выражения:$$3+\\frac{1}{3}\\cdot0.39$$[[fill_choice_big-1104]][[image-397]]","widgets":{"fill_choice_big-1104":{"type":"fill_choice_big","options":["$3.10$","$3.13$","$2.13$"],"placeholder":0,"answer":1},"image-397":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/11/obrazavr_break.svg","width":"300"}},"hints":["Выполним сначала умножение, а потом сложение:$$3+\\frac{1}{3}\\cdot0.39=3+\\frac{0.39}{3}$$ $$3+\\frac{0.39}{3}=3+0.13=3.13$$"]},{"content":"Найдите значение выражения:$$\\frac{7}{18}+\\frac{5}{2}\\cdot\\frac{4}{9}$$[[fill_choice_big-1348]][[image-455]]","widgets":{"fill_choice_big-1348":{"type":"fill_choice_big","options":["$0.2$","$0.5$","$1.5$"],"placeholder":0,"answer":2},"image-455":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2022/11/divan-torsher-kniga-chitaet-kgigu.svg","width":"300"}},"hints":["$$\\frac{7}{18}+\\frac{5}{2}\\cdot\\frac{4}{9}=\\frac{7}{18}+\\frac{5\\cdot4}{2\\cdot9}$$ $$\\frac{7}{18}+\\frac{20}{18}=\\frac{27}{18}=1.5$$"]}]}

{"questions":[{"content":"Найдите значение выражения: $$\\Big(-2\\frac{3}{4}-\\frac{3}{8}\\Big)\\cdot160$$[[fill_choice_big-1]][[image-310]]","widgets":{"fill_choice_big-1":{"type":"fill_choice_big","options":["$-500$","$-400$","$-550$"],"placeholder":0,"answer":0},"image-310":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/02/student-uchenik.svg","width":"300"}},"hints":["$$\\Big(-2\\frac{3}{4}-\\frac{3}{8}\\Big)\\cdot160=\\Big(-\\frac{22}{8}-\\frac{3}{8}\\Big)\\cdot160$$ $$\\Big(-\\frac{22}{8}-\\frac{3}{8}\\Big)\\cdot160=-\\frac{25\\cdot160}{8}$$ $$-\\frac{25\\cdot{}^{20}\\cancel{160}}{{}^{1}\\cancel{8}}=-500$$"]},{"content":"Найдите значение выражения: $$\\Big(\\frac{3}{4}+2\\frac{3}{8}\\Big)\\cdot25.8$$[[fill_choice_big-18]][[image-271]]","widgets":{"fill_choice_big-18":{"type":"fill_choice_big","options":["$79.725$","$80.625$","$83.115$"],"placeholder":0,"answer":1},"image-271":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/04/uchitel-doska-globus.svg","width":"300"}},"hints":["$$\\Big(\\frac{3}{4}+2\\frac{3}{8}\\Big)\\cdot25.8=\\Big(\\frac{6}{8}+\\frac{19}{8}\\Big)\\cdot25\\frac{4}{5}$$ $$\\Big(\\frac{6}{8}+\\frac{19}{8}\\Big)\\cdot25\\frac{4}{5}=\\frac{25\\cdot129}{8\\cdot5}$$ $$\\frac{{}^{5}\\cancel{25}\\cdot129}{8\\cdot{}^{1}\\cancel{5}}=\\frac{645}{8}$$ $$\\frac{645}{8}=80.625$$"]},{"content":"Найдите значение выражения: $$\\frac{2}{5}+\\frac{1}{4}+2$$[[fill_choice_big-87]][[image-234]]","widgets":{"fill_choice_big-87":{"type":"fill_choice_big","options":["$2.55$","$2.85$","$2.65$"],"placeholder":0,"answer":2},"image-234":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/03/arhitektor-stroitel-doska-chertezh-rulon-bumaga-3.svg","width":"300"}},"hints":["$$\\frac{2}{5}+\\frac{1}{4}+2=0.4+0.25+2=2.65$$"]},{"content":"Найдите значение выражения: $$0.86:\\frac{43}{20}$$[[fill_choice_big-137]][[image-199]]","widgets":{"fill_choice_big-137":{"type":"fill_choice_big","options":["$0.4$","$0.45$","$0.5$"],"placeholder":0,"answer":0},"image-199":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/04/bolit-golova.svg","width":"300"}},"hints":["$$0.86:\\frac{43}{20}=\\frac{86}{100}:\\frac{43}{20}$$ $$\\frac{86}{100}:\\frac{43}{20}=\\frac{86\\cdot20}{100\\cdot43}$$ $$\\frac{86\\cdot{}^{1}\\cancel{20}}{{}^{5}\\cancel{100}\\cdot43}=0.4$$"]},{"content":"Найдите значение выражения: $$\\frac{1}{3}\\cdot0.99+2$$[[fill_choice_big-201]][[image-166]]","widgets":{"fill_choice_big-201":{"type":"fill_choice_big","options":["$2.33$","$3.33$","$2.45$"],"placeholder":0,"answer":0},"image-166":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/10/robot-fantastika.svg","width":"300"}},"hints":["$$\\frac{1}{3}\\cdot0.99+2=\\frac{1}{3}\\cdot\\frac{99}{100}+2$$ $$\\frac{1}{3}\\cdot\\frac{99}{100}+2=\\frac{1\\cdot99}{3\\cdot100}+2$$ $$\\frac{1\\cdot99}{3\\cdot100}+2=0.33+2=2.33$$"]},{"content":"Найдите значение выражения: $$\\frac{29}{7}:\\Big(\\frac{2}{7}+\\frac{3}{4}\\Big)$$[[fill_choice_big-359]][[image-135]]","widgets":{"fill_choice_big-359":{"type":"fill_choice_big","options":["$4$","$6$","$5$"],"placeholder":0,"answer":0},"image-135":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/10/obrazavr_v-stresse.svg","width":"300"}},"hints":["$$\\frac{29}{7}:\\Big(\\frac{2}{7}+\\frac{3}{4}\\Big)=\\frac{29}{7}:\\frac{8+21}{28}$$ $$\\frac{29}{7}:\\frac{8+21}{28}=\\frac{29}{7}:\\frac{29}{28}$$ $$\\frac{29}{7}:\\frac{29}{28}=\\frac{29\\cdot28}{7\\cdot29}$$ $$\\frac{{}^{}\\cancel{29}\\cdot28}{7\\cdot{}^{}\\cancel{29}}=4$$"]},{"content":"Найдите значение выражения: $$\\Big(\\frac{7}{8}-\\frac{17}{12}\\Big):\\frac{5}{12}$$[[fill_choice_big-185]][[image-106]]","widgets":{"fill_choice_big-185":{"type":"fill_choice_big","options":["$-1.3$","$1.5$","$-1.5$"],"placeholder":0,"answer":0},"image-106":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/10/obrazavr_ozadachennyj.svg","width":"300"}},"hints":["$$\\Big(\\frac{7}{8}-\\frac{17}{12}\\Big):\\frac{5}{12}=\\Big(\\frac{21-34}{24}\\Big):\\frac{5}{12}$$ $$\\Big(\\frac{21-34}{24}\\Big):\\frac{5}{12}=-\\frac{13}{24}:\\frac{5}{12}$$ $$-\\frac{13}{24}:\\frac{5}{12}=-\\frac{13\\cdot12}{24\\cdot5}$$ $$-\\frac{13\\cdot{}^{1}\\cancel{12}}{{}^{2}\\cancel{24}\\cdot5}=-1.3$$"]},{"content":"Найдите значение выражения: $$\\frac{4}{11}:\\Big(-\\frac{16}{33}\\Big)+5\\frac{3}{4}$$[[fill_choice_big-497]][[image-79]]","widgets":{"fill_choice_big-497":{"type":"fill_choice_big","options":["$4.5$","$5$","$-4.5$"],"placeholder":0,"answer":1},"image-79":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/10/obrazavr_skuchayushhij.svg","width":"300"}},"hints":["$$\\frac{4}{11}:\\Big(-\\frac{16}{33}\\Big)+5\\frac{3}{4}=-\\frac{4\\cdot33}{11\\cdot16}+5\\frac{3}{4}$$ $$-\\frac{{}^{1}\\cancel{4}\\cdot33}{11\\cdot{}^{4}\\cancel{16}}+5\\frac{3}{4}=-\\frac{3}{4}+5\\frac{3}{4}=5$$"]},{"content":"Найдите значение выражения: $$\\Big(\\frac{11}{12}+\\frac{11}{20}\\Big)\\cdot\\frac{15}{8}$$[[fill_choice_big-772]][[image-54]]","widgets":{"fill_choice_big-772":{"type":"fill_choice_big","options":["$2.85$","$2.75$","$-3.15$"],"placeholder":0,"answer":1},"image-54":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/11/obrazavr_angl_3_klass_papa_uchitel.svg","width":"300"}},"hints":["$$\\Big(\\frac{11}{12}+\\frac{11}{20}\\Big)\\cdot\\frac{15}{8}=\\Big(\\frac{55+33}{60}\\Big)\\cdot\\frac{15}{8}$$ $$\\Big(\\frac{55+33}{60}\\Big)\\cdot\\frac{15}{8}=\\frac{88}{60}\\cdot\\frac{15}{8}$$ $$\\frac{88}{60}\\cdot\\frac{15}{8}=\\frac{88\\cdot15}{60\\cdot8}$$ $$\\frac{{}^{11}\\cancel{88}\\cdot{}^{1}\\cancel{15}}{{}^{4}\\cancel{60}\\cdot{}^{1}\\cancel{8}}=2.75$$"]},{"content":"Найдите значение выражения: $$\\frac{18}{4}\\cdot\\frac{14}{3}:\\frac{4}{5}$$[[fill_choice_big-1142]][[image-31]]","widgets":{"fill_choice_big-1142":{"type":"fill_choice_big","options":["$26.25$","$25.25$","$27.56$"],"placeholder":0,"answer":0},"image-31":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/11/obrazavr_angl-2-urok_penal.svg","width":"300"}},"hints":["$$\\frac{18}{4}\\cdot\\frac{14}{3}:\\frac{4}{5}=\\frac{18}{4}\\cdot\\frac{14}{3}\\cdot\\frac{5}{4}$$ $$\\frac{18}{4}\\cdot\\frac{14}{3}\\cdot\\frac{5}{4}=\\frac{6}{2}\\cdot\\frac{7}{1}\\cdot\\frac{5}{4}$$ $$\\frac{6\\cdot7\\cdot5}{2\\cdot1\\cdot4}=\\frac{210}{8}=26.25$$"]}]}

{"questions":[{"content":"Найдите значение выражения: $$(3.9−2.4)\\cdot8.2$$[[fill_choice_big-2]][[image-31]]","widgets":{"fill_choice_big-2":{"type":"fill_choice_big","options":["$12.3$","$11$","$13.2$"],"placeholder":0,"answer":0},"image-31":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2025/01/pic_1-01.svg","width":"300"}},"hints":["$$(3.9−2.4)\\cdot8.2=1.5\\cdot8.2=12.3$$"]},{"content":"Найдите значение выражения: $$\\frac{9.5+8.9}{2.3}$$ [[fill_choice_big-40]][[image-54]]","widgets":{"fill_choice_big-40":{"type":"fill_choice_big","options":["$9$","$10$","$8$"],"placeholder":0,"answer":2},"image-54":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2024/02/parabola-01.svg","width":"300"}},"hints":["$$\\frac{9.5+8.9}{2.3}=\\frac{18.4}{2.3}=8$$"]},{"content":"Найдите значение выражения: $$3.8+1.08:0.9 $$[[fill_choice_big-132]][[image-79]]","widgets":{"fill_choice_big-132":{"type":"fill_choice_big","options":["$4.5$","$5$","$6$"],"placeholder":0,"answer":1},"image-79":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2024/02/obrazavr-01.svg","width":"300"}},"hints":["$$3.8+1.08:0.9=3.8+1.2=5$$"]},{"content":"Найдите значение выражения: $$(3.1+3.4) \\cdot 3.8$$[[fill_choice_big-264]][[image-106]]","widgets":{"fill_choice_big-264":{"type":"fill_choice_big","options":["$24.7$","$25.5$","$24.3$"],"placeholder":0,"answer":0},"image-106":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2024/02/obrazavr_giperbola-1.svg","width":"300"}},"hints":["$$(3.1+3.4)\\cdot3.8=6.5\\cdot3.8=24.7$$"]},{"content":"Найдите значение выражения: $$\\frac{2.7}{1.4+0.1}$$[[fill_choice_big-375]][[image-135]]","widgets":{"fill_choice_big-375":{"type":"fill_choice_big","options":["$3.3$","$2.2$","$1.8$"],"placeholder":0,"answer":2},"image-135":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/12/pisatel-01.svg","width":"300"}},"hints":["$$\\frac{2.7}{1.4+0.1}=\\frac{2.7}{1.5}=1.8$$"]},{"content":"Найдите значение выражения: $$\\frac{1.23\\cdot 45.7}{12.3+0.457}$$[[fill_choice_big-632]][[image-166]]","widgets":{"fill_choice_big-632":{"type":"fill_choice_big","options":["$10$","$15$","$9$"],"placeholder":0,"answer":0},"image-166":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/12/obrazavr_udostoverenie-lichnosti.svg","width":"300"}},"hints":["Для получения целых чисел умножим числитель и знаменатель на $10\\space000$: $$\\frac{1.23\\cdot 45.7}{12.3\\cdot0.457}=\\frac{{}^{}\\cancel{123}\\cdot{}^{}\\cancel{457}\\cdot10}{{}^{}\\cancel{123}\\cdot{}^{}\\cancel{457}}=10$$"]},{"content":"Найдите значение выражения: $$4.6\\cdot 3.9+1.74$$[[fill_choice_big-596]][[image-199]]","widgets":{"fill_choice_big-596":{"type":"fill_choice_big","options":["$19.68$","$19.55$","$19.23$"],"placeholder":0,"answer":0},"image-199":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/11/obrazavr_angl-4-urok_ruchka.svg","width":"300"}},"hints":["$$4.6\\cdot3.9+1.74=17.94+1.74=19.68$$"]},{"content":"Найдите значение выражения: $$\\frac{4.4}{5.8-5.3}$$[[fill_choice_big-792]][[image-234]]","widgets":{"fill_choice_big-792":{"type":"fill_choice_big","options":["$9.2$","$8.8$","$7.4$"],"placeholder":0,"answer":1},"image-234":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/07/obrazavr_with_a_map3-01.svg","width":"300"}},"hints":["$$\\frac{4.4}{5.8-5.3}=\\frac{4.4}{0.5}$$ Умножаем числитель и знаменатель на $10$: $$\\frac{4.4}{0.5}=\\frac{44}{5}=8.8$$"]},{"content":"Найдите значение выражения: $$2.4+1.56:1.3$$[[fill_choice_big-931]][[image-271]]","widgets":{"fill_choice_big-931":{"type":"fill_choice_big","options":["$4.6$","$3.6$","$5.6$"],"placeholder":0,"answer":1},"image-271":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/04/podozritelno-dumaet-1.svg","width":"300"}},"hints":["$$2.4+1.56:1.3=2.4+1.2=3.6$$"]},{"content":"Найдите значение выражения: $$\\frac{6}{2.8+0.2}$$[[fill_choice_big-1122]][[image-310]]","widgets":{"fill_choice_big-1122":{"type":"fill_choice_big","options":["$2$","$4$","$3$"],"placeholder":0,"answer":0},"image-310":{"type":"image","url":"https://obrazavr.ru/wp-content/uploads/2023/04/flashcards.svg","width":"300"}},"hints":["$$\\frac{6}{2.8+0.2}=\\frac{6}{3}=2$$"]}]}