1. 直接写出得数。
$\frac{4}{5} ÷ \frac{3}{5} =$
$\frac{5}{12} × 18 =$
$\frac{1}{5} ÷ 2 ÷ \frac{1}{5} =$
$\frac{1}{8} ÷ \frac{3}{4} =$
$\frac{7}{12} ÷ \frac{3}{7} =$
$\frac{13}{9} ÷ \frac{26}{27} =$
$15 ÷ \frac{3}{5} =$
$\frac{1}{4} ÷ \frac{3}{2} =$
$\frac{1}{4} ÷ \frac{4}{5} =$
$\frac{2}{13} × 26 =$
$12 ÷ \frac{2}{3} =$
$1 ÷ \frac{2}{5} =$
$\frac{1}{5} ÷ \frac{5}{6} =$
$48 × \frac{11}{16} =$
$\frac{5}{7} ÷ 1\frac{5}{6} =$
$\frac{3}{11} ÷ \frac{2}{11} =$
$\frac{4}{5} ÷ \frac{3}{5} =$
$\frac{5}{12} × 18 =$
$\frac{1}{5} ÷ 2 ÷ \frac{1}{5} =$
$\frac{1}{8} ÷ \frac{3}{4} =$
$\frac{7}{12} ÷ \frac{3}{7} =$
$\frac{13}{9} ÷ \frac{26}{27} =$
$15 ÷ \frac{3}{5} =$
$\frac{1}{4} ÷ \frac{3}{2} =$
$\frac{1}{4} ÷ \frac{4}{5} =$
$\frac{2}{13} × 26 =$
$12 ÷ \frac{2}{3} =$
$1 ÷ \frac{2}{5} =$
$\frac{1}{5} ÷ \frac{5}{6} =$
$48 × \frac{11}{16} =$
$\frac{5}{7} ÷ 1\frac{5}{6} =$
$\frac{3}{11} ÷ \frac{2}{11} =$
答案
$\frac{4}{5} ÷ \frac{3}{5} = \frac{4}{3}$
$\frac{5}{12} × 18 = \frac{15}{2}$
$\frac{1}{5} ÷ 2 ÷ \frac{1}{5} = \frac{1}{2}$
$\frac{1}{8} ÷ \frac{3}{4} = \frac{1}{6}$
$\frac{7}{12} ÷ \frac{3}{7} = \frac{49}{36}$
$\frac{13}{9} ÷ \frac{26}{27} = \frac{3}{2}$
$15 ÷ \frac{3}{5} = 25$
$\frac{1}{4} ÷ \frac{3}{2} = \frac{1}{6}$
$\frac{1}{4} ÷ \frac{4}{5} = \frac{5}{16}$
$\frac{2}{13} × 26 = 4$
$12 ÷ \frac{2}{3} = 18$
$1 ÷ \frac{2}{5} = \frac{5}{2}$
$\frac{1}{5} ÷ \frac{5}{6} = \frac{6}{25}$
$48 × \frac{11}{16} = 33$
$\frac{5}{7} ÷ 1\frac{5}{6} = \frac{30}{77}$
$\frac{3}{11} ÷ \frac{2}{11} = \frac{3}{2}$
$\frac{5}{12} × 18 = \frac{15}{2}$
$\frac{1}{5} ÷ 2 ÷ \frac{1}{5} = \frac{1}{2}$
$\frac{1}{8} ÷ \frac{3}{4} = \frac{1}{6}$
$\frac{7}{12} ÷ \frac{3}{7} = \frac{49}{36}$
$\frac{13}{9} ÷ \frac{26}{27} = \frac{3}{2}$
$15 ÷ \frac{3}{5} = 25$
$\frac{1}{4} ÷ \frac{3}{2} = \frac{1}{6}$
$\frac{1}{4} ÷ \frac{4}{5} = \frac{5}{16}$
$\frac{2}{13} × 26 = 4$
$12 ÷ \frac{2}{3} = 18$
$1 ÷ \frac{2}{5} = \frac{5}{2}$
$\frac{1}{5} ÷ \frac{5}{6} = \frac{6}{25}$
$48 × \frac{11}{16} = 33$
$\frac{5}{7} ÷ 1\frac{5}{6} = \frac{30}{77}$
$\frac{3}{11} ÷ \frac{2}{11} = \frac{3}{2}$
2.计算下面各题。
$\frac{2}{3} ÷ \frac{1}{15} × \frac{5}{6}$
$\frac{6}{7} ÷ 12 + \frac{1}{7} ÷ 12$
$\frac{2}{3} ÷ ( \frac{14}{15} ÷ \frac{7}{8} )$
$\frac{2}{3} ÷ \frac{1}{15} × \frac{5}{6}$
$\frac{6}{7} ÷ 12 + \frac{1}{7} ÷ 12$
$\frac{2}{3} ÷ ( \frac{14}{15} ÷ \frac{7}{8} )$
答案
$\frac{2}{3} ÷ \frac{1}{15} × \frac{5}{6}$
$= \frac{2}{3} × 15 × \frac{5}{6}$
$= 10 × \frac{5}{6}$
$= \frac{25}{3}$
$\frac{6}{7} ÷ 12 + \frac{1}{7} ÷ 12$
$= \frac{6}{7} × \frac{1}{12} + \frac{1}{7} × \frac{1}{12}$
$= (\frac{6}{7} + \frac{1}{7}) × \frac{1}{12}$
$= 1 × \frac{1}{12}$
$= \frac{1}{12}$
$\frac{2}{3} ÷ (\frac{14}{15} ÷ \frac{7}{8})$
$= \frac{2}{3} ÷ (\frac{14}{15} × \frac{8}{7})$
$= \frac{2}{3} ÷ \frac{16}{15}$
$= \frac{2}{3} × \frac{15}{16}$
$= \frac{5}{8}$
$= \frac{2}{3} × 15 × \frac{5}{6}$
$= 10 × \frac{5}{6}$
$= \frac{25}{3}$
$\frac{6}{7} ÷ 12 + \frac{1}{7} ÷ 12$
$= \frac{6}{7} × \frac{1}{12} + \frac{1}{7} × \frac{1}{12}$
$= (\frac{6}{7} + \frac{1}{7}) × \frac{1}{12}$
$= 1 × \frac{1}{12}$
$= \frac{1}{12}$
$\frac{2}{3} ÷ (\frac{14}{15} ÷ \frac{7}{8})$
$= \frac{2}{3} ÷ (\frac{14}{15} × \frac{8}{7})$
$= \frac{2}{3} ÷ \frac{16}{15}$
$= \frac{2}{3} × \frac{15}{16}$
$= \frac{5}{8}$
3. 想一想,填一填。
观察 $\frac{2}{5} × \frac{b}{a}$ 和 $\frac{2}{5} ÷ \frac{b}{a}$($a、b ≠ 0$)两个算式,想一想:
(1)如果 $\frac{2}{5} × \frac{b}{a} > \frac{2}{5} ÷ \frac{b}{a}$,那么 $a ◯ b$;
(2)如果 $\frac{2}{5} × \frac{b}{a} = \frac{2}{5} ÷ \frac{b}{a}$,那么 $a ◯ b$;
(3)如果 $\frac{2}{5} × \frac{b}{a} < \frac{2}{5} ÷ \frac{b}{a}$,那么 $a ◯ b$。
观察 $\frac{2}{5} × \frac{b}{a}$ 和 $\frac{2}{5} ÷ \frac{b}{a}$($a、b ≠ 0$)两个算式,想一想:
(1)如果 $\frac{2}{5} × \frac{b}{a} > \frac{2}{5} ÷ \frac{b}{a}$,那么 $a ◯ b$;
(2)如果 $\frac{2}{5} × \frac{b}{a} = \frac{2}{5} ÷ \frac{b}{a}$,那么 $a ◯ b$;
(3)如果 $\frac{2}{5} × \frac{b}{a} < \frac{2}{5} ÷ \frac{b}{a}$,那么 $a ◯ b$。
答案
$\frac{2}{5} ÷ \frac{b}{a} = \frac{2}{5} × \frac{a}{b}$
(1)
$\frac{2}{5} × \frac{b}{a} > \frac{2}{5} × \frac{a}{b}$
$\frac{b}{a} > \frac{a}{b}$
$b > a$
$a < b$
(2)
$\frac{2}{5} × \frac{b}{a} = \frac{2}{5} × \frac{a}{b}$
$\frac{b}{a} = 1$
$a = b$
(3)
$\frac{2}{5} × \frac{b}{a} < \frac{2}{5} × \frac{a}{b}$
$\frac{b}{a} < 1$
$a > b$
答:(1)$a < b$;(2)$a = b$;(3)$a > b$。
(1)
$\frac{2}{5} × \frac{b}{a} > \frac{2}{5} × \frac{a}{b}$
$\frac{b}{a} > \frac{a}{b}$
$b > a$
$a < b$
(2)
$\frac{2}{5} × \frac{b}{a} = \frac{2}{5} × \frac{a}{b}$
$\frac{b}{a} = 1$
$a = b$
(3)
$\frac{2}{5} × \frac{b}{a} < \frac{2}{5} × \frac{a}{b}$
$\frac{b}{a} < 1$
$a > b$
答:(1)$a < b$;(2)$a = b$;(3)$a > b$。
一辆客车从甲地开往乙地,一辆货车从乙地开往甲地。客车行驶完全程要8小时,货车行驶完全程要10小时。客车先行驶2小时后货车再出发。货车出发几小时后两车相遇?
反思 我错了()道题。
自我评价:
反思 我错了()道题。
自我评价:
答案
把全程看作单位“1”。
$(1 - \frac{1}{8}×2)÷(\frac{1}{8} + \frac{1}{10})$
$= \frac{3}{4}÷\frac{9}{40}$
$= \frac{10}{3}$(小时)
答:货车出发$\frac{10}{3}$小时后两车相遇。
$(1 - \frac{1}{8}×2)÷(\frac{1}{8} + \frac{1}{10})$
$= \frac{3}{4}÷\frac{9}{40}$
$= \frac{10}{3}$(小时)
答:货车出发$\frac{10}{3}$小时后两车相遇。
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