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1. 按规律在括号里填适当的数。
(1) $\frac{1}{2},\frac{1}{3},\frac{1}{6},\frac{1}{18}$, (
(2) $\frac{4}{5},\frac{2}{5},\frac{1}{5},\frac{1}{10}$, (
(3) $1,\frac{1}{2},\frac{3}{2},2$, (
(4) $\frac{1}{2},\frac{3}{4},\frac{9}{8},\frac{27}{16}$, (
(1) $\frac{1}{2},\frac{1}{3},\frac{1}{6},\frac{1}{18}$, (
$\frac{1}{108}$
), ($\frac{1}{1944}$
)。(2) $\frac{4}{5},\frac{2}{5},\frac{1}{5},\frac{1}{10}$, (
$\frac{1}{20}$
), ($\frac{1}{40}$
)。(3) $1,\frac{1}{2},\frac{3}{2},2$, (
$\frac{7}{2}$
), ($\frac{11}{2}$
)。(4) $\frac{1}{2},\frac{3}{4},\frac{9}{8},\frac{27}{16}$, (
$\frac{81}{32}$
), ($\frac{243}{64}$
)。
答案：
1.
(1)$\frac{1}{108}$ $\frac{1}{1944}$
(2)$\frac{1}{20}$ $\frac{1}{40}$
(3)$\frac{7}{2}$ $\frac{11}{2}$
(4)$\frac{81}{32}$ $\frac{243}{64}$
(1)$\frac{1}{108}$ $\frac{1}{1944}$
(2)$\frac{1}{20}$ $\frac{1}{40}$
(3)$\frac{7}{2}$ $\frac{11}{2}$
(4)$\frac{81}{32}$ $\frac{243}{64}$
2. 先观察,再填空。
$\frac{3}{2}= 1+\frac{1}{2}$ $\frac{5}{6}= \frac{1}{2}+\frac{1}{3}$ $\frac{9}{20}= \frac{(
$\frac{3}{2}= 1+\frac{1}{2}$ $\frac{5}{6}= \frac{1}{2}+\frac{1}{3}$ $\frac{9}{20}= \frac{(
1
)}{(4
)}+\frac{(1
)}{(5
)}$ $\frac{11}{30}= \frac{(1
)}{(5
)}+\frac{(1
)}{(6
)}$
答案：
2.$\frac{1}{4}$ $\frac{1}{5}$ $\frac{1}{5}$ $\frac{1}{6}$
3. 根据规律填空。
$\frac{1}{2}-\frac{1}{3}= \frac{1}{2×3}= \frac{1}{6},\frac{1}{3}-\frac{1}{4}= \frac{1}{3×4}= \frac{1}{12},\frac{1}{4}-\frac{1}{5}= \frac{1}{4×5}= \frac{1}{20},……$
(1) $\frac{1}{6}-\frac{1}{7}= $(
(2) $\frac{1}{2}×\frac{1}{3}+\frac{1}{3}×\frac{1}{4}+\frac{1}{4}×\frac{1}{5}+……+\frac{1}{19}×\frac{1}{20}= $(
$\frac{1}{2}-\frac{1}{3}= \frac{1}{2×3}= \frac{1}{6},\frac{1}{3}-\frac{1}{4}= \frac{1}{3×4}= \frac{1}{12},\frac{1}{4}-\frac{1}{5}= \frac{1}{4×5}= \frac{1}{20},……$
(1) $\frac{1}{6}-\frac{1}{7}= $(
$\frac{1}{6×7}$
)= ($\frac{1}{42}$
) $\frac{1}{14}-\frac{1}{15}= $($\frac{1}{14×15}$
)= ($\frac{1}{210}$
)(2) $\frac{1}{2}×\frac{1}{3}+\frac{1}{3}×\frac{1}{4}+\frac{1}{4}×\frac{1}{5}+……+\frac{1}{19}×\frac{1}{20}= $(
$\frac{9}{20}$
)
答案：
3.
(1)$\frac{1}{6×7}$ $\frac{1}{42}$ $\frac{1}{14×15}$ $\frac{1}{210}$
(2)$\frac{9}{20}$
(1)$\frac{1}{6×7}$ $\frac{1}{42}$ $\frac{1}{14×15}$ $\frac{1}{210}$
(2)$\frac{9}{20}$
4. 找规律,计算。
(1) $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+……+\frac{1}{9900}$
(2) 在$\frac{3}{2},\frac{5}{4},\frac{7}{6},\frac{9}{8},……$中,$\frac{2021}{2020}$是第几个数？
(1) $\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+……+\frac{1}{9900}$
(2) 在$\frac{3}{2},\frac{5}{4},\frac{7}{6},\frac{9}{8},……$中,$\frac{2021}{2020}$是第几个数？
答案：
4.
(1)$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\cdots\cdots+\frac{1}{9900}$
$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\cdots\cdots+\frac{1}{99}-\frac{1}{100}$
$=1-\frac{1}{100}$
$=\frac{99}{100}$
(2)$2020÷2=1010$ $\frac{2021}{2020}$是第1010个数。
(1)$\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\cdots\cdots+\frac{1}{9900}$
$=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\cdots\cdots+\frac{1}{99}-\frac{1}{100}$
$=1-\frac{1}{100}$
$=\frac{99}{100}$
(2)$2020÷2=1010$ $\frac{2021}{2020}$是第1010个数。
5. 观察下面的算式,找出规律,再填一填。
(1) $\frac{4}{3}÷8= \frac{1}{6}$
$\frac{2}{3}÷4= \frac{1}{6}$
$\frac{1}{3}÷2= \frac{1}{6}$
$\frac{1}{6}÷$
(2) $\frac{6}{5}÷3= \frac{2}{5}$
$\frac{4}{5}÷2= \frac{2}{5}$
$\frac{8}{15}÷\frac{4}{3}= \frac{2}{5}$
$\frac{16}{45}÷$
(1) $\frac{4}{3}÷8= \frac{1}{6}$
$\frac{2}{3}÷4= \frac{1}{6}$
$\frac{1}{3}÷2= \frac{1}{6}$
$\frac{1}{6}÷$
1
$=$$\frac{1}{6}$
$\frac{1}{12}$
$÷$$\frac{1}{2}$
$=$$\frac{1}{6}$
(2) $\frac{6}{5}÷3= \frac{2}{5}$
$\frac{4}{5}÷2= \frac{2}{5}$
$\frac{8}{15}÷\frac{4}{3}= \frac{2}{5}$
$\frac{16}{45}÷$
$\frac{8}{9}$
$=$$\frac{2}{5}$
$\frac{32}{135}$
$÷$$\frac{16}{27}$
$=$$\frac{2}{5}$
答案：
5.
(1)1 $\frac{1}{6}$ $\frac{1}{12}$ $\frac{1}{2}$ $\frac{1}{6}$
(2)$\frac{8}{9}$ $\frac{2}{5}$ $\frac{32}{135}$ $\frac{16}{27}$ $\frac{2}{5}$
(1)1 $\frac{1}{6}$ $\frac{1}{12}$ $\frac{1}{2}$ $\frac{1}{6}$
(2)$\frac{8}{9}$ $\frac{2}{5}$ $\frac{32}{135}$ $\frac{16}{27}$ $\frac{2}{5}$
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