Đáp án:$\dfrac{x}{{30}} \in \left\{ {\dfrac{9}{{30}};\dfrac{{10}}{{30}}} \right\}$
Giải thích các bước giải:
Gọi tử số là x
Ta có: phân số cần tìm là: $\dfrac{x}{{30}}$
Theo bài ra ta có:
$\begin{array}{l}\dfrac{5}{{17}} < \dfrac{x}{{30}} < \dfrac{6}{{17}}\\ \Leftrightarrow \dfrac{{5.30}}{{17.30}} < \dfrac{{x.17}}{{30.17}} < \dfrac{{6.30}}{{17.30}}\\ \Leftrightarrow 150 < 17x < 180\\ \Leftrightarrow 17x \in \left\{ {153;170} \right\}\\ \Leftrightarrow x \in \left\{ {9;10} \right\}\\ \Leftrightarrow \dfrac{x}{{30}} \in \left\{ {\dfrac{9}{{30}};\dfrac{{10}}{{30}}} \right\}\end{array}$
Đáp án + Giải thích các bước giải:
Gọi phân số cần tìm là: `x/30`
Ta có:
`5/17 < x/30 < 6/17`
`⇒ (5 . 30)/(17. 30) < (17x)/(17.30) < (6 . 30)/(17 . 30)`
`⇒ 150 < 17x < 180`
`⇒ 150/17 < x < 180/17`
Mà `150/17 < 153/17 ⇒ 150/17 < 9`
`180/17 > 170/17 ⇒ 180/17 > 10`
`⇒ 9 ≤ x ≤ 10`
`⇒ x \in {9 ; 10}`
Vậy phân số cần tìm là: `9/30 ; 10/30`
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