Question

The number 4/15 and 3/10 lie between 1/4 and 1/3

answer please​

Answer 1

$Given \: fractions \: \frac{4}{15} ,\:\frac{3}{10}$

$\frac{1}{4} \:and \: \frac{1}{3}$

$Find \: LCM \:of \:the \: denominators , we\:get$

2 | 15,10,4,3

____________

5 | 15, 5, 2 , 3

____________

**** 3 , 1, 2 , 3

$LCM \:of \: (15,10,4,3)$

$= 2 \times 5 \times 3 \times 2 \times 3$

$= 180$

$i) \frac{4}{15}$

$= \frac{4\times 12}{15\times 12}$

$= \frac{48}{180} \: --(1)$

$ii) \frac{3}{10}$

$= \frac{3\times 18}{10\times 18}$

$= \frac{54}{180} \: --(2)$

$iii) \frac{1}{4}$

$= \frac{ 45}{4\times 45}$

$= \frac{45}{180} \: --(3)$

$iv) \frac{1}{3}$

$= \frac{1\times 60}{3\times 60}$

$= \frac{60}{180} \: --(4)$

$\therefore \frac{45}{180} \lt \frac{48}{180}\lt \frac{54}{180}\lt \frac{60}{180}$

/* From (1), (2), (3) and (4) */

$\green { \frac{1}{4} \lt \frac{4}{15}\lt \frac{3}{10}\lt \frac{1}{3}}$

$\red{ The \: number \:\frac{4}{15} \:and}$

$\red{\frac{3}{10}\: lie \: between \: \frac{1}{4} }$

$\red{and \: \frac{1}{3} }$

$\green { Given \: statement \:is \: True }$

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