Question

Find 5 rational numbers between 1/8 and 1/9

Answer 1

Answer:

$5 \: rational\: numbers \: between \\\frac{1}{8}\: and \:\frac{1}{9}\:are$

$\frac{49}{432},\frac{50}{432},\frac{51}{432},\frac{52}{432},\frac{53}{432}$

Step-by-step explanation:

$Given \: two \: rational \: numbers \: are \\\frac{1}{8} \:and \: \frac{1}{9}.$

/* Make them like fractions , we get

$\frac{1}{8}=\frac{1\times 9}{8\times 9}=\frac{9}{72} \: ---(1)$

$\frac{1}{9}=\frac{1\times 8}{9\times 8}=\frac{8}{72} \: ---(2)$

Since , we want 5 rational numbers , we multiply numerator and denominator by 5+1 = 6 , we get

$\frac{1}{8}=\frac{9}{72}\\=\frac{9\times 6}{72\times 6}=\frac{54}{432} \: ---(3)$

$\frac{1}{9}=\frac{8}{72}\\=\frac{8\times 6}{72\times 6}=\frac{48}{432} \: ---(4)$

$Now,\\5 \: rational\: numbers \: between \\\frac{1}{8}\: and \:\frac{1}{9}\:are$

$\frac{1}{9}=\frac{48}{432}\:<\left(\frac{49}{432},\frac{50}{432},\frac{51}{432},\frac{52}{432},\frac{53}{432}\right)< \frac{54}{432}=\frac{1}{8}$

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