Insert 5 rational numbers between 1-3 and 5-9-

1/3 = 1 × 12/3 × 12 = 12/36 5/9 = 5 × 4/9 × 4 = 20/36 So, 5 rational numbers between them are 13/36, 14/36, 15/36, 16/36 and 17/36. ...

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Standard IX

Mathematics

Rational Numbers

Insert 5 rati...

Question

Insert 5 rational numbers between $\frac{1}{3}$ and $\frac{5}{9}$ .

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Solution

$\frac{1}{3} = \frac{1 \times 12}{3 \times 12} = \frac{12}{36}$

$\frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36}$

So, 5 rational numbers between them are $\frac{13}{36}$ , $\frac{14}{36}$ , $\frac{15}{36}$ , $\frac{16}{36}$ and $\frac{17}{36}$ .

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Insert 3 eqivalent rational numbers between $\frac{- 1}{2}$ and $\frac{1}{5}$ .

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Insert 5 rational numbers between 13 and 59.

13=1×123×12=1236 59=5×49×4=2036 So, 5 rational numbers between them are 1336, 1436, 1536, 1636 and 1736.

Insert 5 rational numbers between $\frac{1}{3}$ and $\frac{5}{9}$ .

$\frac{1}{3} = \frac{1 \times 12}{3 \times 12} = \frac{12}{36}$

$\frac{5}{9} = \frac{5 \times 4}{9 \times 4} = \frac{20}{36}$

So, 5 rational numbers between them are $\frac{13}{36}$ , $\frac{14}{36}$ , $\frac{15}{36}$ , $\frac{16}{36}$ and $\frac{17}{36}$ .