What rational number lies exactly halfway between 23 and 34-

The correct option is E 1724 Consider 3 × 4 = 12 , #160;So, 23 = 812 34 = 912 Multiplying the numerator and denominator by 2 : 1 ...

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Standard IX

Mathematics

Rational Numbers

What rational...

Question

What rational number lies exactly halfway between $\frac{2}{3}$ and $\frac{3}{4}$ ?

\frac{3}{5}

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\frac{5}{6}

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\frac{7}{12}

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\frac{9}{16}

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\frac{17}{24}

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Solution

The correct option is E $\frac{17}{24}$
Consider $3 \times 4 = 12$ ,

So, $\frac{2}{3} = \frac{8}{12}$

$\frac{3}{4} = \frac{9}{12}$
Multiplying the numerator and denominator by $2$ :

$\frac{16}{24}$ and $\frac{18}{24}$ .

The mid point is $\frac{17}{24}$
Hence option $E$ is correct.

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Similar questions

Question 93 (c)

Find a rational number exactly halfway between
$\frac{5}{- 13} a n d \frac{- 7}{9}$

Q. Write three rational numbers that lie between the two given numbers:

(1) \frac{2}{7}, \frac{6}{7}

(2) \frac{4}{5}, \frac{2}{3}

(3) - \frac{2}{3}, \frac{4}{5}

(4) \frac{7}{9}, - \frac{5}{9}

(5) \frac{- 3}{4}, \frac{+ 5}{4}

(6) \frac{7}{8}, \frac{- 5}{3}

(7) \frac{5}{7}, \frac{11}{7}

(8) 0, \frac{- 3}{4}

Question 93 (a)

Find a rational number exactly halfway between
$\frac{- 1}{3} a n d \frac{1}{3}$

Verify the following :

(i) $\frac{3}{7} \times (\frac{5}{6} + \frac{12}{13}) = (\frac{3}{7} \times \frac{5}{6}) + (\frac{3}{7} \times \frac{12}{13})$
(ii) $\frac{- 15}{4} \times (\frac{3}{7} + \frac{- 12}{5}) = (\frac{- 15}{4} \times \frac{3}{7}) + (\frac{- 15}{4} \times \frac{- 12}{5})$
(iii) $(\frac{- 8}{3} + \frac{- 13}{12}) \times \frac{5}{6} = (\frac{- 8}{3} \times \frac{5}{6}) + (\frac{- 13}{12} \times \frac{5}{6})$
(iv) $\frac{- 16}{7} \times (\frac{- 8}{9} + \frac{- 7}{6}) = (\frac{- 16}{7} \times \frac{- 8}{9}) + (\frac{- 16}{7} \times \frac{- 7}{6})$

Prove that:
(i) $\frac{1}{3 + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{3}} + \frac{1}{\sqrt{3} + 1} = 1$
(ii) $\frac{1}{1 + \sqrt{2}} + \frac{1}{\sqrt{2} + \sqrt{3}} + \frac{1}{\sqrt{3} + \sqrt{4}} + \frac{1}{\sqrt{4} + \sqrt{5}} + \frac{1}{\sqrt{5} + \sqrt{6}} + \frac{1}{\sqrt{6} + \sqrt{7}} + \frac{1}{\sqrt{7} + \sqrt{8}} + \frac{1}{\sqrt{8} + \sqrt{9}} = 2$

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What rational number lies exactly halfway between 23 and 34?

The correct option is E 1724Consider 3×4=12, So, 23=81234=912Multiplying the numerator and denominator by 2:1624 and 1824.The mid point is 1724Hence option E is correct.

What rational number lies exactly halfway between $\frac{2}{3}$ and $\frac{3}{4}$ ?

The correct option is E $\frac{17}{24}$
Consider $3 \times 4 = 12$ ,

So, $\frac{2}{3} = \frac{8}{12}$

$\frac{3}{4} = \frac{9}{12}$
Multiplying the numerator and denominator by $2$ :

$\frac{16}{24}$ and $\frac{18}{24}$ .

The mid point is $\frac{17}{24}$
Hence option $E$ is correct.