Find 7 rational numbers between 1-3 and 1-2-

The correct option is A 31/90,16/45,11/30,17/45,7/18,2/5,37/90We can write 1/3=1×30/3×30=30/90 1/2=1×45/2×45=45/90 ∴30/90 lt;31/90..... lt;35/90......45/ ...

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Standard VIII

Mathematics

Rational Numbers between Two Rational Numbers

Find 7 ration...

Question

Find 7 rational numbers between $\frac{1}{3}$ and $\frac{1}{2}$ .

\frac{31}{90}, \frac{16}{45}, \frac{11}{30}, \frac{17}{45}, \frac{7}{18}, \frac{2}{5}, \frac{37}{90}

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\frac{30}{90}, \frac{16}{45}, \frac{11}{30}, \frac{17}{45}, \frac{7}{18}, \frac{2}{5}, \frac{37}{90}

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\frac{31}{90}, \frac{16}{45}, \frac{29}{30}, \frac{17}{45}, \frac{7}{18}, \frac{2}{5}, \frac{37}{90}

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\frac{31}{90}, \frac{32}{45}, \frac{11}{30}, \frac{17}{45}, \frac{7}{18}, \frac{4}{5}, \frac{37}{90}

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Solution

The correct option is A $\frac{31}{90}, \frac{16}{45}, \frac{11}{30}, \frac{17}{45}, \frac{7}{18}, \frac{2}{5}, \frac{37}{90}$
We can write $\frac{1}{3} = \frac{1 \times 30}{3 \times 30} = \frac{30}{90}$

$\frac{1}{2} = \frac{1 \times 45}{2 \times 45} = \frac{45}{90}$

$∴ \frac{30}{90} < \frac{31}{90} . . . . . < \frac{35}{90} . . . . . . \frac{45}{90}$
Thus, the required rational numbers between $\frac{1}{3}$ and $\frac{1}{2}$ are
$\frac{31}{90}, \frac{32}{90}, \frac{33}{90}, \frac{34}{90}, \frac{35}{90}, \frac{36}{90}, \frac{37}{90}$

Simplifying them we have,
$\frac{31}{90}, \frac{16}{45}, \frac{11}{30}, \frac{17}{45}, \frac{7}{18}, \frac{2}{5}, \frac{37}{90}$

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Similar questions

Compare the following rational numbers and choose the correct option(s):
$\frac{4}{- 9}$ , $\frac{5}{- 12}$ , $\frac{7}{- 18}$ , $\frac{2}{- 3}$

Q. Which of the rational numbers

\frac{4}{- 3}

\frac{5}{- 6}

\frac{7}{- 18}

\frac{2}{- 12}

is the smallest?

Q. Arrange the following rational numbers in ascending order:
(i)

\frac{3}{5}, \frac{- 17}{- 30}, \frac{8}{- 15}, \frac{- 7}{10}

(ii)

\frac{- 4}{9}, \frac{5}{- 12}, \frac{7}{- 18}, \frac{2}{- 3}

Q. A plane

x + y + z = 1

intersects with a sphere which passes through the origin. The image of the center of the sphere about the plane lies on the line

6 x + 8 = 6 y + 8 = - 3 z - 4

. If the area of the cross section is

16 π

, then

Q. Find

3

rational numbers between

\frac{1}{6}

and

\frac{1}{7}

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Find 7 rational numbers between 13 and 12.

The correct option is A 3190,1645,1130,1745,718,25,3790We can write 13=1×303×30=3090 12=1×452×45=4590 ∴3090<3190.....<3590......4590 Thus, the required rational numbers between 13 and 12 are 3190,3290,3390,3490,3590,3690,3790 Simplifying them we have, 3190,1645,1130,1745,718,25,3790

Find 7 rational numbers between $\frac{1}{3}$ and $\frac{1}{2}$ .