Write the following rational numbers in ascending order:
$(i)$. $\frac{-3}{5},\ \frac{-2}{5},\ \frac{-1}{5}$
$(ii)$. $\frac{1}{3},\ \frac{-2}{9},\ \frac{-4}{3}$
$(iii)$. $\frac{-3}{7},\ \frac{-3}{2},\ \frac{-3}{4}$
Given:
$(i)$. $\frac{-3}{5},\ \frac{-2}{5},\ \frac{-1}{5}$
$(ii)$. $\frac{-1}{3},\ \frac{-2}{9},\ \frac{-4}{3}$
$(iii)$. $\frac{-3}{7},\ \frac{-3}{2},\ \frac{-3}{4}$
To do: To write the given rational numbers in ascending order.
Solution:
$(i)$. $-\frac{3}{5},\ -\frac{2}{5},\ -\frac{1}{5}$
Here, denominators are the same for each rational number. We just need to compare the numerators of the given rational numbers.
On arranging numerators of the given rational numbers in ascending order we have:
$-3$<$-2$ < $-1$
Therefore, the given rational number in ascending order is as below:
$-\frac{3}{5}$ < $-\frac{2}{5}$ < $-\frac{1}{5}$
$(ii).\ -\frac{1}{3},\ -\frac{2}{9},\ -\frac{4}{3}$
To write the given rational numbers in ascending order, first of all, their denominators have to be equal.
Taking L.C.M of the denominators $3,\ 9$ and $3$ is $9$
Therefore,
$-\frac{1}{3} = \frac{(-1\times 3)}{(3\times 3)} = -\frac{3}{9}$
$-\frac{2}{9} = \frac{(-2\times 1)}{(9\times 1)} = -\frac{2}{9}$
$-\frac{4}{3} = \frac{(-4\times 3)}{(3\times 3)} = -\frac{12}{9}$
On arranging the obtained fractions into ascending order we have,
$-\frac{12}{9}$ < $-\frac{3}{9}$ < $-\frac{2}{9}$
Or, $-\frac{4}{3}$ < $-\frac{1}{3}$ < $-\frac{2}{9}$
$(iii).\ -\frac{3}{7},\ -\frac{3}{2},\ -\frac{3}{4}$
To write the given rational numbers in ascending order, first of all, their denominators have to be equal.
Taking L.C.M of $7,\ 2$ and $4$ is $28$
So, $-\frac{3}{7} = \frac{(-3\times 4)}{(7\times 4)} = -\frac{12}{28}$
$-\frac{3}{2} = \frac{(-3\times 14)}{(2\times 14)} = -\frac{42}{28}$
$-\frac{3}{4} = \frac{(-3\times 7)}{(4\times 7)} = -\frac{21}{28}$
On arranging the obtained fractions into ascending order we have:
$-\frac{42}{28}$ < $-\frac{21}{28}$ < $-\frac{12}{28}$
Or, $-\frac{3}{2}$ < $-\frac{3}{4}$ < $-\frac{3}{7}$
Related Articles
- Solve(a) \( \frac{2}{3}+\frac{1}{7} \)(b) \( \frac{3}{10}+\frac{7}{15} \)(c) \( \frac{4}{9}+\frac{2}{7} \)(d) \( \frac{5}{7}+\frac{1}{3} \)(e) \( \frac{2}{5}+\frac{1}{6} \)(f) \( \frac{4}{5}+\frac{2}{3} \)(g) \( \frac{3}{4}-\frac{1}{3} \)(h) \( \frac{5}{6}-\frac{1}{3} \)(i) \( \frac{2}{3}+\frac{3}{4}+\frac{1}{2} \)(j) \( \frac{1}{2}+\frac{1}{3}+\frac{1}{6} \)(k) \( 1 \frac{1}{3}+3 \frac{2}{3} \)(l) \( 4 \frac{2}{3}+3 \frac{1}{4} \)(m) \( \frac{16}{5}-\frac{7}{5} \)(n) \( \frac{4}{3}-\frac{1}{2} \)
- Which is greater in each of the following:$(i)$. $\frac{2}{3},\ \frac{5}{2}$$(ii)$. $-\frac{5}{6},\ -\frac{4}{3}$$(iii)$. $-\frac{3}{4},\ \frac{2}{-3}$$(iv)$. $-\frac{1}{4},\ \frac{1}{4}$$(v)$. $-3\frac{2}{7\ },\ -3\frac{4}{5}$
- Solve:(i) $3-\frac{2}{5}$(ii) $4+\frac{7}{8}$(iii) $\frac{3}{5}+\frac{2}{7}$(iv) $\frac{9}{11}-\frac{4}{15}$(v) $\frac{7}{10}+\frac{2}{5}+\frac{3}{2}$(vi) $2\frac{2}{3}+3\frac{1}{2}$(vii) $8\frac{1}{2}-3\frac{5}{8}$
- Simplify:(i) \( \frac{-3}{2}+\frac{5}{4}-\frac{7}{4} \)(ii) \( \frac{5}{3}-\frac{7}{6}+\frac{-2}{3} \)(iii) \( \frac{5}{4}-\frac{7}{6}-\frac{-2}{3} \)(iv) \( \frac{-2}{5}-\frac{-3}{10}-\frac{-4}{7} \)(v) \( \frac{5}{6}+\frac{-2}{5}-\frac{-2}{15} \)(vi) \( \frac{3}{8}-\frac{-2}{9}+\frac{-5}{36} \)
- Multiply the following fractions:(i) $\frac{2}{5}\times5\frac{1}{4}$(ii) $6\frac{2}{5}\times\frac{7}{9}$(iii) $\frac{3}{2}\times5\frac{1}{3}$(iv) $\frac{5}{6}\times2\frac{3}{7}$(v) $3\frac{2}{5}\times\frac{4}{7}$(vi) $2\frac{3}{5}\times3$(vii) $3\frac{4}{7}\times\frac{3}{5}$
- Write the following in ascending order:$\frac{1}{2},\ \frac{4}{5},\ \frac{-2}{3},\ \frac{-1}{2},\ \frac{-5}{7}$.
- Find:(i) $\frac{2}{5}\div\frac{1}{2}$(ii) $\frac{4}{9}\div\frac{2}{3}$(iii) $\frac{3}{7}\div\frac{8}{7}$(iv) $2\frac{1}{3}\div\frac{3}{5}$(v) $3\frac{1}{2}\div\frac{8}{3}$(vi) $\frac{2}{5}\div1\frac{1}{2}$(vii) $3\frac{1}{5}\div1\frac{2}{3}$(viii) $2\frac{1}{5}\div1\frac{1}{5}$
- Find five rational numbers between.(i) \( \frac{2}{3} \) and \( \frac{4}{5} \)(ii) \( \frac{-3}{2} \) and \( \frac{5}{3} \)(iii) \( \frac{1}{4} \) and \( \frac{1}{2} \).
- Take away:(i) \( \frac{6}{5} x^{2}-\frac{4}{5} x^{3}+\frac{5}{6}+\frac{3}{2} x \) from \( \frac{x^{3}}{3}-\frac{5}{2} x^{2}+ \) \( \frac{3}{5} x+\frac{1}{4} \)(ii) \( \frac{5 a^{2}}{2}+\frac{3 a^{3}}{2}+\frac{a}{3}-\frac{6}{5} \) from \( \frac{1}{3} a^{3}-\frac{3}{4} a^{2}- \) \( \frac{5}{2} \)(iii) \( \frac{7}{4} x^{3}+\frac{3}{5} x^{2}+\frac{1}{2} x+\frac{9}{2} \) from \( \frac{7}{2}-\frac{x}{3}- \) \( \frac{x^{2}}{5} \)(iv) \( \frac{y^{3}}{3}+\frac{7}{3} y^{2}+\frac{1}{2} y+\frac{1}{2} \) from \( \frac{1}{3}-\frac{5}{3} y^{2} \)(v) \( \frac{2}{3} a c-\frac{5}{7} a b+\frac{2}{3} b c \) from \( \frac{3}{2} a b-\frac{7}{4} a c- \) \( \frac{5}{6} b c \)
- Prove that:\( \frac{2^{\frac{1}{2}} \times 3^{\frac{1}{3}} \times 4^{\frac{1}{4}}}{10^{\frac{-1}{5}} \times 5^{\frac{3}{5}}} \p \frac{3^{\frac{4}{3}} \times 5^{\frac{-7}{5}}}{4^{\frac{-3}{5}} \times 6}=10 \)
- Simplify:\( 5 \frac{1}{4} \p 2 \frac{1}{3}-4 \frac{2}{3} \p 5 \frac{1}{3} \times 3 \frac{1}{2} \)
- Find the sum:$(i)$. $\frac{5}{4}+(-\frac{11}{4})$$(ii)$. $\frac{5}{3}+\frac{3}{5}$$(iii)$. $\frac{-9}{10}+\ \frac{22}{15}$$(iv)$. $\frac{-3}{11}+\frac{5}{9}$$(v)$. $\frac{-8}{19}+(-\frac{2}{57})$$(vi)$. $-\frac{2}{3}+0$$(vii)$. $-2\frac{1}{3}\ +\ 4\frac{3}{5}$
- Find: (a) $\frac{1}{2}$ of (i) $2\frac{3}{4}$ (ii) $4\frac{2}{9}$(b) $\frac{5}{8}$ of (i) $3\frac{5}{6}$ (ii) $9\frac{2}{3}$
- Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:(i) \( \frac{2}{5}+\frac{7}{3}+\frac{-4}{5}+\frac{-1}{3} \)(ii) \( \frac{3}{7}+\frac{-4}{9}+\frac{-11}{7}+\frac{7}{9} \)(iii) \( \frac{2}{5}+\frac{8}{3}+\frac{-11}{15}+\frac{4}{5}+\frac{-2}{3} \)(iv) \( \frac{4}{7}+0+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{21} \)
- Find:(i) \( 9^{\frac{3}{2}} \)(ii) \( 32^{\frac{2}{5}} \)(iii) \( 16^{\frac{3}{4}} \)(iv) \( 125^{\frac{-1}{3}} \)
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies