Find the sum:
$(i)$. $\frac{5}{4}+(-\frac{11}{4})$
$(ii)$. $\frac{5}{3}+\frac{3}{5}$
$(iii)$. $\frac{-9}{10}+\ \frac{22}{15}$
$(iv)$. $\frac{-3}{11}+\frac{5}{9}$
$(v)$. $\frac{-8}{19}+(-\frac{2}{57})$
$(vi)$. $-\frac{2}{3}+0$
$(vii)$. $-2\frac{1}{3}\ +\ 4\frac{3}{5}$
Given: $(i)$. $\frac{5}{4}+(-\frac{11}{4})$
$(ii)$. $\frac{5}{3}+\frac{3}{5}$
$(iii)$. $\frac{-9}{10}+\ \frac{22}{15}$
$(iv)$. $\frac{-3}{-11}+\frac{5}{9}$
$(v)$. $\frac{-8}{19}+(-\frac{2}{57})$
$(vi)$. $-\frac{2}{3}+0$
$(vii)$. $-2\frac{1}{3}\ +\ 4\frac{3}{5}$
To do: To find the sum of the given expressions.
Solution: $(i)$. $\frac{5}{4}+(-\frac{11}{4})$
$=\frac{5}{4}-\frac{11}{4}$
$=\frac{5-11}{4}$
$=\frac{-6}{4}$
$(ii)$. $\frac{5}{3}+\frac{3}{5}$
$=\frac{5\times 5}{3\times 5}+\frac{3\times 3}{5\times 3}$ [On taking LCM of 3 and 5, we obtain 15]
$=\frac{25}{15}+\frac{9}{15}$
$=\frac{25+9}{15}$
$=\frac{34}{15}$
$(iii)$. $\frac{-9}{10}+\ \frac{22}{15}$
$=\frac{-9\times 3}{10\times 3}+\frac{22\times 2}{15\times 2}$ [on taking LCM of 10 and 15, we obtain 30]
$=\frac{-27}{30}+\frac{44}{30}$
$=\frac{-27+44}{30}$
$=\frac{13}{30}$
$(iv)$. $\frac{-3}{-11}+\frac{5}{9}$
$=\frac{3\times 9}{11\times 9}+\frac{5\times 11}{9\times 11}$ [On taking LCM of 11 and 9 we obtain 99]
$=\frac{27}{99}+\frac{55}{99}$
$=\frac{27+55}{99}$
$=\frac{82}{99}$
$(v)$. $\frac{-8}{19}+(-\frac{2}{57})$
$=\frac{-8\times 3}{19\times 3}-\frac{2\times 1}{57\times 1}$ [On taking LCM of 19 and 57 we obtain 57]
$=-\frac{24}{57}-\frac{2}{57}$
$=-(\frac{24}{57}+\frac{2}{57}$)
$=-(\frac{24+2}{57})$
$=-\frac{26}{57}$
$(vi)$. $-\frac{2}{3}+0$
$=-\frac{2\times 1}{3\times 1}+\frac{0\times 3}{1\times 3}$ [On taking LCM of 3 and 1 we obtain 3]
$=-\frac{2}{3}+\frac{0}{3}$
$=-\frac{2-0}{3}$
$=-\frac{2}{3}$
$(vii)$. $-2\frac{1}{3}\ + 4\frac{3}{5}$
$=-\frac{2\times 3+1}{3}+\frac{5\times 4+3}{5}$
$=-\frac{7}{3}+\frac{23}{5}$
$=-\frac{7\times 5}{3\times 5}+\frac{23\times 3}{5\times 3}$ [On taking LCM of 3 and 5 we obtain 15]
$=-\frac{35}{15}+\frac{69}{15}$
$=\frac{-35+69}{15}$
$=\frac{34}{15}$
Related Articles
- 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) \( \frac{3}{8}-\frac{-2}{9}+\frac{-5}{36} \)
- Find the product:$(i)$. $\frac{9}{2}\times(-\frac{7}{4})$$(ii)$. $\frac{3}{10}\times(-9)$$(iii)$. $-\frac{6}{5}\times\frac{9}{11}$$(iv)$. $\frac{3}{7}\times(-\frac{2}{5})$$(v)$. $\frac{3}{11}\times\ \frac{2}{5}$$(vi)$. $\frac{3}{-5}\times(-\frac{5}{3})$
- Simplify:(i) \( \frac{8}{9}+\frac{-11}{5} \)(ii) \( 3+\frac{5}{-7} \)(iii) \( \frac{1}{-12} \) and \( \frac{2}{-15} \)(iv) \( \frac{-8}{19}+\frac{-4}{57} \)(v) \( \frac{7}{9}+\frac{3}{-4} \)(vi) \( \frac{5}{26}+\frac{11}{-39} \)(vii) \( \frac{-16}{9}+\frac{-5}{12} \)(viii) \( \frac{-13}{8}+\frac{5}{36} \)(ix) \( 0+\frac{-3}{5} \)(x) \( 1+\frac{-4}{5} \)(xi) \( \frac{-5}{16}+\frac{7}{24} \)
- Re-arrange suitably and find the sum in each of the following:(i) \( \frac{11}{12}+\frac{-17}{3}+\frac{11}{2}+\frac{-25}{2} \)(ii) \( \frac{-6}{7}+\frac{-5}{6}+\frac{-4}{9}+\frac{-15}{7} \)(iii) \( \frac{3}{5}+\frac{7}{3}+\frac{9}{5}+\frac{-13}{15}+\frac{-7}{3} \)(iv) \( \frac{4}{13}+\frac{-5}{8}+\frac{-8}{13}+\frac{9}{13} \)(v) \( \frac{2}{3}+\frac{-4}{5}+\frac{1}{3}+\frac{2}{5} \)(vi) \( \frac{1}{8}+\frac{5}{12}+\frac{2}{7}+\frac{7}{12}+\frac{9}{7}+\frac{-5}{16} \)
- 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) $2\frac{1}{5}\div1\frac{1}{5}$
- Multiply:(i) \( \frac{7}{11} \) by \( \frac{5}{4} \)(ii) \( \frac{5}{7} \) by \( \frac{-3}{4} \)(iii) \( \frac{-2}{9} \) by \( \frac{5}{11} \)(iv) \( \frac{-3}{17} \) by \( \frac{-5}{-4} \)(v) \( \frac{9}{-7} \) by \( \frac{36}{-11} \)(vi) \( \frac{-11}{13} \) by \( \frac{-21}{7} \)(vii)\( -\frac{3}{5} \) by \( -\frac{4}{7} \)(viii) \( -\frac{15}{11} \) by 7
- 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) $3\frac{4}{7}\times\frac{3}{5}$
- Simplify each of the following and write as a rational number of the form:(i) \( \frac{3}{4}+\frac{5}{6}+\frac{-7}{8} \)(ii) \( \frac{2}{3}+\frac{-5}{6}+\frac{-7}{9} \)(iii) \( \frac{-11}{2}+\frac{7}{6}+\frac{-5}{8} \)(iv) \( \frac{-4}{5}+\frac{-7}{10}+\frac{-8}{15} \)(v) \( \frac{-9}{10}+\frac{22}{15}+\frac{13}{-20} \)(vi) \( \frac{5}{3}+\frac{3}{-2}+\frac{-7}{3}+3 \)
- Fill in the blanks:(i) \( -4 \times \frac{7}{9}=\frac{7}{9} \times -4 \)(ii) \( \frac{5}{11} \times \frac{-3}{8}=\frac{-3}{8} \times\frac{5}{11} \)(iii) \( \frac{1}{2} \times\left(\frac{3}{4}+\frac{-5}{12}\right)=\frac{1}{2} \times(\frac{3}{4})+\frac{1}{2} \times \frac{-5}{12}\)(iv) $\frac{-4}{5} \times(\frac{5}{7} \times \frac{-8}{9})=(\frac{-4}{5} \times$____ ) $\times\frac{-8}{9}$
- 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)$. $-3\frac{2}{7\ },\ -3\frac{4}{5}$
- Multiply and reduce to lowest form (if\ possible):(i) $\frac{2}{3}\times2\frac{2}{3}$(ii) $\frac{2}{7}\times\frac{7}{9}$(iii) $\frac{3}{8}\times\frac{6}{4}$(iv) $\frac{9}{5}\times\frac{3}{5}$(v) $\frac{1}{3}\times\frac{15}{8}$(vi) $\frac{11}{2}\times\frac{3}{10}$(vii) $\frac{4}{5}\times\frac{12}{7}$
- 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) \( \frac{4}{3}-\frac{1}{2} \)
- 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)$. $\frac{-3}{7},\ \frac{-3}{2},\ \frac{-3}{4}$
- Express each of the following as a rational number of the form $\frac{p}{q}$(i) \( -\frac{8}{3}+\frac{-1}{4}+\frac{-11}{6}+\frac{3}{8}-3 \)(ii) \( \frac{6}{7}+1+\frac{-7}{9}+\frac{19}{21}+\frac{-12}{7} \)(iii) \( \frac{15}{2}+\frac{9}{8}+\frac{-11}{3}+6+\frac{-7}{6} \)(iv) \( \frac{-7}{4}+0+\frac{-9}{5}+\frac{19}{10}+\frac{11}{14} \)(v) \( \frac{-7}{4}+\frac{5}{3}+\frac{-1}{2}+\frac{-5}{6}+2 \)
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