Addition of Rational Numbers

Q.

From a rope $11m$ long, two pieces of lengths $2\frac{3}{5}m$ and $3\frac{3}{10}m$ are cut off. What is the length of the remaining rope?

Q.

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) $\frac{1}{8}+\frac{5}{12}+\frac{2}{7}+\frac{7}{12}+\frac{9}{7}+\frac{-5}{16}$

Q.

What number should be subtracted from $\frac{-3}{5}\text{to get}-2?$

(a) $-\frac{7}{5}$

(b) $-\frac{13}{5}$

(c) $\frac{13}{5}$

(d) $\frac{7}{5}$

Q.

Add the following rational numbers:
(i) $\frac{3}{4}$ and $\frac{-3}{5}$
(ii) $\frac{5}{8}$ and $\frac{-7}{12}$
(iii) $\frac{-8}{9}$ and $\frac{11}{6}$
(iv) $\frac{-5}{16}$ and $\frac{7}{24}$
(v) $\frac{7}{-18}$ and $\frac{8}{27}$
(vi) $\frac{1}{-12}$ and $\frac{2}{-15}$
(vii) $-1$ and $\frac{3}{4}$
(viii) $2$ and $\frac{-5}{4}$
(ix) $0$ and $\frac{-2}{5}$

Q.

$\frac{2}{3}+\frac{-4}{5}+\frac{7}{15}+\frac{-11}{20}=?$

(a) $-\frac{1}{5}$

(b) $-\frac{4}{15}$

(c) $-\frac{13}{60}$

(d) $-\frac{7}{30}$

Q.

On one day a rickshaw puller earned Rs 80. Out of his earnings he spent Rs. $13\frac{3}{5}$ on tea and snacks Rs. $25\frac{1}{2}$ on food and Rs. $4\frac{2}{5}$ on repairs of the rickshaw. How much did he save on that day ?

Q.

Add the following rational numbers :

(i) $\frac{-2}{5}$ and $\frac{4}{5}$ (ii) $\frac{-6}{11}$ and $\frac{-4}{11}$ (iii) $\frac{-11}{8}$ and $\frac{5}{8}$

(iv) $\frac{-7}{3}$ and $\frac{1}{3}$ (v) $\frac{5}{6}$ and $\frac{-1}{6}$ (iv) $\frac{-17}{15}$ and $\frac{-1}{15}$

Q.

$\left(i\right)\frac{3}{7}+\frac{-4}{9}-\frac{-11}{7}-\frac{7}{9}\left(ii\right)\frac{2}{3}+\frac{-4}{5}-\frac{1}{3}-\frac{2}{5}\left(iii\right)\frac{4}{7}-\frac{-8}{9}-\frac{-13}{7}+\frac{17}{9}$

Q.

The sum of two numbers is $\frac{-1}{3}$. If one of the numbers is $\frac{-12}{3}$, find the other.

Q. Question 112(iv)
Simplify:
$\frac{7}{8}+\frac{1}{16}-\frac{1}{12}$

Q.

Add and express the sum as mixed fraction: (i)$\frac{-12}{5}and\frac{43}{10}$ (ii)$\frac{24}{7}and\frac{-11}{4}$ (iii)$\frac{-31}{6}and\frac{-27}{8}$ (iv)$\frac{101}{6}and\frac{7}{8}$

Q. Question 112(i)
Simplify
$\frac{32}{5}+\frac{23}{11}\times \frac{22}{15}$

Q.

Evaluate :

$\left(i\right)\frac{3}{7}+\frac{-4}{9}+\frac{-11}{7}+\frac{7}{9}\left(ii\right)\frac{2}{3}+\frac{-4}{5}+\frac{1}{3}+\frac{2}{5}\left(iii\right)\frac{4}{7}+0+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{9}\left(iv\right)\frac{3}{8}+\frac{-5}{12}+\frac{3}{7}+\frac{3}{12}+\frac{-5}{8}+\frac{-2}{7}$

Q.

$\left(i\right)\text{What should be subtracted from -2 to get}\frac{3}{8}?\left(ii\right)\text{What should be added to -2 to get}\frac{3}{8}?$

Q. Question 1
If you subtract $\frac{1}{2}$ from a number and multiply the result by $\frac{1}{2}$, you get $\frac{1}{8}$. what is the number?

Q.

Evaluate : $\left(i\right)\frac{5}{9}+\frac{-7}{6}\left(ii\right)4+\frac{3}{-5}\left(iii\right)\frac{1}{-15}+\frac{5}{-12}\left(iv\right)\frac{5}{9}+\frac{3}{-4}\left(v\right)\frac{-8}{9}+\frac{-5}{12}\left(vi\right)0+\frac{-2}{7}\left(vii\right)\frac{5}{-11}+0\left(viii\right)2+\frac{-3}{5}\left(ix\right)\frac{4}{-9}+1$

Q.

$(\frac{7}{-26}+\frac{16}{39})=?$

(a) $\frac{11}{78}$

(b) $\frac{-11}{78}$

(c) $\frac{11}{39}$

(d) $\frac{-11}{39}$

Q.

The sum of two numbers is 9. If one of the numbers is 3, find the other.

Q. Question 112(iii)
Simplify:
$\frac{3}{7}+\frac{-2}{21}\times \frac{-5}{6}$

Q.

$(\frac{31}{-4}+\frac{-5}{8})=?$

(a) $\frac{67}{8}$

(b) $\frac{57}{8}$

(c) $\frac{-57}{8}$

(d) $\frac{-67}{8}$

Q. Question 104
Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.

Q.

Add the following rational numbers:

(i) $\frac{-5}{7}and\frac{3}{7}$

(ii) $\frac{-15}{4}and\frac{7}{4}$

(iii) $\frac{-8}{11}and\frac{-4}{11}$

(iv) $\frac{6}{13}and\frac{-9}{13}$

Q.

Find the sum of the rational numbers
$\frac{-7}{19}and\frac{-2}{57}.$

1. $\frac{-21}{57}$

2. $\frac{-23}{57}$

3. $\frac{-22}{47}$

4. $\frac{-32}{47}$

Q. Add the following rational numbers:​

(vii) $\frac{-5}{16}\text{and}\frac{7}{24}$

Q. How do you evaluate ${}^3{P}_1$?

Q. Question 112(iii)
Simplify:
$\frac{3}{7}+\frac{-2}{21}\times \frac{-5}{6}$

Q.

source $\left(i\right)\frac{8}{9}+\frac{-11}{6}\left(ii\right)3+\frac{5}{-7}\left(iii\right)\frac{1}{-12}and\frac{2}{-15}\left(iv\right)\frac{-8}{19}+\frac{-4}{57}\left(v\right)\frac{7}{9}+\frac{3}{-4}\left(vi\right)\frac{5}{26}+\frac{11}{-39}\left(vii\right)\frac{-16}{9}+\frac{-5}{12}\left(viii\right)\frac{-13}{8}+\frac{5}{36}\left(ix\right)0+\frac{-3}{5}\left(x\right)1+\frac{-4}{5}\left(xi\right)\frac{-5}{16}+\frac{7}{24}$

Q. Question 112(i)
Simplify
$\frac{32}{5}+\frac{23}{11}\times \frac{22}{15}$

Q. Give one example each to show that the rational numbers are closed under addition, subtraction and multiplication. Are rational numbers closed under division? Give two examples in support of your answer.

Q. Divide the number $26244$ by the smallest number so that the quotient is a perfect cube.