Rd Sharma 2019 2020 Solutions for Class 8 Math Chapter 1 Rational Numbers are provided here with simple step-by-step explanations. These solutions for Rational Numbers are extremely popular among Class 8 students for Math Rational Numbers Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rd Sharma 2019 2020 Book of Class 8 Math Chapter 1 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rd Sharma 2019 2020 Solutions. All Rd Sharma 2019 2020 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

#### Question 1:

Verify commutativty of addition of rational numbers for each of the following pairs of rotional numbers:
(i)

(ii)

(iii)

(iv)

(v)

(vi)

#### Question 2:

Verify associativity of addition of rational numbers i.e., (x + y) + z = x + (y + z), when:
(i)
(ii)
(iii)
(iv)

#### Question 3:

Write the additive inverse of each of the following rational numbers:
(i) $\frac{-2}{17}$
(ii) $\frac{3}{-11}$
(iii) $\frac{-17}{5}$
(iv) $\frac{-11}{-25}$

#### Question 4:

Write the negative (additive inverse) of each of the following:
(i) $\frac{-2}{5}$
(ii) $\frac{7}{-9}$
(iii) $\frac{-16}{13}$
(iv) $\frac{-5}{1}$
(v) 0
(vi) 1
(vii) −1

#### Question 5:

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) $\frac{4}{7}+0+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{21}$

#### Question 6:

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

#### Question 1:

Subtract the first rational number from the second in each of the following:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)

#### Question 2:

Evaluate each of the following:
(i) $\frac{2}{3}-\frac{3}{5}$
(ii) $-\frac{4}{7}-\frac{2}{-3}$
(iii) $\frac{4}{7}-\frac{-5}{-7}$
(iv) $-2-\frac{5}{9}$
(v) $\frac{-3}{-8}-\frac{-2}{7}$
(vi) $\frac{-4}{13}-\frac{-5}{26}$
(vii) $\frac{-5}{14}-\frac{-2}{7}$
(viii) $\frac{13}{15}-\frac{12}{25}$
(ix) $\frac{-6}{13}-\frac{-7}{13}$
(x) $\frac{7}{24}-\frac{19}{36}$
(xi) $\frac{5}{63}-\frac{-8}{21}$

#### Question 3:

The sum of the two numbers is $\frac{5}{9}.$ If one of the numbers is $\frac{1}{3},$ find the other.

#### Question 4:

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

#### Question 5:

The sum of two numbers is $\frac{-4}{3}.$ If one of the numbers is −5, find the other.

#### Question 6:

The sum of two rational numbers is −8. If one of the numbers is $\frac{-15}{7},$ find the other.

#### Question 7:

What should be added to $\frac{-7}{8}$ so as to get $\frac{5}{9}?$

#### Question 8:

What number should be added to $\frac{-5}{11}$ so as to get $\frac{26}{33}?$

#### Question 9:

What number should be added to $\frac{-5}{7}$ to get $\frac{-2}{3}?$

#### Question 10:

What number should be subtracted from $\frac{-5}{3}$ to get $\frac{5}{6}?$

#### Question 11:

What number should be subtracted from $\frac{3}{7}$ to get $\frac{5}{4}?$

#### Question 12:

What should be added to $\left(\frac{2}{3}+\frac{3}{5}\right)$ to get $\frac{-2}{15}?$

#### Question 13:

What should be added to $\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{5}\right)$ to get 3?

#### Question 14:

What should be subtracted from $\left(\frac{3}{4}-\frac{2}{3}\right)$ to get $\frac{-1}{6}?$

#### Question 15:

Fill in the blanks:
(i)
(ii)
(iii)
(iv)

#### Question 1:

Simplify each of the following and write as a rational number of the form $\frac{p}{q}:$
(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) $\frac{5}{3}+\frac{3}{-2}+\frac{-7}{3}+3$

#### Question 2:

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) $\frac{-7}{4}+\frac{5}{3}+\frac{-1}{2}+\frac{-5}{6}+2$

#### Question 3:

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:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)

Multiply:
(i)

(ii)

(iii)

(iv)

(v)

(vi)

#### Question 3:

Simplify each of the following and express the result as a rational number in standard form:
(i) $\frac{-16}{21}×\frac{14}{5}$

(ii) $\frac{7}{6}×\frac{-3}{28}$

(iii) $\frac{-19}{36}×16$

(iv) $\frac{-13}{9}×\frac{27}{-26}$

(v) $\frac{-9}{16}×\frac{-64}{-27}$

(vi) $\frac{-50}{7}×\frac{14}{3}$

(vii) $\frac{-11}{9}×\frac{-81}{-88}$

(viii) $\frac{-5}{9}×\frac{72}{-25}$

#### Question 4:

Simplify:
(i) $\left(\frac{25}{8}×\frac{2}{5}\right)-\left(\frac{3}{5}×\frac{-10}{9}\right)$

(ii) $\left(\frac{1}{2}×\frac{1}{4}\right)+\left(\frac{1}{2}×6\right)$

(iii) $\left(-5×\frac{2}{15}\right)-\left(-6×\frac{2}{9}\right)$

(iv) $\left(\frac{-9}{4}×\frac{5}{3}\right)+\left(\frac{13}{2}×\frac{5}{6}\right)$

(v) $\left(\frac{-4}{3}×\frac{12}{-5}\right)+\left(\frac{3}{7}×\frac{21}{15}\right)$

(vi) $\left(\frac{13}{5}×\frac{8}{3}\right)-\left(\frac{-5}{2}×\frac{11}{3}\right)$

(vii) $\left(\frac{13}{7}×\frac{11}{26}\right)-\left(\frac{-4}{3}×\frac{5}{6}\right)$

(viii) $\left(\frac{8}{5}×\frac{-3}{2}\right)+\left(\frac{-3}{10}×\frac{11}{16}\right)$

#### Question 5:

Simplify:
(i) $\left(\frac{3}{2}×\frac{1}{6}\right)+\left(\frac{5}{3}×\frac{7}{2}\right)-\left(\frac{13}{8}×\frac{4}{3}\right)$

(ii) $\left(\frac{1}{4}×\frac{2}{7}\right)-\left(\frac{5}{14}×\frac{-2}{3}\right)+\left(\frac{3}{7}×\frac{9}{2}\right)$

(iii) $\left(\frac{13}{9}×\frac{-15}{2}\right)+\left(\frac{7}{3}×\frac{8}{5}\right)+\left(\frac{3}{5}×\frac{1}{2}\right)$

(iv) $\left(\frac{3}{11}×\frac{5}{6}\right)-\left(\frac{9}{12}×\frac{4}{3}\right)+\left(\frac{5}{13}×\frac{6}{15}\right)$

#### Question 1:

Verify the property: x × y = y × x by taking:
(i)
(ii)
(iii)
(iv)

#### Question 2:

Verify the property: x × (y × z) = (x × y) × z by taking:

(i)

(ii)

(iii)

(iv)

#### Question 3:

Verify the property: x × (y + z) = x × y + x × z by taking:

(i)

(ii)

(iii)

(iv)

#### Question 4:

Use the distributivity of multiplication of rational numbers over their addition to simplify:
(i) $\frac{3}{5}×\left(\frac{35}{24}+\frac{10}{1}\right)$

(ii) $\frac{-5}{4}×\left(\frac{8}{5}+\frac{16}{5}\right)$

(iii) $\frac{2}{7}×\left(\frac{7}{16}-\frac{21}{4}\right)$

(iv) $\frac{3}{4}×\left(\frac{8}{9}-40\right)$

#### Question 5:

Find the multiplicative inverse (reciprocal) of each of the following rational numbers:
(i) 9
(ii) −7
(iii) $\frac{12}{5}$
(iv) $\frac{-7}{9}$
(v) $\frac{-3}{-5}$
(vi) $\frac{2}{3}×\frac{9}{4}$
(vii) $\frac{-5}{8}×\frac{16}{15}$
(viii) $-2×\frac{-3}{5}$
(ix) −1
(x) $\frac{0}{3}$
(xi) 1

#### Question 6:

Name the property of multiplication of rational numbers illustrated by the following statements:
(i) $\frac{-5}{16}×\frac{8}{15}=\frac{8}{15}×\frac{-5}{16}$

(ii) $\frac{-17}{5}×9=9×\frac{-17}{5}$

(iii) $\frac{7}{4}×\left(\frac{-8}{3}+\frac{-13}{12}\right)=\frac{7}{4}×\frac{-8}{3}+\frac{7}{4}×\frac{-13}{12}$

(iv) $\frac{-5}{9}×\left(\frac{4}{15}×\frac{-9}{8}\right)=\left(\frac{-5}{9}×\frac{4}{15}\right)×\frac{-9}{8}$

(v) $\frac{13}{-17}×1=\frac{13}{-17}=1×\frac{13}{-17}$

(vi) $\frac{-11}{16}×\frac{16}{-11}=1$

(vii) $\frac{2}{13}×0=0=0×\frac{2}{13}$

(viii) $\frac{-3}{2}×\frac{5}{4}+\frac{-3}{2}×\frac{-7}{6}=\frac{-3}{2}×\left(\frac{5}{4}+\frac{-7}{6}\right)$

(i) Commutative property
(ii) Commutative property
(iii) Distributivity of multiplication over addition
(iv) Associativity of multiplication
(v) Existence of identity for multiplication
(vi) Existence of multiplicative inverse
(vii) Multiplication by 0
(viii) Distributive property

#### Question 7:

Fill in the blanks:
(i) The product of two positive rational numbers is always .....
(ii) The product of a positive rational number and a negative rational number is always .....
(iii) The product of two negative rational numbers is always .....
(iv) The reciprocal of a positive rational number is .....
(v) The reciprocal of a negative rational number is .....
(vi) Zero has ..... reciprocal.
(vii) The product of a rational number and its reciprocal is .....
(viii) The numbers ..... and ..... are their own reciprocals.
(ix) If a is reciprocal of b, then the reciprocal of b is .....
(x) The number 0 is ..... the reciprocal of any number.
(xi) Reciprocal of is .....
(xii) (17 × 12)−1 = 17−1 × .....

(i) Positive
(ii) Negative
(iii) Positive
(iv) Positive
(v) Negative
(vi) No
(vii) 1
(viii) -1 and 1
(ix) a
(x) not
(xi) a
(xii) ${12}^{-1}$

#### Question 8:

Fill in the blanks:
(i)
(ii)
(iii) $\frac{1}{2}×\left(\frac{3}{4}+\frac{-5}{12}\right)=\frac{1}{2}×......+......×\frac{-5}{12}$
(iv) $\frac{-4}{5}×\left(\frac{5}{7}+\frac{-8}{9}\right)=\left(\frac{-4}{5}×.....\right)×\frac{-8}{9}$

Divide:
(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

(x)

#### Question 2:

Find the value and express as a rational number in standard form:
(i) $\frac{2}{5}÷\frac{26}{15}$

(ii) $\frac{10}{3}÷\frac{-35}{12}$

(iii) $-6÷\left(\frac{-8}{17}\right)$

(iv) $\frac{-40}{99}÷\left(-20\right)$

(v) $\frac{-22}{27}÷\frac{-110}{18}$

(vi) $\frac{-36}{125}÷\frac{-3}{75}$

#### Question 3:

The product of two rational numbers is 15. If one of the numbers is −10, find the other.

#### Question 4:

The product of two rational numbers is $\frac{-8}{9}.$ If one of the numbers is $\frac{-4}{15},$ find the other.

#### Question 5:

By what number should we multiply $\frac{-1}{6}$ so that the product may be $\frac{-23}{9}?$

#### Question 6:

By what number should we multiply $\frac{-15}{28}$ so that the product may be $\frac{-5}{7}?$

#### Question 7:

By what number should we multiply $\frac{-8}{13}$ so that the product may be 24?

#### Question 8:

By what number should $\frac{-3}{4}$ be multiplied in order to produce $\frac{2}{3}?$

#### Question 9:

Find (x + y) ÷ (x − y), if
(i)
(ii)
(iii)
(iv)
(v)

#### Question 10:

The cost of $7\frac{2}{3}$ metres of rope is Rs $12\frac{3}{4}.$ Find its cost per metre.

#### Question 11:

The cost of $2\frac{1}{3}$ metres of cloth is Rs $75\frac{1}{4}.$ Find the cost of cloth per metre.

#### Question 12:

By what number should $\frac{-33}{16}$ be divided to get $\frac{-11}{4}?$

#### Question 13:

Divide the sum of $\frac{-13}{5}$ and $\frac{12}{7}$ by the product of

$\phantom{\rule{0ex}{0ex}}\left(\frac{-13}{5}+\frac{12}{7}\right)÷\left(\frac{-31}{7}×\frac{-1}{2}\right)\phantom{\rule{0ex}{0ex}}=\frac{-13×7+12×5}{35}÷\frac{31}{14}\phantom{\rule{0ex}{0ex}}=\frac{-91+60}{35}÷\frac{31}{14}\phantom{\rule{0ex}{0ex}}=\frac{-31}{35}×\frac{14}{31}\phantom{\rule{0ex}{0ex}}=\frac{-2}{5}$

#### Question 14:

Divide the sum of by their difference.

$\phantom{\rule{0ex}{0ex}}\left(\frac{65}{12}+\frac{12}{7}\right)÷\left(\frac{65}{12}-\frac{12}{7}\right)\phantom{\rule{0ex}{0ex}}=\frac{65×7+12×12}{84}÷\frac{65×7-12×12}{84}\phantom{\rule{0ex}{0ex}}=\frac{455+144}{84}÷\frac{455-144}{84}\phantom{\rule{0ex}{0ex}}=\frac{599}{84}÷\frac{311}{84}\phantom{\rule{0ex}{0ex}}=\frac{599}{84}×\frac{84}{311}\phantom{\rule{0ex}{0ex}}=\frac{599}{311}$

#### Question 15:

If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser?

#### Question 1:

Find a rational number between −3 and 1.

#### Question 2:

Find any five rational numbers less than 2.

#### Question 3:

Find two rational numbers between

#### Question 4:

Find two rational numbers between

#### Question 5:

Find ten rational numbers between

#### Question 6:

Find ten rational numbers between

#### Question 7:

Find ten rational numbers between

(i)
(ii)
(iii)
(iv)

(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)

#### Question 3:

Simplify:
(i) $\frac{8}{9}+\frac{-11}{6}$
(ii) $3+\frac{5}{-7}$
(iii) $\frac{1}{-12}+\frac{2}{-15}$
(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) $1+\frac{-4}{5}$

#### Question 4:

Add and express the sum as a mixed fraction:
(i)

(ii)

(iii)

(iv)