Selina solutions concise mathematica class 7 icse Solutions for Chapter 2 rational numbers

Q1) Write down a rational number whose numerator is the largest number of two digits and denominator is the smallest number of four digits.

Q2) Write the numerator of each of the following rational numbers:

(i) \frac{-125}{127}

(ii) \frac{37}{-137}

(iii) \frac{-85}{93}

(iv) 2

(v) 0

Q3) Write the denominator of each of the following rational numbers:

(i) \frac{7}{-15}

(ii) \frac{-18}{29}

(iii) \frac{-3}{4}

(iv) -7

(v) 0

Q4) Write down a rational number numerator (-5) × (-4) and denominator (28 – 27) × (8 – 5)

Q5) (i) \frac{-15}{1} in integer form is ___.

(ii) \frac{23}{-1} in integer form is _____.

(iii) If 18=\frac{18}{a}, then a = _____.

(iv) If -57=\frac{57}{a}, then a = _____.

Q6) Separate positive and negative rational numbers from the following:

\frac{-3}{5},\ \frac{3}{-5},\ \frac{-3}{-5},\ \frac{3}{5},\ 0,\ \frac{-13}{-3},\ \frac{15}{-8},\ \frac{-15}{8}

Q7) Find three rational numbers equivalent to

\left(i\right)\ \frac{3}{5}\ \left(ii\right)\ \frac{4}{-7}\ \left(iii\right)\ \frac{-5}{9}\ \left(iv\right)\ \frac{8}{-15}

Q8) Which of the following are not rational numbers:

(i) -3

(ii) 0

(iii) \frac{0}{4}

(iv) \frac{8}{0}

(v) \frac{0}{0}

Q9) Express each of the following integers as a rational number with denominator 7 :

(i) 5

(ii) -8

(iii) 0

(iv) -16

(v) 7

Q10) Express \frac{3}{5} as a rational number with denominator:

(i) 20

(ii) -20

(iii) 45

(iv) 25

(v) -35

Q11) Express \frac{4}{7} as a rational number with numerator :

(i) 12

(ii) -12

(iii) -16

(iv) -20

(v) 20

Q12) Find x, such that:

(i) \frac{-2}{3}=\frac{6}{x}

(ii) \frac{7}{-4}=\frac{x}{8}

(iii) \frac{3}{7}=\frac{x}{-35}

(iv) \frac{-48}{x}=6

(v) \frac{36}{x}=3

(vi) \frac{-27}{x}=9

Q13) Express each of the following rational numbers to the lowest terms:

(i) \frac{12}{15}

(ii) \frac{-120}{144}

(iii) \frac{-48}{-72}

(iv) \frac{14}{-56}

Q14) Express each of the following rational numbers in the standard form:

(i) \frac{-7}{-8}

(ii) \frac{5}{-12}

(iii) \frac{-7}{-20}

(iv) \frac{4}{-9}

Q1) Mark the following pairs of rational numbers on the separate number line:

(i) \frac{3}{4}and\ -\frac{1}{4}

(ii) \frac{2}{5}and\ \frac{-3}{5}

(iii) \frac{5}{6}and\ -\frac{2}{3}

(iv) \frac{2}{5}and\ -\frac{4}{5}

Q2) Compare:

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

(ii) \frac{-7}{2}and\ \frac{5}{2}

(iii) -3\ and\ 2\frac{3}{4}

(iv) -1\frac{1}{2}and\ 0

(v) 0\ and\ \frac{3}{4}

(vi) 3\ and\ -1

Q3) Compare:

(i) -\frac{1}{4}and\ 0

(ii) \frac{1}{4}and\ 0

(iii) -\frac{3}{8}and\ \frac{2}{5}

(iv) \frac{-5}{8}and\ \frac{7}{-12}

(v) \frac{5}{-9}and\ \frac{-5}{-9}

(vi) \frac{-7}{8}and\ \frac{5}{-6}

(vii) \frac{2}{7}and\ \frac{-3}{-8}

(viii) \frac{-5}{8}and\ \frac{7}{-12}

Q4) Arrange the given rational numbers in ascending order:

(i) \frac{7}{10},\ \frac{-11}{-30}and\ \frac{5}{-15}

(ii) \frac{4}{-9},\ \frac{-5}{12}\ and\ \frac{2}{-3}

Q5) Arrange the given rational numbers in descending order:

(i) \frac{5}{8},\frac{13}{-16}and\ \frac{-7}{12}

(ii) \frac{3}{-10},\ \frac{-13}{30}and\ \frac{8}{-20}

Q6) Fill in the blanks:

(i) \frac{5}{8}and\ \frac{3}{10} are on the ____ side of zero.

(ii) -\frac{5}{8}and\ \frac{3}{10} are on the ____ side of zero.

(iii) -\frac{5}{8}and\ -\frac{3}{10} are on the ____ side of zero.

(iv) \frac{5}{8}and\ -\frac{3}{10} are on the ____ side of zero.

Q1) Add:

(i) \frac{7}{5}and\ \frac{2}{5}

(ii) \frac{-4}{9}and\ \frac{2}{9}

(iii) \frac{5}{-12}and\ \frac{1}{12}

(iv) \frac{4}{-15}and\ \frac{-7}{-15}

(v) \frac{-7}{25}and\ \frac{9}{-25}

(vi) \frac{-7}{26}and\ \frac{7}{-26}

Q2) Add:

(i) \frac{-2}{5}and\ \frac{3}{7}

(ii) \frac{-5}{6}and\ \frac{4}{9}

(iii) -3\ and\ \frac{2}{3}

(iv) \frac{-5}{9}and\ \frac{7}{18}

(v) \frac{-7}{24}and\ \ \frac{-5}{48}

(vi) \frac{1}{-18}and\ \frac{5}{-27}

(vii) \frac{-9}{-16}and\ \frac{1}{-75}

(viii) \frac{13}{-16}and\ \frac{-11}{24}

(ix) \frac{-9}{-16}and\ \frac{-11}{8}

Q3) Evaluate:

(i) \frac{-2}{5}+\frac{3}{5}+\frac{-1}{5}

(ii) \frac{-8}{9}+\frac{4}{9}+\frac{-2}{9}

(iii) \frac{5}{-24}+\frac{-1}{8}+\frac{3}{16}

(iv) \frac{-7}{6}+\frac{4}{-15}+\frac{-4}{-30}

(v) -2+\frac{2}{5}+\frac{-2}{15}

(vi) \frac{-11}{12}+\frac{5}{16}+\frac{-3}{8}

Q4) Evaluate:

(i) -\frac{11}{18}+\frac{-3}{9}+\frac{2}{-3}

(ii) \frac{-9}{4}+\frac{13}{3}+\frac{25}{6}

(iii) -5+\frac{5}{-8}+\frac{-5}{-12}

(iv) -\frac{2}{3}+\frac{5}{2}+2

(v) 5+\frac{-3}{4}+\frac{-5}{8}

Q5) Subtract:

(i) \frac{2}{9}from\ \frac{5}{9}

(ii) \frac{-6}{11}from\ \frac{-3}{-11}

(iii) \frac{-2}{15}from\ \frac{-8}{15}

(iv) \frac{11}{18}from\ \frac{-5}{18}

(v) \frac{-4}{11}from\ -2

Q6) Subtract:

(i) -\frac{3}{10}from\ \frac{1}{5}

(ii) \frac{-6}{25}from\ \frac{-8}{5}

(iii) \frac{-7}{4}from\ -2

(iv) \frac{-16}{21}from\ 1

(v) \frac{-8}{15}from\ 0

(vi) 0\ from\ \frac{-3}{8}

(vii) -2\ from\ \frac{-3}{10}

(viii) \frac{5}{8}from\ \frac{-5}{16}

(ix) 4\ from\ -\frac{3}{13}

Q7) The sum of two rational numbers is \frac{11}{24}. If one of them is \frac{3}{8}, find the other.

Q8) The sum of two rational numbers is \frac{-7}{12} . If one of them is \frac{13}{24} , find the other.

Q9) The sum of two rational numbers is -4. If one of them is \frac{-13}{12} , find the other.

Q10) What should be added to -\frac{3}{16} to get \frac{11}{24} ?

Q11) What should be added to-\frac{3}{5} to get 2?

Q12) What should be subtracted from \frac{-4}{5} to get 1?

Q13) The sum of two numbers is \frac{-6}{5}. If one of them is -2, find the other.

Q14) What should be added to \frac{-7}{12} to get \frac{3}{8}?

Q15) What should be subtracted from \frac{5}{9\ } to get \frac{9}{5}?

Q1) Evaluate:

(i)

\frac{5}{4}\times\frac{3}{7}

(ii) \frac{2}{3}\times\left(-\frac{6}{7}\right)

(iii) \frac{-12}{5}\times\frac{10}{-3}

(iv) \frac{-45}{39}\times\frac{-13}{15}

(v) 3\frac{1}{8}\times\left(-2\frac{2}{5}\right)

(vi) 2\frac{14}{24}\times\frac{-5}{16}

(vii) \frac{-8}{9}\times\frac{-3}{16}

(viii) \frac{5}{-27}\times\frac{-9}{20}

Q2) Multiply:

(i) \frac{3}{25}\ and\ \frac{4}{5}

(ii) 1\frac{1}{8}and\ 10\frac{2}{3}

(iii) 6\frac{2}{3}and\ \frac{-3}{8}

(iv) \frac{-13}{15}and\ \frac{-25}{26}

(v) 1\frac{1}{6}and\ 18

(vi) 2\frac{1}{14}and\ -7

(vii) 5\frac{1}{8}and\ -16

(viii) 35\ and\ \frac{-18}{25}

(ix) 6\frac{2}{3}and\ -\frac{3}{8}

(x) 3\frac{3}{5}and\ -10

(xi) \frac{27}{28}and\ -14

(xii) -24\ and\ \frac{5}{16}

Q3) Evaluate:

(i) \left(-6\times\frac{5}{18}\right)-\left(4\frac{2}{9}\right)

(ii) \left(\frac{7}{8}\times\frac{8}{7}\right)+\left(\frac{-5}{9}\right)\times\left(\frac{6}{-25}\right)

(iii) \left(\frac{11}{-9}\times\frac{21}{44}\right)+\left(\frac{-5}{9}\right)\times\left(\frac{63}{-100}\right)

(iv) \left(\frac{-5}{9}\times\frac{6}{-25}\right)\times\left(\frac{24}{21}\times\frac{7}{8}\right)

(v) \left(\frac{-35}{39}\times\frac{-13}{7}\right)-\left(\frac{7}{90}\times\frac{-18}{14}\right)

(vi) \left(\frac{-4}{5}\times\frac{3}{2}\right)+\left(\frac{9}{-5}\times\frac{10}{3}\right)-\left(\frac{-3}{2}\times\frac{-1}{4}\right)

Q4) Find the cost of3\frac{1}{2} m cloth, if one metre cloth costs Rs. 325\frac{1}{2}.

Q5) A bus is moving with a speed of 65\frac{1}{2} km per hour. How much distance will it cover in 1\frac{1}{3} hours.

Q6) Divide:

(i) \frac{15}{28}by\ \frac{3}{4}

(ii) \frac{-20}{9}by\ \frac{-5}{9}

(iii) \frac{16}{-5}by\ \frac{-8}{7}

(iv) -7\ by\ \frac{-14}{5}

(v) -14\ by\ \frac{7}{-2}

(vi) \frac{-22}{9}by\ \frac{11}{18}

(vii) 35\ by\ \frac{-7}{9}

(viii) \frac{21}{44}\ by-\ \frac{11}{9}

Q7) (i) 3\frac{5}{12}+1\frac{2}{3}

(ii) 3\frac{5}{12}-1\frac{2}{3}

(iii) \left(3\frac{5}{12}+1\frac{2}{3}\right)\div\left(3\frac{5}{12}-1\frac{2}{3}\right)

Q8) The product of two numbers is 14. If one number is \frac{-8}{7} , Find the other.

Q9) The cost of 11 pens is Rs. 3\frac{2}{3} . Find the cost of one pen.

Q10) If 6 identical articles can be bought for Rs. 2\frac{6}{17}. Find the cost of each article.

Q11) By what number should \frac{-3}{8} be multiplied so that the product is \frac{-9}{16} ?

Q12) By what number should \frac{-5}{7} be divided so that the result is \frac{-15}{28}?

Q13) Evaluate:

\left(\frac{32}{15}+\frac{8}{5}\right)\div\left(\frac{32}{15}-\frac{8}{5}\right)

Q14) Seven equal piece are made out of a rope of 21\frac{5}{7} m. Find the length of each piece.

Q1) Evaluate:

(i) \frac{-2}{3}+\frac{3}{4}

(ii) \frac{7}{-27}+\frac{11}{18}

(iii) \frac{-3}{8}+\frac{-5}{12}

(iv) \frac{9}{-16}+\frac{-5}{-12}

(v) \frac{-5}{9}+\frac{-7}{12}+\frac{11}{18}

(vi) \frac{7}{-26}+\frac{16}{39}

(vii) -\frac{2}{3}-\left(\frac{-5}{7}\right)

(viii) -\frac{5}{7}-\left(-\frac{3}{8}\right)

(ix) \frac{7}{26}+2+\frac{-11}{13}

(x) -1+\frac{2}{-3}+\frac{5}{6}

Q2) The sum of two rational numbers is \frac{-3}{8}. If one of them is \frac{3}{16} , find the other.

Q3) The sum of two rational numbers is -5. If one of them is \frac{-52}{25} , find the other.

Q4) What rational number should be added to \frac{-3}{16} to get \frac{11}{24}?

Q5) What rational number should be added to -\frac{3}{5} to get 2?

Q6) What rational number should be subtracted from -\frac{5}{12} to get \frac{5}{24} ?

Q7) What rational number should be subtracted from \frac{5}{8} to get \frac{8}{5}?

Q8) Evaluate:

(i) \left(\frac{7}{8}\times\frac{24}{21}\right)+\left(\frac{-5}{9}\times\frac{6}{-25}\right)

(ii) \left(\frac{8}{15}\times\frac{-25}{16}\right)+\left(\frac{-18}{35}\times\frac{5}{6}\right)

(iii) \left(\frac{18}{33}\times\frac{-22}{27}\right)-\left(\frac{13}{25}\times\frac{-75}{26}\right)

(iv) \left(\frac{-13}{7}\times\frac{-35}{39}\right)-\left(\frac{-7}{45}\times\frac{9}{14}\right)

Q9) The product of two rational numbers is 24. If one of them is \frac{-36}{11} , find the other.

Q10) By what rational should we multiply \frac{20}{-9} , so that the product may be \frac{-5}{9} ?