Selina solutions concise mathematica class 7 icse Solutions for Chapter 3 fractions including problems

Exercises in Chapter 3 fractions including problems Grade 7

Exercise 3(A)

Exercise 3(B)

Exercise 3(C)

Exercise 3(D)

Exercise 3(E)

Questions in Exercise 3(A)

Q1)Classify, each fraction given below, as decimal or vulgar fraction, proper or improper fraction and mixed fraction:

(i) $\frac{3}{5}$

(ii) $\frac{11}{10}$

(iii) $\frac{13}{20}$

(iv) $\frac{18}{7}$

(v) $3\frac{2}{9}$

(vi) $\frac{19}{10^3}$

(vii) $2\frac{7}{10}$

(viii) $\frac{23}{500}$

Q2) Express the following improper fractions as mixed fractions:

(i) $\frac{18}{5}$

(ii) $\frac{7}{4}$

(iii) $\frac{25}{6}$

(iv) $\frac{38}{5}$

(v) $\frac{22}{5}$

Q3) Express the following mixed fractions as improper fractions:

(i) $2\frac{4}{9}$

(ii) $7\frac{5}{13}$

(iii) $3\frac{1}{4}$

(iv) $2\frac{5}{48}$

(v) $12\frac{7}{11}$

Q4)Reduce the given fractions to lowest terms :

(i) $\frac{8}{18}$

(ii) $\frac{27}{36}$

(iii) $\frac{18}{42}$

(iv) $\frac{35}{75}$

(v) $\frac{18}{45}$

Q5) State : True or False

(i) $\frac{30}{40}\$ and $\frac{12}{16}$ are equivalent fractions.

(ii) $\frac{10}{25}$ and $\frac{25}{10}$ are equivalent fractions.

(iii) $\frac{35}{49},\ \frac{20}{28},\frac{45}{63}$ and $\frac{100}{140}$ are equivalent fractions.

Q6)Distinguish each of the following fractions, given below, as a simple fraction or complex fraction:

(i) $\frac{0}{8}$

(ii) $\frac{-3}{-8}$

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

(iv) $\frac{3\frac{3}{5}}{18}$

(v) $\frac{-6}{2\ \frac{2}{5}}$

(vi) $\frac{3\frac{1}{3}}{7\frac{2}{7}}$

(vii) $\frac{-5\frac{2}{9}}{5}$

(viii) $\frac{-8}{0}$

Questions in Exercise 3(B)

Q1) For each pair, given below, state whether it forms like fractions of unlike fractions:

(i) $\frac{5}{8}$ and $\frac{7}{8}$

(ii) $\frac{8}{15}$ and $\frac{8}{21}$

(iii) $\frac{4}{9}$ and $\frac{9}{4}$

Q2) Convert given fractions into fractions with equal denominators:

(i) $\frac{5}{6}$ and $\frac{7}{9}$

(ii) $\frac{2}{3},\ \frac{5}{6}$ and $\frac{7}{12}$

(iii) $\frac{4}{5},\frac{17}{20},\frac{23}{40}$ and $\frac{11}{16}$

Q3) Convert given fractions into fractions with equal numerators:

(i) $\frac{8}{9}$ and $\frac{12}{17}$

(ii) $\frac{6}{13},\frac{15}{23}$ and $\frac{12}{17}$

(iii) $\frac{15}{19},\frac{25}{28},\frac{9}{11}$ and $\frac{45}{47}$

Q4)Put the given fractions in ascending order by making denominators equal :

(i) $\frac{1}{3},\frac{2}{5},\frac{3}{4}$ and $\frac{1}{6}$

(ii) $\frac{5}{6},\frac{7}{8},\frac{11}{12}$ and $\frac{3}{10}$

(iii) $\frac{5}{7},\frac{3}{8},\frac{9}{14}$ and $\frac{20}{21}$

Q5)Arrange the given fractions in descending order by making numerators equal:

(i) $\frac{5}{6},\frac{4}{15},\ \frac{8}{9}$ and $\frac{1}{3}$

(ii) $\frac{3}{7},\frac{4}{9},\frac{5}{7}$ and $\frac{8}{11}$

(iii) $\frac{1}{10},\ \frac{6}{11},\frac{8}{11}$ and $\frac{3}{5}$

Q6)Find the greater fraction:

(i) $\frac{3}{5}$ and $\frac{11}{15}$

(ii) $\frac{4}{5}$ and $\frac{3}{10}$

(iii) $\frac{6}{7}$ and $\frac{5}{9}$

(iv) $\frac{3}{8}$ and $\frac{4}{9}$

(v) $\frac{-2}{7}$ and $\frac{-3}{10}$

Q7)Insert one fraction between:

(i) $\frac{3}{7}$ and $\frac{4}{9}$

(ii) $2$ and $\frac{8}{3}$

(iii) $\frac{9}{17}$ and $\frac{6}{13}$

Q8)Insert three fractions between:

(i) $\frac{2}{5}$ and $\frac{4}{9}$

(ii) $\frac{1}{2}$ and $\frac{5}{7}$

(iii) $\frac{3}{8}$ and $\frac{6}{11}$

(iv) $\frac{11}{12}$ and $\frac{2}{3}$

(v) $\frac{4}{7}$ and $\frac{3}{4}$

Q9) Insert two fractions between:

(i) 1 and $\frac{3}{11}$

(ii) $\frac{5}{9}$ and $\frac{1}{4}$

(iii) $\frac{5}{6}$ and $1\frac{1}{5}$

Questions in Exercise 3(C)

Q1)Reduce to a single fraction:

(i) $\frac{1}{2}+\frac{2}{3}$

(ii) $\frac{3}{5}-\frac{1}{10}$

(iii) $\frac{2}{3}-\frac{1}{6}$

(iv) $1\frac{1}{3}+2\frac{1}{4}$

(v) $\frac{1}{4}+\frac{5}{6}-\frac{1}{12}$

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

(vii) $\frac{2}{3}-\frac{1}{5}+\frac{1}{10}$

(viii) $2\frac{1}{2}+2\frac{1}{3}-1\frac{1}{4}$

(ix) $2\frac{5}{8}-2\frac{1}{6}+4\frac{3}{4}$

Q2) Simplify :

(i) $\frac{3}{4}\times6$

(ii) $\frac{2}{3}\times15$

(iii) $\frac{3}{4}\times\frac{1}{2}$

(iv) $\frac{9}{12}\times\frac{4}{7}$

(v) $45\times2\frac{1}{3}$

(vi) $36\times3\frac{1}{4}$

(vii) $2\div\frac{1}{3}$

(viii) $3\div\frac{2}{5}$

(ix) $1\div\frac{3}{5}$

(x) $\frac{1}{3}\div\frac{1}{4}$

(xi) $-\frac{5}{8}\div\frac{3}{4}$

(xii) $3\frac{3}{7}\div1\frac{1}{14}$

(xiii) $3\frac{3}{4}\times1\frac{1}{5}\times\frac{20}{21}$

Q3)Subtract :

(i)2 from $\frac{2}{3}$

(ii) $\frac{1}{8}$ from $\frac{5}{8}$

(iii) $-\frac{2}{5}$ from $\frac{2}{5}$

(iv) $-\frac{3}{7}$ from $\frac{3}{7}$

(v) 0 from $-\frac{4}{5}$

(vi) $\frac{2}{9}$ from $\frac{4}{5}$

(vii) $-\frac{4}{7}$ from $-\frac{6}{11}$

Q4)Find the value of

(i) $\frac{1}{2}$ of 10 kg

(ii) $\frac{3}{5}$ of 1 hour

(iii) $\frac{4}{7}$ of $2\frac{1}{3}$ kg

(iv) $3\frac{1}{2}$ times of 2 metres

(v) $\frac{1}{2}$ of $2\frac{2}{3}$

(vi) $\frac{5}{11}$ of $\frac{4}{5}$ of 22 kg

Q5)Simplify and reduce to a simple Fraction:

(i) $\frac{3}{3\frac{3}{4}}$

(ii) $\frac{\frac{3}{5}}{7}$

(iii) $\frac{3}{\frac{5}{7}}$

(iv) $\frac{2\frac{1}{5}}{1\frac{1}{10}}$

(v) $\frac{2}{5}$ of $\frac{6}{11}\times1\frac{1}{4}$

(vi) $2\frac{1}{4}\div\frac{1}{7}\times\frac{1}{3}$

(vii) $\frac{1}{3}\times4\frac{1}{3}\div3\frac{1}{2}\times\frac{1}{2}$

(viii) $\frac{2}{3}\times1\frac{1}{4}\div\frac{3}{7}$ of $2\frac{5}{8}$

(ix) $0\div\frac{8}{11}$

(x) $\frac{4}{5}\div\frac{7}{15}$ of $\frac{8}{9}$

(xi) $\frac{4}{5}\div\frac{7}{15}\times\frac{8}{9}$

(xii) $\frac{4}{5}$ of $\frac{7}{15}\div\frac{8}{9}$

(xiiii) $\frac{1}{2}$ of $\frac{3}{4}\times\frac{1}{2}\div\frac{2}{3}$

Q6)A bought $3\frac{3}{4}$ kg of wheat $2\frac{1}{2}$ kg of rice.Find the total weight of wheat and rice bought.

Q7)Which one is greater, $\frac{3}{5}$ or $\frac{7}{10}$ and by how much?

Q8)What number should be added to $8\frac{2}{3}$ to get $12\frac{5}{6}$ ?

Q9)What should be subtracted from $8\frac{3}{4}$ to get $2\frac{2}{3}$ ?

Q10)A field is $16\ \frac{1}{2}$ m long and $12\frac{2}{5}$ m wide. Find the perimeter of the field.

Q11)Sugar costs ₹ $37\frac{1}{2}$ per kg. Find the cost of $8\frac{3}{4}$ kg of sugar.

Q12)A Motorcycle runs $31\frac{1}{4}$ km consuming 1 litre of petrol. How much distance will it run consuming $1\frac{3}{5}$ litre of petrol ?

Q13)A rectangular park has length = $23\frac{2}{5}$ m and breadth = $16\frac{2}{3}$ m. Find the area of the park.

Q14)Each of 40 identical boxes weighs $4\frac{4}{5}$ kg. Find the total weight of all the boxes.

Q15)Out of 24 kg of wheat, $\frac{5}{6}$ th wheat is consumed . Find, how much wheat is still left?

Q16)A rod of length $2\frac{2}{5}$ metre is divided into five equal parts. Find the length of each part so obtained.

Q17) If A = $3\frac{3}{8}$ and B= $6\frac{5}{8}$

(i)A $\div$ B

(ii)B $\div$ A

Q18)Cost of $3\frac{5}{7}$ litres of oil is ₹ $83\frac{1}{2}$ . Find the cost of one litre oil.

Q19)The product of two numbers is $20\frac{5}{7}$ . If one of these numbers is $6\frac{2}{3}$ find the other.

Q20)By what number should $5\frac{5}{6}$ be multiplied to get $3\frac{1}{3}$ ?

Questions in Exercise 3(D)

Q1)Simplify :

$6+\left\{\frac{4}{3}+\left(\frac{3}{4}-\frac{1}{3}\right)\right\}$

Q2) Simplify :

$8-\left\{\frac{3}{2}+\left(\frac{3}{5}-\frac{1}{2}\right)\right\}$

Q3) Simplify :

$\frac{1}{4}\left(\frac{1}{4}+\frac{1}{3}\right)-\frac{2}{5}$

Q4)Simplify :

$2\frac{3}{4}-\left[3\frac{1}{8}\div\left\{5-\left(4\frac{2}{3}-\frac{11}{12}\right)\right\}\right]$

Q5) Simplify :

$12\frac{1}{2}-\left[8\frac{1}{2}+\left\{9-\left(5-\overline{3-2}\right)\right\}\right]$

Q6) Simplify :

$1\frac{1}{5}\div\left\{2\frac{1}{3}-\left(5+\overline{2-3}\right)\right\}-3\frac{1}{2}$

Q7) Simplify :

$\left(\frac{1}{2}+\frac{2}{3}\right)\div\left(\frac{3}{4}-\frac{2}{9}\right)$

Q8) Simplify :

$\frac{6}{5}$ of $\left(3\frac{1}{3}-2\frac{1}{2}\right)\div\left(2\frac{5}{21}-2\right)$

Q9)Simplify:

$10\frac{1}{8}$ of $\frac{4}{5}\div\frac{35}{36}$ of $\frac{20}{49}$

Q10) Simplify :

$5\frac{3}{4}-\frac{3}{7}\times15\frac{3}{4}+2\frac{2}{35}\div1\frac{11}{25}$

Q11) Simplify :

$\frac{3}{4}$ of $7\frac{3}{7}-5\frac{3}{5}\div3\frac{4}{15}$

Questions in Exercise 3(E)

Q1)A line AB is of length 6cm. Another line CD is of length 15 cm. What fraction is:

(i) The length of AB to that of CD ?

(ii) $\frac{1}{2}$ the length of AB to that $\frac{1}{3}$ of CD ?

(iii) $\frac{1}{5}$ of CD to that of AB?

Q2)Subtract $\frac{2}{7}-\frac{5}{21}$ from the sum of $\frac{3}{4},\frac{5}{7}$ and $\frac{7}{12}$

Q3)From a sack of potatoes weighing 120 kg, a merchant sells portions weighing $6kg,\ 5\frac{1}{4}kg,\ 9\frac{1}{2}kg$ and $9\frac{3}{4}kg$ respectively?

(i) How many kg did he sell ?

(ii) How many kg are still left in the sack ?

Q4)If a boy works for six consecutive days for 8 hours , $7\frac{1}{2}$ hours, $8\frac{1}{4}$ hours, $6\frac{1}{4}$ hours, $6\frac{3}{4}$ hours and 7 hours respectively. How much money will he earn at the rate of Rs. 36 per hour?

Q5)A student bought $4\frac{1}{3}m$ of yellow ribbon, $6\frac{1}{6}m$ of red ribbon and $3\frac{2}{9}m$ of blue ribbon for decorating a room.How many metres of ribbon did he buy?

Q6)In a business , Ram and Deepak invest $\frac{3}{5}$ and $\frac{2}{5}$ of the total investment. If Rs.40,000 is the total investment, calculate the amount invested by each?

Q7)Geeta had 30 problems for homework. She worked out $\frac{2}{5}$ of them. How many problems were still left to be worked out by her?

Q8)A picture was marked at Rs. 90. It was sold at of $\frac{3}{4}$ its marked price. What was the sale price ?

Q9)Mani had sent fifteen parcels of oranges. What was the total weight of the parcels, if each weighed $10\frac{1}{2}$ kg?

Q10) A rope is $25\frac{1}{2}m$ long. How many pieces $1\frac{1}{2}m$ each of length can be cut out from it ?

Q11)The heights of two vertical poles , above the earth’s surface are $14\frac{1}{4}m$ and $22\frac{1}{3}m$ respectively. How much higher is the second pole as compared with the height of the first pole ?

Q12)Vijay weighed $65\frac{1}{2}$ kg. He gained $1\frac{1}{5}$ kg during first week, $1\frac{1}{4}$ kg during the second week, but lost $\frac{5}{16}$ kg during the third week.What was his weight after the third week ?

Q13)A man spends $\frac{2}{5}$ of his salary on food and $\frac{3}{10}$ on house rent, electricity, etc. What fraction of his salary is still left with him?

Q14)A man spends $\frac{2}{5}$ of his salary on food and $\frac{3}{10}$ of the remaining on house rent, electricity, etc. What fraction of his salary is still left with him?

Q15)Shyam bought a refrigerator for Rs.5000. He paid $\frac{1}{10}$ of the price in cash and the rest in 12 equal monthly installments . How much he had to pay each month ?

Q16)A lamp post has half of its length in mud, and $\frac{1}{3}$ of its length in water.

(i) what fraction of its length is above the water ?

(ii) if $3\frac{1}{3}$ m of the lamp post is above the water, find the whole length of the lamp post.

Q17)I spent $\frac{3}{5}$ of my savings and still have Rs. 2,000 left. What were my savings ?

Q18)In a school , $\frac{4}{5}$ of the children are boys . If the number of girls is 200, find the number of boys.

Q19)If $\frac{4}{5}$ of an estate is Rs. 42,000, find the worth of the whole estate. Also,find the value $\frac{3}{7}$ of it.

Q20) After going $\frac{3}{4}$ of my journey , I find that I have covered 16 km. How much journey is still left ?

Q21)When Krishna travelled 25 km, he found that $\frac{3}{5}$ of his journey was still left. What was the length of the whole journey?

Q22)From a piece of land, one-third is bought by Rajesh and one - third of remaining is bought by Manoj. If $600m^2$ land is still left unsold ,find the total area of the piece of land.

Q23)A boy spent $\frac{3}{5}$ of his money on buying cloth and $\frac{1}{4}$ of the remaining on buying shoes. If initially he had Rs. 2400, how much did he spend on shoes ?

Q24)A boy spent $\frac{3}{5}$ of his money on buying cloth and $\frac{1}{4}$ of his money on buying shoes. If initially he had Rs. 2400, how much did he spend on shoes ?