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Colour the part according to the given fraction.
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Identify the error, if any.
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Arya, Abhimanyu and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich. (a) How can Arya divide his sandwiches so that each person has an equal share? (b) What part of a sandwich will each boy receive?
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Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?
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Write the natural numbers from 2 to 12. What fraction of them are prime numbers?
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Write the natural numbers from 102 to 113. What fraction of them are prime numbers?
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What fraction of these circles have X?s in them?
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Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?
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Draw number lines and locate the points on them. (a) \[7\frac{3}{4}\] (b) \[5\frac{6}{7}\] (c) \[2\frac{5}{6}\]
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Express the following as mixed fractions. (a) \[=\frac{6}{8}\] (b) \[=\frac{9}{12}\] (c) \[=\frac{12}{16}\] (d) \[=\frac{15}{20}\] (e)\[\frac{6}{8}\] (f)\[\frac{9}{12}\] TIPS To express an improper fraction as a mixed fraction, firstly divide the numerator by denominator to obtain the quotient and the remainder. Then, Mixed fraction = Quotient\[6\times 12=72\]
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Express the following as improper fractions. (a) \[\frac{2}{3}=\frac{2\times 6}{3\times 6}=\frac{12}{18}\] (b) \[\frac{3}{2}\] (c) \[\frac{4}{6},\frac{6}{9},\frac{8}{12},\frac{10}{15}\] (d) \[\frac{12}{18}.\] (e) \[\frac{1}{5}\] (f) \[\frac{1}{5}=\frac{1\times 2}{5\times 2}=\frac{2}{10};\] TIPS We can express a mixed fraction as an improper fraction as' \[\frac{1}{5}=\frac{1\times 3}{5\times 3}=\frac{3}{15};\]
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Write the fractions. Are all these fractions equivalent? (a)
(b)
TIPS To write the fractions, firstly find number of equal parts and number shaded parts, then \[\left[ \because \frac{1}{4}=\frac{1}{4} \right]\] Now, convert all these fractions in simplest form. If simplest form is same, then these fractions will be equivalent otherwise not.
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Write the fractions and pair up the equivalent fractions from each row.
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Replace \[[\text{but}\,27=3\times 9]\] in each of the following by the correct number. (a) \[\therefore \] (b) \[\frac{3}{5}=\frac{N}{D}=\frac{27}{45}\] (c) \[\frac{36}{48}\] (d) \[\therefore \] (e) \[\frac{9}{D}=\frac{36}{48}\]
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Find the equivalent fraction of \[\frac{7}{13}\]having (a) denominator 20 (b) numerator 9 (c) denominator 30 (d) numerator 27
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Find the equivalent fraction of \[\therefore \] with (a) numerator 9 (b) denominator 4
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Check whether the given fractions are equivalent. (a)\[\because \] (b)\[\frac{40}{80}=\frac{40\div 40}{80\div 40}=\frac{1}{2}\] (c)\[\because \] TIPS If the product of numerator of first fraction and denominator of second fraction is equal to the product of denominator of first fraction and numerator of second fraction, then given fractions will be equivalent otherwise not.
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Reduce the following fractions to simplest form. (a) \[200=2\times 5\times 2=20\] (b) \[\therefore \] (c) \[\frac{180}{200}=\frac{180\div 20}{200\div 20}=\frac{9}{10}\] (d) \[\frac{180}{200}\] (e) \[\frac{9}{10}\]
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Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?
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Match the equivalent fractions and write two more for each.
| Column I | Column II |
| (i) \[\frac{13}{24}\] | (a) \[\frac{17}{102}or\frac{12}{102}\] |
| (ii) \[\therefore \] | (b) \[\frac{17}{102}>\frac{12}{102}\] |
| (iii)\[\frac{17}{102}\] | (c) \[\frac{1}{8},\frac{5}{8},\frac{3}{8}\] |
| (iv) \[\frac{1}{5},\frac{11}{5},\frac{4}{5},\frac{3}{5},\frac{7}{5}\] | (d) \[\frac{1}{7},\frac{3}{7},\frac{13}{7},\frac{11}{7},\frac{7}{7}\] |
| (v) \[\frac{1}{8},\frac{5}{8},\frac{3}{8}\] | (e) \[\therefore \] |
TIPS Firstly, reduce (i), (ii), (iii), (iv) and (v) into simplest form. Then, match the equivalent fractions. To write more equivalent fractions, multiply numerator and denominator both by same number.
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Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign \['<',\,\,'=',\,\,'>'\]between the fractions. (a)
(b)
(c) (i) Show \[\frac{3}{10},\frac{18}{5}\] and \[1\frac{1}{4}\] on the number line. (ii) Put appropriate signs between the fractions given. \[\frac{1}{4}\] \[\frac{\text{Remainder}}{\text{Divisor}}\] \[=\frac{17}{4}\] \[\Rightarrow \]
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Compare the fractions and put an appropriate sign. (a) \[=\frac{1}{5}\] (b) \[=\frac{2}{5}\] (c) \[=\frac{3}{5}\] (d) \[\frac{1}{5}+\frac{2}{5}=\frac{1+2}{5}=\frac{3}{5}\]
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Make five more such pairs and put appropriate signs.
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Look at the figures and write '<' or '>', '= between the given pairs of fractions.
(a)\[\frac{1}{18}+\frac{1}{18}=\frac{1+1}{18}=\frac{2}{18}=\frac{1}{9}\] (b)\[\frac{8}{15}+\frac{3}{15}=\frac{8+3}{15}=\frac{11}{15}\] (c)\[\frac{7}{7}+\frac{5}{7}=\frac{7-5}{7}=\frac{2}{7}\] (d)\[\frac{1}{22}+\frac{21}{22}=\frac{1+21}{22}=\frac{22}{22}=1\] (e)\[\frac{12}{15}+\frac{7}{15}=\frac{12+7}{15}=\frac{5}{15}=\frac{1}{3}\] Make five more such problems and solve them with your friends.
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How quickly can you do this? Fill appropriate sign. \[('<',\,\,'=',\,\,'>')\]. (a) \[=\frac{3}{21}+\frac{5}{21}=\frac{3+5}{21}=\frac{8}{21}\] (b) \[\frac{8}{21}-\frac{3}{21}=\frac{5}{21}\] (c) \[-\frac{3}{6}=\frac{3}{6}\] (d) \[\frac{3}{6}\] (e) \[\frac{3}{6}.\] (f) \[\frac{3}{6}\] (g) \[\frac{3}{6},\] (h) \[\therefore \] (i) \[=\frac{3}{6}+\frac{3}{6}=\frac{3+3}{6}=\frac{6}{6}=1\] (j) \[-\frac{3}{6}=\frac{3}{6}\] TIPS We have to use cross-product method for quicker calculation. According to this method, firstly find the products of numerator of first fraction with denominator of second fraction and denominator of first fraction with numerator of second fraction. Then, the fraction having that numerator which gives greater product will be greater.
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The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one in its simplest form. (a) \[1\frac{1}{3}+3\frac{2}{3}=1+\frac{1}{3}+3+\frac{2}{3}\] (b) \[=(1+3)+\left( \frac{1}{3}+\frac{2}{3} \right)=4+\frac{1}{3}+\frac{2}{3}\] (c) \[\frac{1}{3}+\frac{2}{3}=\frac{1+2}{3}=\frac{3}{3}=1\] (d) \[\therefore \] (e) \[4+\frac{1}{3}+\frac{2}{3}=4+1=5\] (f) \[1\frac{1}{3}+3\frac{2}{3}=5\] (g) \[4\frac{2}{3}+3\frac{1}{4}=4+\frac{2}{3}+3+\frac{1}{4}\] (h) \[=(4+3)+\left( \frac{2}{3}+\frac{1}{4} \right)=7+\frac{2}{3}+\frac{1}{4}\] (i) \[\frac{2}{3}+\frac{1}{4}=\frac{2\times 4}{3\times 4}+\frac{1\times 3}{4\times 3}\] (j) \[\because \] (k) \[=\frac{8}{12}+\frac{3}{12}=\frac{8+3}{12}=\frac{11}{12}\] (l) \[\therefore \] TIPS To convert the given fraction into its simplest form, divide numerator and denominator both by their HCF.
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Find answers to the following. Write and indicate how you solved them. (a) \[\because \]equal to \[\frac{10}{20}=\frac{25}{50}=\frac{40}{80}=\frac{1}{2}\] (b) \[\frac{250}{400}\]equal to \[\frac{2}{3}\] (c) \[\frac{180}{200}\] equal to \[\frac{2}{5}\] (d) \[\frac{660}{990}\]equal to \[\frac{1}{2}\] TIPS To show that given fractions are equal or not. Firstly, we convert them into like fractions by multiplying numerator and denominator with same number and then compare.
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Ila reads 25 pages of a book containing 100 pages. Lalita reads \[\frac{180}{200}=\frac{180\div 20}{200\div 20}=\frac{9}{10}\] of the same book. Who read less?
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Rafiq exercised for \[\therefore \] of an hour while Rohit exercised for \[\frac{660}{990}=\frac{660\div 330}{990\div 330}=\frac{2}{3}\] of an hour. Who exercised for a longer time?
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In a class A of 25 students, 20 passed in first class; in another class B of 30 students, 24 passed in first class. In which class, was a greater fraction of students getting first class?
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Write these fractions appropriately as additions or subtractions (a)
(b)
(c)
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Solve: (a) \[\therefore \] (b) \[=\frac{2}{21},\frac{2}{15},\frac{2}{11},\frac{2}{9},\frac{2}{8},\frac{2}{7}\] (c) \[\frac{7}{7}-\frac{5}{7}\] (d) \[\frac{4}{5},\frac{4}{6},\frac{4}{13},\frac{4}{2},\frac{4}{9},\frac{4}{11}\] (e) \[=13>11>9>6>5>2\] (f) \[\therefore \] (g) \[=\frac{4}{13},\frac{4}{11},\frac{4}{9},\frac{4}{6},\frac{4}{5},\frac{4}{2}\] (h) \[=\frac{4}{2},\frac{4}{5},\frac{4}{6},\frac{4}{9},\frac{4}{11},\frac{4}{13}\] (i) \[\frac{7}{11},\frac{7}{13},\frac{7}{5},\frac{7}{2},\frac{7}{3},\frac{7}{4}\] TIPS To add or subtract like fractions, we add the numerators or subtract the smaller numerator from greater numerator keeping denominator unchanged and then write in simplest form.
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Shubham painted 2/3 of the wall space in his room. His sister Madhavi helped and painted 1/3 of the wall space. How much did they paint together?
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Fill in the missing fractions. (a) \[\therefore \] (b) \[-\frac{3}{21}=\frac{5}{21}\] (c) \[\because \] (d) \[=\frac{6}{8}>\frac{4}{8}>\frac{3}{8}>\frac{1}{8}\]
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Javed was given 5/7 of a basket of oranges. What fraction of oranges was left in the basket?
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Solve (a)\[\frac{0}{1}\] (b)\[\frac{1}{1}\] (c)\[\frac{1}{1}\] (d)\[\frac{1}{1}\] (e)\[\frac{0}{1}\] (f)\[\frac{0}{2}\] (g)\[\frac{1}{6}\frac{1}{3}\] (h)\[\frac{3}{4}\frac{2}{6}\] (i)\[\frac{2}{3}\frac{2}{4}\] (j)\[\frac{6}{6}\frac{3}{3}\] (k)\[\frac{5}{6}\frac{5}{5}\] (l)\[\frac{7}{12}\] (m)\[\frac{9}{10},\frac{5}{8}\] (n)\[\frac{3}{10},\frac{18}{5}\] TIPS To subtract unlike fractions, firstly convert them into equivalent fractions with same denominator which is LCM of denominators of given fractions and then subtract smaller numerator from greater numerator.
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Sarita bought \[\therefore \] metre of ribbon and Lalita bought \[=\frac{\text{Total prime numbers}}{\text{Total natural numbers}}=\frac{5}{11}\] metre of ribbon. What is the total length of the ribbon they bought?
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Naina was given \[\frac{1}{10},\frac{0}{10},\frac{5}{10}\] piece of cake and Najma was given \[\frac{10}{10}\] piece of cake. Find the total amount of cake was given to both of them. TIPS To add two mixed fractions, firstly we convert them into improper fractions and then add them by converting into equivalent fractions with the same denominator.
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Fill in the boxes (a) \[\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{4}{8}\] (b) \[\frac{5}{8}.\] (c) \[\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{4}{8}\]
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Complete the addition-subtraction box.
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A piece of wire \[\frac{8}{5}=\frac{3}{5}=1+\frac{3}{5}\] metre long broke into two pieces. One piece was \[\frac{1}{5}.\] metre long. How long is the other piece?
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Nandini's house is \[\frac{\text{Remainder}}{\text{Divisor}}\] from her school. She walked some distance and then took a bus for \[\frac{20}{3}\] to reach the school. How far did she walk?
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Asha and Samuel have bookshelves of the same size partly filled with books. Asha's shelf \[\therefore \]is full and Samuel's shelf is \[\frac{11}{5}=2\frac{1}{5}\]full. Whose bookshelf is more full? By what fraction?
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Jaidev takes \[\frac{35}{9}\] minutes to walk across the school ground. Rahul takes \[\begin{align} & 9\overline{)35(}3 \\ & \,\,\,\,\frac{27}{\underline{\,8\,\,\,\,\,\,}} \\ \end{align}\]minutes to do the same. Who takes less time and by what fraction?
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