Questions are taken verbatim from the NCERT textbook; answers were grounded against the chapter's content during generation. Items needing review are marked.
Your Progress - Chapter 20% complete
1Exercise 2.11 questions
Q.1-81. Which of the drawings (a) to (d) show: (i) $2\times\frac{1}{5}$ (ii) $2\times\frac{1}{2}$ (iii) $3\times\frac{2}{3}$ (iv) $3\times\frac{1}{4}$? Drawing (a) shows three circles divided into thirds with two-thirds shaded in each circle; drawing (b) shows two rectangles divided into halves with one-half shaded in each rectangle; drawing (c) shows three rectangles divided into four equal parts with one-fourth shaded in each rectangle; drawing (d) shows two circles divided into fifths with one-fifth shaded in each circle.
2. Some pictures (a) to (c) are given below. Tell which of them show: (i) $3\times\frac{1}{5}=\frac{3}{5}$ (ii) $2\times\frac{1}{3}=\frac{2}{3}$ (iii) $3\times\frac{3}{4}=2\frac{1}{4}$? Picture (a) shows two one-third circle parts making two-thirds; picture (b) shows three triangles each with three-fourths shaded, making two whole triangles and one-fourth; picture (c) shows three one-fifth strips making three-fifths.
3. Multiply and reduce to lowest form and convert into a mixed fraction: (i) $7\times\frac{3}{5}$ (ii) $4\times\frac{1}{3}$ (iii) $2\times\frac{6}{7}$ (iv) $5\times\frac{2}{9}$ (v) $\frac{2}{3}\times4$ (vi) $\frac{5}{2}\times6$ (vii) $11\times\frac{4}{7}$ (viii) $20\times\frac{4}{5}$ (ix) $13\times\frac{1}{3}$ (x) $15\times\frac{3}{5}$.
4. Shade: (i) $\frac{1}{2}$ of the circles in box (a), where box (a) has 12 circles (ii) $\frac{2}{3}$ of the triangles in box (b), where box (b) has 9 triangles (iii) $\frac{3}{5}$ of the squares in box (c), where box (c) has 15 squares.
5. Find: (a) $\frac{1}{2}$ of (i) 24 (ii) 46 (b) $\frac{2}{3}$ of (i) 18 (ii) 27 (c) $\frac{3}{4}$ of (i) 16 (ii) 36 (d) $\frac{4}{5}$ of (i) 20 (ii) 35.
6. Multiply and express as a mixed fraction: (a) $3\times5\frac{1}{5}$ (b) $5\times6\frac{3}{4}$ (c) $7\times2\frac{1}{4}$ (d) $4\times6\frac{1}{3}$ (e) $3\frac{1}{4}\times6$ (f) $3\frac{2}{5}\times8$.
7. Find: (a) $\frac{1}{2}$ of (i) $2\frac{3}{4}$ (ii) $4\frac{2}{9}$ (b) $\frac{5}{8}$ of (i) $3\frac{5}{6}$ (ii) $9\frac{2}{3}$.
8. Vidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed $\frac{2}{5}$ of the water. Pratap consumed the remaining water. (i) How much water did Vidya drink? (ii) What fraction of the total quantity of water did Pratap drink?v
SolutionMultiply whole numbers by fractions using $n\times\frac{a}{b}=\frac{na}{b}$, then reduce. For Q8, Vidya drinks $\frac{2}{5}\times5=2$ litres, so Pratap drinks $5-2=3$ litres, i.e. $\frac{3}{5}$ of the total.
Answer:1. (i) (d) (ii) (b) (iii) (a) (iv) (c).
2. (i) (c) (ii) (a) (iii) (b).
3. (i) $4\frac{1}{5}$ (ii) $1\frac{1}{3}$ (iii) $1\frac{5}{7}$ (iv) $1\frac{1}{9}$ (v) $2\frac{2}{3}$ (vi) $15$ (vii) $6\frac{2}{7}$ (viii) $16$ (ix) $4\frac{1}{3}$ (x) $9$.
4. (i) Shade 6 of the 12 circles in box (a) (ii) shade 6 of the 9 triangles in box (b) (iii) shade 9 of the 15 squares in box (c).
5. (a) (i) 12 (ii) 23 (b) (i) 12 (ii) 18 (c) (i) 12 (ii) 27 (d) (i) 16 (ii) 28.
6. (a) $15\frac{3}{5}$ (b) $33\frac{3}{4}$ (c) $15\frac{3}{4}$ (d) $25\frac{1}{3}$ (e) $19\frac{1}{2}$ (f) $27\frac{1}{5}$.
7. (a) (i) $1\frac{3}{8}$ (ii) $2\frac{1}{9}$ (b) (i) $2\frac{19}{48}$ (ii) $6\frac{1}{24}$.
8. (i) 2 litres (ii) $\frac{3}{5}$.
2Exercise 2.21 questions
Q.1-81. Find: (i) $\frac{1}{4}$ of (a) $\frac{1}{4}$ (b) $\frac{3}{5}$ (c) $\frac{4}{3}$ (ii) $\frac{1}{7}$ of (a) $\frac{2}{9}$ (b) $\frac{6}{5}$ (c) $\frac{3}{10}$
2. Multiply and reduce to lowest form (if possible): (i) $2\frac{2}{3}\times\frac{2}{3}$ (ii) $\frac{2}{7}\times\frac{7}{9}$ (iii) $\frac{3}{8}\times\frac{6}{4}$ (iv) $\frac{9}{5}\times\frac{3}{5}$ (v) $\frac{1}{3}\times\frac{15}{8}$ (vi) $\frac{11}{2}\times\frac{3}{10}$ (vii) $\frac{4}{5}\times\frac{12}{7}$
3. Multiply the following fractions: (i) $5\frac{1}{4}\times\frac{2}{5}$ (ii) $6\frac{2}{5}\times\frac{7}{9}$ (iii) $2\frac{3}{5}\times\frac{1}{3}$ (iv) $6\frac{5}{7}\times\frac{3}{2}$ (v) $5\frac{2}{7}\times3\frac{4}{5}$ (vi) $3\frac{3}{5}\times\frac{2}{3}$ (vii) $3\frac{4}{5}\times3\frac{3}{7}$
4. Which is greater: (i) $\frac{2}{7}$ of $\frac{3}{4}$ or $\frac{3}{5}$ of $\frac{5}{8}$ (ii) $\frac{1}{2}$ of $\frac{6}{7}$ or $\frac{2}{3}$ of $\frac{3}{7}$
5. Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is $\frac{3}{4}$ m. Find the distance between the first and the last sapling.
6. Lipika reads a book for $1\frac{3}{4}$ hours everyday. She reads the entire book in 6 days. How many hours in all were required by her to read the book?
7. A car runs 16 km using 1 litre of petrol. How much distance will it cover using $2\frac{3}{4}$ litres of petrol.
8. (a) (i) Provide the number in the box, such that $\frac{2}{3}\times\Box=\frac{10}{30}$. (ii) The simplest form of the number obtained is _____. (b) (i) Provide the number in the box, such that $\frac{3}{5}\times\Box=\frac{24}{75}$. (ii) The simplest form of the number obtained is _____.v
SolutionFor Q5, four saplings create three gaps, so distance $=3\times\frac{3}{4}=\frac{9}{4}=2\frac{1}{4}$ m. For Q6, $6\times1\frac{3}{4}=6\times\frac{7}{4}=10\frac{1}{2}$ hours. For Q7, distance $=16\times2\frac{3}{4}=16\times\frac{11}{4}=44$ km.
Answer:1. (i) (a) $\frac{1}{16}$ (b) $\frac{3}{20}$ (c) $\frac{1}{3}$ (ii) (a) $\frac{2}{63}$ (b) $\frac{6}{35}$ (c) $\frac{3}{70}$.
2. (i) $1\frac{7}{9}$ (ii) $\frac{2}{9}$ (iii) $\frac{9}{16}$ (iv) $\frac{27}{25}$ or $1\frac{2}{25}$ (v) $\frac{5}{8}$ (vi) $1\frac{13}{20}$ (vii) $1\frac{13}{35}$.
3. (i) $2\frac{1}{10}$ (ii) $4\frac{44}{45}$ (iii) $\frac{13}{15}$ (iv) $10\frac{1}{14}$ (v) $20\frac{33}{35}$ (vi) $2\frac{2}{5}$ (vii) $13\frac{1}{35}$.
4. (i) $\frac{3}{5}$ of $\frac{5}{8}$ is greater. (ii) Both are equal, $\frac{3}{7}$.
5. $2\frac{1}{4}$ m.
6. $10\frac{1}{2}$ hours.
7. 44 km.
8. (a) (i) $\frac{5}{10}$ (ii) $\frac{1}{2}$ (b) (i) $\frac{8}{15}$ (ii) $\frac{8}{15}$.
3Exercise 2.31 questions
Q.1-41. Find: (i) $12\div\frac{3}{4}$ (ii) $14\div\frac{5}{6}$ (iii) $8\div\frac{7}{3}$ (iv) $4\div\frac{8}{3}$ (v) $3\frac{1}{2}\div\frac{3}{3}$ (vi) $3\frac{4}{7}\div\frac{5}{3}$
2. Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers. (i) $\frac{3}{7}$ (ii) $\frac{5}{8}$ (iii) $\frac{9}{7}$ (iv) $\frac{6}{5}$ (v) $\frac{12}{7}$ (vi) $\frac{1}{8}$ (vii) $\frac{1}{11}$
3. Find: (i) $\frac{2}{3}\div7$ (ii) $\frac{5}{9}\div4$ (iii) $\frac{7}{13}\div6$ (iv) $3\frac{1}{3}\div4$ (v) $2\frac{3}{4}\div3\frac{1}{2}$ (vi) $7\frac{3}{7}\div7\frac{4}{7}$
4. Find: (i) $\frac{2}{5}\div\frac{1}{2}$ (ii) $\frac{4}{9}\div\frac{2}{3}$ (iii) $\frac{3}{7}\div\frac{8}{7}$ (iv) $2\frac{1}{3}\div3\frac{3}{5}$ (v) $3\frac{1}{2}\div\frac{2}{8}$ (vi) $1\frac{2}{5}\div\frac{1}{2}$ (vii) $3\frac{1}{5}\div1\frac{2}{3}$ (viii) $1\frac{1}{5}\div1\frac{1}{5}$v
SolutionDivide by a fraction by multiplying by its reciprocal: $a\div\frac{b}{c}=a\times\frac{c}{b}$. Convert mixed fractions to improper fractions first.
Answer:1. (i) 16 (ii) $\frac{84}{5}$ (iii) $\frac{24}{7}$ (iv) $\frac{3}{2}$ (v) $\frac{9}{7}$ (vi) $\frac{7}{5}$.
2. (i) $\frac{7}{3}$, improper fraction (ii) $\frac{8}{5}$, improper fraction (iii) $\frac{7}{9}$, proper fraction (iv) $\frac{5}{6}$, proper fraction (v) $\frac{7}{12}$, proper fraction (vi) $8$, whole number (vii) $11$, whole number.
3. (i) $\frac{2}{21}$ (ii) $\frac{5}{36}$ (iii) $\frac{7}{78}$ (iv) $\frac{5}{6}$ (v) $\frac{11}{14}$ (vi) $\frac{13}{14}$.
4. (i) $\frac{4}{5}$ (ii) $\frac{2}{3}$ (iii) $\frac{3}{8}$ (iv) $\frac{35}{54}$ (v) $14$ (vi) $\frac{14}{5}$ (vii) $\frac{48}{25}$ (viii) $1$.
4Exercise 2.41 questions
Q.1-51. Find: (i) $0.2\times6$ (ii) $8\times4.6$ (iii) $2.71\times5$ (iv) $20.1\times4$ (v) $0.05\times7$ (vi) $211.02\times4$ (vii) $2\times0.86$
2. Find the area of rectangle whose length is 5.7 cm and breadth is 3 cm.
3. Find: (i) $1.3\times10$ (ii) $36.8\times10$ (iii) $153.7\times10$ (iv) $168.07\times10$ (v) $31.1\times100$ (vi) $156.1\times100$ (vii) $3.62\times100$ (viii) $43.07\times100$ (ix) $0.5\times10$ (x) $0.08\times10$ (xi) $0.9\times100$ (xii) $0.03\times1000$
4. A two-wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litres of petrol?
5. Find: (i) $2.5\times0.3$ (ii) $0.1\times51.7$ (iii) $0.2\times316.8$ (iv) $1.3\times3.1$ (v) $0.5\times0.05$ (vi) $11.2\times0.15$ (vii) $1.07\times0.02$ (viii) $10.05\times1.05$ (ix) $101.01\times0.01$ (x) $100.01\times1.1$v
SolutionFor decimal multiplication, multiply as whole numbers and place the decimal according to the total number of decimal places. Q2: area $=5.7\times3=17.1\text{ cm}^2$. Q4: distance $=55.3\times10=553$ km.
Answer:1. (i) 1.2 (ii) 36.8 (iii) 13.55 (iv) 80.4 (v) 0.35 (vi) 844.08 (vii) 1.72.
2. $17.1\text{ cm}^2$.
3. (i) 13 (ii) 368 (iii) 1537 (iv) 1680.7 (v) 3110 (vi) 15610 (vii) 362 (viii) 4307 (ix) 5 (x) 0.8 (xi) 90 (xii) 30.
4. 553 km.
5. (i) 0.75 (ii) 5.17 (iii) 63.36 (iv) 4.03 (v) 0.025 (vi) 1.68 (vii) 0.0214 (viii) 10.5525 (ix) 1.0101 (x) 110.011.
5Exercise 2.51 questions
Q.1-61. Find: (i) $0.4\div2$ (ii) $0.35\div5$ (iii) $2.48\div4$ (iv) $65.4\div6$ (v) $651.2\div4$ (vi) $14.49\div7$ (vii) $3.96\div4$ (viii) $0.80\div5$
2. Find: (i) $4.8\div10$ (ii) $52.5\div10$ (iii) $0.7\div10$ (iv) $33.1\div10$ (v) $272.23\div10$ (vi) $0.56\div10$ (vii) $3.97\div10$
3. Find: (i) $2.7\div100$ (ii) $0.3\div100$ (iii) $0.78\div100$ (iv) $432.6\div100$ (v) $23.6\div100$ (vi) $98.53\div100$
4. Find: (i) $7.9\div1000$ (ii) $26.3\div1000$ (iii) $38.53\div1000$ (iv) $128.9\div1000$ (v) $0.5\div1000$
5. Find: (i) $7\div3.5$ (ii) $36\div0.2$ (iii) $3.25\div0.5$ (iv) $30.94\div0.7$ (v) $0.5\div0.25$ (vi) $7.75\div0.25$ (vii) $76.5\div0.15$ (viii) $37.8\div1.4$ (ix) $2.73\div1.3$
6. A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it cover in one litre of petrol?v
SolutionWhen dividing by 10, 100 or 1000, shift the decimal point left by 1, 2 or 3 places. For Q6, distance per litre $=43.2\div2.4=18$ km.
Answer:1. (i) 0.2 (ii) 0.07 (iii) 0.62 (iv) 10.9 (v) 162.8 (vi) 2.07 (vii) 0.99 (viii) 0.16.
2. (i) 0.48 (ii) 5.25 (iii) 0.07 (iv) 3.31 (v) 27.223 (vi) 0.056 (vii) 0.397.
3. (i) 0.027 (ii) 0.003 (iii) 0.0078 (iv) 4.326 (v) 0.236 (vi) 0.9853.
4. (i) 0.0079 (ii) 0.0263 (iii) 0.03853 (iv) 0.1289 (v) 0.0005.
5. (i) 2 (ii) 180 (iii) 6.5 (iv) 44.2 (v) 2 (vi) 31 (vii) 510 (viii) 27 (ix) 2.1.
6. 18 km.