Q: 1. 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 _____.

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) $\frac{8}{15}$.

Q: 1. 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) $1\frac{1}{5}\div1\frac{1}{5}$

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) $1$.

Question 1

1. Which of the drawings (a) to (d) show: (i) $2	imes\frac{1}{5}$ (ii) $2	imes\frac{1}{2}$ (iii) $3	imes\frac{2}{3}$ (iv) $4	imes\frac{1}{3}$ 2. Some pictures (a) to (c) are given below. Tell which of them show: (i) $3	imes\frac{1}{5}=\frac{3}{5}$ (ii) $2	imes\frac{1}{3}=\frac{2}{3}$ (iii) $3	imes\frac{3}{4}=2\frac{1}{4}$ 3. Multiply and reduce to lowest form and convert into a mixed fraction: (i) $5	imes\frac{3}{7}$ (ii) $3	imes\frac{1}{4}$ (iii) $7	imes\frac{6}{2}$ (iv) $9	imes\frac{2}{5}$ (v) $3	imes\frac{2}{4}$ (vi) $2	imes\frac{5}{6}$ (vii) $7	imes\frac{4}{11}$ (viii) $5	imes\frac{4}{20}$ (ix) $3	imes\frac{1}{13}$ (x) $5	imes\frac{3}{15}$ 4. Shade: (i) $\frac{1}{2}$ of the circles in box (a) (ii) $\frac{2}{3}$ of the triangles in box (b) (iii) $\frac{3}{5}$ of the squares in box (c). 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) $5	imes3\frac{1}{5}$ (b) $6	imes5\frac{3}{4}$ (c) $4	imes7\frac{1}{2}$ (d) $3	imes8\frac{1}{3}$ (e) $4	imes6\frac{1}{3}$ (f) $5	imes8\frac{2}{3}$ 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?

Accepted Answer

1. (i) (d) (ii) (b) (iii) (a) (iv) (c). 2. (i) (c) (ii) (a) (iii) (b). 3. (i) $2\frac{1}{7}$ (ii) $\frac{3}{4}$ (iii) $21$ (iv) $3\frac{3}{5}$ (v) $1\frac{1}{2}$ (vi) $1\frac{2}{3}$ (vii) $2\frac{6}{11}$ (viii) $1$ (ix) $\frac{3}{13}$ (x) $1$. 4. Figure-shading answer depends on copied boxes. 5. (a) (i) 12 (ii) 23 (b) (i) 12 (ii) 18 (c) (i) 12 (ii) 27 (d) (i) 16 (ii) 28. 6. (a) $16$ (b) $34\frac{1}{2}$ (c) $30$ (d) $25$ (e) $25\frac{1}{3}$ (f) $43\frac{1}{3}$. 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) $\frac{3}{5}$.

Question 2

1. 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) $2\frac{2}{3}	imes\frac{2}{3}$ (ii) $\frac{2}{7}	imes\frac{7}{9}$ (iii) $\frac{3}{8}	imes\frac{6}{4}$ (iv) $\frac{9}{5}	imes\frac{3}{5}$ (v) $\frac{1}{3}	imes\frac{15}{8}$ (vi) $\frac{11}{2}	imes\frac{3}{10}$ (vii) $\frac{4}{5}	imes\frac{12}{7}$ 3. Multiply the following fractions: (i) $5\frac{1}{4}	imes\frac{2}{5}$ (ii) $6\frac{2}{5}	imes\frac{7}{9}$ (iii) $2\frac{3}{5}	imes\frac{1}{3}$ (iv) $6\frac{5}{7}	imes\frac{3}{2}$ (v) $5\frac{2}{7}	imes3\frac{4}{5}$ (vi) $3\frac{3}{5}	imes\frac{2}{3}$ (vii) $3\frac{4}{5}	imes3\frac{3}{7}$ 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 $\frac{2}{3}	imes\Box=\frac{10}{30}$. (ii) The simplest form of the number obtained is _____. (b) (i) Provide the number in the box, such that $\frac{3}{5}	imes\Box=\frac{24}{75}$. (ii) The simplest form of the number obtained is _____.

Accepted 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}

.

Question 3

1. 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) $1\frac{1}{5}\div1\frac{1}{5}$

Accepted 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)

$1$

.

Question 4

1. Find: (i) $0.2	imes6$ (ii) $8	imes4.6$ (iii) $2.71	imes5$ (iv) $20.1	imes4$ (v) $0.05	imes7$ (vi) $211.02	imes4$ (vii) $2	imes0.86$ 2. Find the area of rectangle whose length is 5.7 cm and breadth is 3 cm. 3. Find: (i) $1.3	imes10$ (ii) $36.8	imes10$ (iii) $153.7	imes10$ (iv) $168.07	imes10$ (v) $31.1	imes100$ (vi) $156.1	imes100$ (vii) $3.62	imes100$ (viii) $43.07	imes100$ (ix) $0.5	imes10$ (x) $0.08	imes10$ (xi) $0.9	imes100$ (xii) $0.03	imes1000$ 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) $2.5	imes0.3$ (ii) $0.1	imes51.7$ (iii) $0.2	imes316.8$ (iv) $1.3	imes3.1$ (v) $0.5	imes0.05$ (vi) $11.2	imes0.15$ (vii) $1.07	imes0.02$ (viii) $10.05	imes1.05$ (ix) $101.01	imes0.01$ (x) $100.01	imes1.1$

Accepted 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.

Question 5

1. 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?

Accepted 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.