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S.chand publication New Learning Composite mathematics solution of class 7 Chapter 2 Fractions and Decimals Exercise 2I

Exercise 2I

Question 1

Multiply :

(a) $\begin{array}{r}0.007 \\\times \quad 5 \\\hline \end{array}$

Sol :

$\begin{array}{r}0.007 \\\times 5 \\\hline 0035\end{array}$

(b) $\begin{array}{r}0.009 \\\times \quad 0.7 \\\hline\end{array}$

Sol :

$\begin{array}{r}0.009 \\\times \quad 0.7 \\\hline 0.0063\end{array}$

(c) $\begin{array}{r}4.05 \\\times \quad 8 \\ \hline\end{array}$

Sol :

$\begin{array}{r}4.05 \\\times 8 \\\hline 32.40 \\\hline\end{array}$

(d) $\begin{array}{r}2.06 \\\times 0.03 \\\hline\end{array}$

Sol :

$\begin{array}{r}2.06 \\\times 0.03 \\\hline 0.0618\end{array}$

Question 2

(a) 39.6×0.8

Sol : 31.68

(b) 7.003×1.6

Sol : 11.2048

(c) 897×0.008

Sol : 7.176

Question 3

(a) 1.025×0.0048

Sol : 0.00492

(b) 0.0035×0.726

Sol : 0.0025410

(c) 7.5089×0.47

Sol : 3.529183

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 2 Fractions and Decimals Exercise 2L

Exercise 2L

Convert:

Question 1

(a) 3 km = How many meter

Sol : = (3×1000)m=3000m

(b) 2 m = How many centimeter

Sol : = (2×100)cm=200cm

(c) 5 cm = How many milimeter

Sol : (5×10)mm=50mm

(d) 2.9 m = How many centimeter

Sol : (2.9×100)cm=290cm

(e) 0.89 km = How many meter

Sol : (0.89×1000)m=890m

(f) 0.3 m = How many milimeter

Sol : (0.3×1000)mm=300mm

(g) 7 dam = How many meter

Sol : (7×10)m=70m

(h) 5 hm = How many meter

Sol : (5×100)m=500m

(i) 2 m = How many decemeter.

Sol : (2×10)dm=20dm

Question 2

(a) 478 cm = How many meter

Sol : $=\frac{478}{100}$m=4.78m

(b) 3209 centimeter = How many meter

Sol : $=\frac{3209}{100}$ m

(c) 90 milimeter = How many how many centimeter.

Sol : $=\frac{9}{10}$cm=0.9cm

(d) 49 meter = How many kilometer.

Sol : $=\frac{49}{1000}$km==0.049km

(e) 2000 m = How many kilometer

Sol : $=\frac{2000}{1000}$km=2km

(f) 200 cm = How many meter.

Sol : $=\frac{200}{100}$m=2m

(g) 428 milimeter = How many meter

Sol : $=\frac{428}{1000}$m=0.428m

(h) 3 milimeter = how many meter

Sol : $=\frac{3}{1000}$m=0.003m

(i) 8 dacemeter = How many kilometer.

Sol : $=\frac{8}{100}km$=0.08km

Question 3

(a) 5 kg = How many gram

Sol : (5×1000)g=5000

(b) 3.7 kg = How many gram

Sol : (3.7×1000)g=3700

(c) 0.289 kg = How many gram

Sol : (0.289×1000)g=289

(d) 3.59 g = How many miligram

Sol : (3.59×1000)g=3590

(e) 9 g = How many miligram.

Sol : (9×1000)g=9000

(f) 0.05 g = How many miligram.

Sol : (0.05×1000)g=50

(g) 2 q = How many kilogram

Sol : (2×100)kg=200kg

(h) 2.9 t = how many kilogram

Sol : (2.9×1000)kg=2900kg

(i) 0.032 kg = How many gram

Sol : (0.032×1000)g=32g

Question 4

(a) 4000 g = How many kilogram

Sol : $=\frac{4000}{1000}$kg=4kg

(b) 1800 gram = How many kilogram.

Sol : $=\frac{1800}{1000}$kg=1.8kg

(c) 46 g = How many kilogram

Sol : $\frac{46}{1000}$kg

(d) 729 mg = How many gram.

Sol : $\frac{729}{1000}$kg=0.729g

(e) 700 mg = How many gram.

Sol : $=\frac{700}{1000}$g=0.7g

(f) 67 mg = How many gram.

Sol : $=\frac{67}{1000}$g=0.067g

(g) 8 mg = How many gram

Sol : $=\frac{8}{1000}$g=0.008g

(h) 9 g = How many kilogram

Sol : $=\frac{9}{1000}$kg=0.009kg

(i) 2 cg = How many miligram.

Sol : (2×10)mg=20

Question 5

(a) 4 hg = How many gram.

Sol : (4×100)g=400g

(b) 1.9 km = How many decemeter.

Sol : (1.9×10000)g=19000g

(c) 8.3 decagram = How many dg.

Sol : (8.3×100)dg=830dg

(d) 75 dam = How many kilometer

Sol : $=\frac{75}{100}$km=0.75km

(e) 4 dg = How many miligram

Sol : =(4×100)mg=400mg

(f) 300 kg = How many quintal.

Sol : $=\frac{300}{100}$q=3q

Question 6

Compare and put <,> or == in the given boxes.

(a) 5,000 mm ____ 5 m

Sol : 5,000 mm = 5 m

(b) 3.8 kg ____ 400 g

Sol : 3.8 kg > 400 g

(c) 5 mg ____ 1 g

Sol : 5 mg < 1 g

(d) 3 g ____ 30,000 mg

Sol : 3 g < 30,000 mg

(e) 0.0087 m ____ 8.7 mm

Sol : 0.0087 m = 8.7 mm

(f) 0.2 km ____ 2000 mm

Sol : 0.2 km > 2000 mm

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 2 Fractions and Decimals Exercise 2J

Exercise 2J

Question 1

Find the value of

(a) 0.132÷6

=0.022

(b) 0.98÷7

=0.14

(c) 1.245÷15

=0.083

(d) 0.837÷9

=0.093

(e) 0.0125÷5

=0.0025

(f) 69.531÷11

=6.321

(g) 72.00120÷24

=3.00005

(h) 87.138÷9

=9.682

(i) 0.01001÷22

=0.000455

Question 2

(a) 20.4÷600

$=\frac{204}{6000}$

=0.034

(b) 47.136÷12000

$=\frac{47136}{12000}$

=0.003928

(c) 1.98÷9000

$=\frac{198}{900000}$

=0.00022

(d) 2.16÷1800

$=\frac{216}{180000}$

=0.0012

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 2 Fractions and Decimals Exercise 2F

Exercise 2F

Question 1

Simplify and express your answers in simplest form and mixed numbers.

(a) $1\frac{1}{4} \times \frac{2}{3} \div \frac{1}{6}$

$=\frac{5}{4} \times \frac{2}{3} \times \frac{6}{1}$

(b) $1\frac{1}{2} \div \left(\frac{1}{4}\times \frac{2}{3}\right)$

Sol :

$=\frac{3}{2}\div \left(\frac{1}{24} \times \frac{2}{3}\right)$

$=\frac{3}{2} \div \frac{1}{6}$

$=\frac{8}{2} \times \frac{6}{1}$

=9

(c) $16 \div \frac{1}{4} \div 4$

$=16\times \frac{4}{1}\times \frac{1}{4}$

=16

(d) $\frac{5}{8} \div 3\times 6$

$=\frac{5}{8} \times \frac{1}{3} \times 6$

$=\frac{5}{4}=1\frac{1}{4}$

(e) $\frac{3}{8}\times 3 -\frac{1}{8}+\frac{2}{3}$

$=\frac{9}{8}-\frac{1}{8}+\frac{2}{3}$

$=\frac{27-3+16}{24}$

$=\frac{40}{24}=\frac{5}{3}=1\frac{2}{3}$

(f) $6\frac{1}{4}\div \frac{5}{8} \div \frac{5}{2} +1$

$=\frac{25}{4} \times \frac{8}{5} \times \frac{2}{5}+1$

=4+1=5

(g) $1\frac{1}{4} \times 7 \div \left(12\frac{7}{12} -11\frac{1}{3}\right)$

$=\frac{5}{4}\times 7 \div \left(\frac{151}{12}- \frac{34}{3}\right)$

$=\frac{5}{4} \times 7 \div \left(\frac{151-136}{12}\right)$

$=\frac{5}{4} \times 7\times \frac{12}{15}$

Question 2

The expression $\frac{1}{2}+\left\{4 \frac{3}{4}-\left(3 \frac{1}{6}-2 \frac{1}{3}\right)\right\}$ is equal to

(a) $3 \frac{2}{3}$

(b) $1 \frac{1}{4}$

(c) $4 \frac{5}{12}$

(d) $1 \frac{2}{3}$

Sol :

$\frac{1}{2} \left\{4\frac{3}{4}-\left(3\frac{1}{6}-2\frac{1}{3}\right)\right\}$

$=\frac{1}{2}+\left\{\frac{19}{4}-\left(\frac{19}{6}-\frac{7}{3}\right)\right\}$

$=\frac{1}{2}+\left\{\frac{19}{4}-\left(\frac{19-14}{6}\right)\right\}$

$=\frac{1}{2}+\left\{\frac{19}{4}-\frac{5}{6}\right\}$

$=\frac{1}{2}+\left\{\frac{15-10}{12}\right\}$

$=\frac{1}{2}+\frac{147}{12}$

$=\frac{6+47}{12}=\frac{53}{12}=4\frac{5}{12}$

Question 3

The value of $\left[3 \frac{1}{4} \div\left\{1 \frac{1}{4}-\frac{1}{2}\left(2 \frac{1}{2}-\frac{1}{4}-\frac{1}{6}\right)\right\}\right] \div\left(\frac{1}{2}\right.$ of $\left.4 \frac{1}{3}\right)$ is

(a) 18

(b) 36

(c) 39

(d) 78

Sol :

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{1}{2}\left(\frac{5}{2}-\frac{1}{4}-\frac{1}{6}\right)\right\}\right]\div \left(\frac{1}{2} \times \frac{13}{3}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{1}{2}\left(\frac{5}{2}-\frac{3-2}{12}\right)\right\}\right]\div \left(\frac{1}{2} \times \frac{13}{3}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{1}{2}\left(\frac{5}{2}-\frac{1}{12}\right)\right\}\right]\div \left(\frac{1}{2} \times \frac{13}{3}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{1}{2}\left(\frac{30-1}{12}\right)\right\}\right]\div \left(\frac{1}{2} \times \frac{13}{3}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{1}{2} \times \frac{29}{12}\right\}\right]\div \left(\frac{13}{6}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{5}{4}-\frac{29}{24}\right\}\right]\div \left(\frac{13}{6}\right)$

$=\left[ \frac{13}{4} \div \left\{\frac{30-29}{24}\right\}\right]\div \left(\frac{13}{6}\right)$

$=\left[\frac{13}{4} \div \frac{1}{24}\right] \div \frac{13}{6}$

$=\left[\frac{13}{4} \times \frac{24}{1}\right] \div \frac{13}{6}$

$=78\times \frac{6}{13}$

=36

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 2 Fractions and Decimals Exercise 2D

Exercise 2D

Q1 | Ex-2D | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

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Question 1

Find the reciprocal of :

(a) $\frac{1}{3}$

(b) $\frac{7}{8}$

(c) $2 \frac{2}{3}$

(d) 5

Sol :

(a) Reciprocal of $\frac{1}{3}=3$

(b) Reciprocal of $\frac{7}{8}=\frac{8}{7}=1\frac{1}{7}$

(d) Reciprocal of $5=\frac{1}{5}$

(e) Reciprocal of $6\frac{1}{6}=\frac{6}{37}$

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Question 2

By taking following examples, show that the product of a number and its reciprocal

(a) $\frac{25}{37}$

(b) $5 \frac{1}{9}$

(c) $7 \frac{1}{7}$

(d) $1 \frac{11}{35}$

Sol :

(a) Reciprocal of $\frac{25}{37}=\frac{37}{25}$

∴$\frac{25}{37}\times \frac{37}{25}$

(b) Reciprocal of $5\frac{1}{9}=\frac{46}{9}$

∴$\frac{46}{9}\times \frac{9}{46}$

∴$\frac{50}{7}\times \frac{7}{50}$

(d) $1\frac{11}{35}=\frac{46}{35}$

Reciprocal of $\frac{46}{35}=\frac{35}{46}$

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Question 3

Think and answer- in defining reciprocal of we have imposed the condition $a\not =0,~ b\not=0$ why ? Give reason.

Sol :

Because division by zero is not defined

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 2 Fractions and Decimals Exercise 2C

Exercise 2C

Q1 | Ex-2C | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

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Question 1

Simplify:

(a) $\frac{3}{4}\times \frac{12}{17}$

Sol :

$=\frac{9}{17}$

(b) $\frac{7}{9}\times \frac{18}{19}$

Sol :

$=\frac{14}{19}$

(c) $\frac{8}{15}\times \frac{5}{16}$

Sol :

$=\frac{1}{6}$

(d) $\frac{5}{26}\times \frac{39}{40}$

Sol :

$=\frac{3}{16}$

Q2 | Ex-2C | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

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Question 2

Multiply and write each answer in simplest form.

(a) $\frac{9}{16}$ by $\frac{8}{15}, \frac{10}{27}, 1 \frac{7}{9}, 3 \frac{5}{9}$

(i)

$\frac{9}{16}\times \frac{8}{15}$

$=\frac{3}{10}$

(ii)

$\frac{9}{16}\times \frac{10}{27}$

$=\frac{5}{24}$

(iii)

$\frac{9}{16}\times 1\frac{7}{9}$

$=\frac{9}{16}\times \frac{16}{9}$

(iv)

$\frac{9}{16}\times 3\frac{5}{9}$

$=\frac{9}{16}\times \frac{32}{9}$

(b) $1 \frac{3}{5}$ by $\frac{5}{8}, 1 \frac{1}{4}, \frac{15}{16}, 3 \frac{3}{4}$

(i)

$1\frac{3}{5}\times \frac{5}{8}$

$=\frac{8}{5}\times \frac{5}{8}$

(ii)

$1\frac{3}{5}\times 1 \frac{1}{4}$

$=\frac{8}{5}\times \frac{5}{4}$

(iii)

$1\frac{3}{5}\times \frac{15}{16}$

$=\frac{8}{5}\times \frac{15}{16}$

$=\frac{3}{2}=1\frac{1}{2}$

(iv)

$1\frac{3}{5}\times 3\frac{3}{4}$

$=\frac{8}{5}\times \frac{15}{4}$

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Question 3

Simplify the following.

(a) $2\frac{3}{8}\times 5\frac{1}{5}$

Sol :

$=\frac{19}{8}\times \frac{26}{5}$

$=\frac{247}{20}=12\frac{7}{20}$

(b) $2\frac{2}{9}\times \frac{3}{5}$

Sol :

$=\frac{20}{9}\times \frac{3}{5}$

$=\frac{4}{3}=1\frac{1}{3}$

(c) $1\frac{1}{2}\times 2\frac{2}{5}$

Sol :

$=\frac{3}{2}\times \frac{12}{5}$

$=\frac{18}{5}=3\frac{3}{5}$

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Question 4

(a) $2 \times \frac{4}{5} \times 1 \frac{2}{3}$

$2\frac{4}{5}\times \frac{5}{3}$

$=\frac{8}{3}$

(b) $2\frac{5}{6}\times \frac{18}{85}\times 3\frac{8}{9}$

$=\frac{17}{6}\times \frac{18}{85}\times \frac{35}{9}$

$=\frac{7}{3}=2\frac{1}{3}$

(c) $1\frac{2}{7}\times 3\times 2\frac{5}{8}$

$=\frac{9}{7}\times 3\times \frac{21}{8}$

$=\frac{81}{8}=10\frac{1}{8}$

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Question 5

Ravi used $1 \frac{2}{5}$ bags of soil for his garden. He is digging another garden that will need $\frac{1}{5}$ as much soil a original. How much soil will he use in total?

Sol :

Ravi used soil in total$=\left(1\frac{2}{5}\times \frac{1}{5}\right)+1\frac{2}{5}$

$=\left(\frac{7}{5}\times \frac{1}{5}\right)+\frac{7}{5}$

$=\frac{7}{25}+\frac{7}{5}$

$=\frac{7+35}{25}=\frac{42}{25}$

$=1\frac{17}{25}$

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 2 Fractions and Decimals Exercise 2B

Exercise 2B

Q1 | Ex-2B | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

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Question 1

Simplify :

(a) $\frac{1}{3}+\frac{1}{3}+\frac{1}{3}+\frac{1}{3}$

Sol :

$=\frac{1+1+1+1}{3}$

$=\frac{4}{3}=1\frac{1}{3}$

(b) $\frac{2}{5}+\frac{2}{5}+\frac{2}{5}+\frac{2}{5}+\frac{2}{5}$

Sol :

$=\frac{2+2+2+2+2}{5}$

$=\frac{10}{5}$

Q2 | Ex-2B | Class 7 | Schand New Learning Composite | Fractions and Decimals | Chapter 2| myhelper

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Question 2

(a) $7\times \frac{1}{8}$
Sol :

$=\frac{7}{8}$

(b) $8\times \frac{2}{15}$

Sol :

$=\frac{16}{15}=1\frac{1}{15}$

(c) $8\times \frac{3}{4}$

Sol :

$=\frac{24}{4}$

(d) $20\times \frac{4}{5}$

Sol :

=16

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Question 3

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

Sol :

$=\frac{43}{9}\times 12=\frac{172}{3}$

$=57\frac{1}{3}$

(b) $\frac{1}{48}\times 6$

Sol :

$=\frac{1}{8}$

(c) $2\frac{1}{10}\times 15$

Sol :

$=\frac{21}{10}\times 15$

$=\frac{63}{2}=31\frac{1}{2}$

(d) $4\frac{1}{6}\times 3$

Sol :

$=\frac{25}{6}\times 3$

$=12\frac{1}{2}$

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Question 4

Evaluate each expression. write each answer in simplest form

(a) 15a for a $=\frac{11}{15}$

Sol :

$=15\times \frac{11}{15}$

=11

(b) $\frac{2}{3} x$ for $x=27$

Sol :

$=\frac{2}{3}\times 21$

=18

(c) $\frac{1}{4} y$ for $y=36$

Sol :

$=\frac{1}{4}\times 36$

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Question 5

Compare write >, < or =

(a) $8 \times \frac{1}{20} \square \frac{1}{3}$

Sol :

$8\times \frac{1}{20}=\frac{2}{5}$

$\frac{2}{5} \square \frac{1}{3}$

L.C.M of 5,3 is 15

$\frac{2\times 3}{5\times 3}=\frac{6}{15}$

$\frac{1 \times 5}{3 \times 5}=\frac{5}{15}$

$8\frac{1}{20}>\frac{1}{3}$

(b) $7 \square 28 \times \frac{2}{7}$

Sol :

$28\times \frac{2}{7}$

$7<28\times \frac{2}{7}$

(c) $8 \times \frac{3}{32} \square \frac{3}{4}$

Sol :

$8\times \frac{3}{32}=\frac{3}{4}$

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Question 6

Nishi spent 90 minutes completing her homework Of those minutes she spent $\frac{1}{9}$ minutes on learning spelling how much time did Nishi spent on learning spelling?

Sol :

Nishi spend time on learning spellings $= \left(90 \times \frac{1}{9}\right)$ m

= 10 m.

S.chand publication New Learning Composite mathematics solution of class 7 Chapter 2 Fractions and Decimals Exercise 2A

Exercise 2A

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Question 1

Find the value of

(a) $\frac{1}{5}$ of 1 hour 10 minutes

Sol :

$\begin{aligned} 1 \mathrm{~h} 10 \mathrm{~m} &=\{(1 \times 60)+10\} \mathrm{m} \\ &=70~m \\ \frac{1}{5} \text { of } 70 &=\frac{1}{5} \times 70 \mathrm{~m} \\ &=14~m \end{aligned}$

(b) $\frac{1}{5}$ of a non-leap year

Sol :

$\begin{aligned} \frac{1}{5} \text { of } 365 \text{days} &=\left(\frac{1}{5} \times 365\right) \text{days} \\ &=73 \end{aligned}$

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Question 2

Express $\frac{1}{2}$ as quarters, sixths, eighths, 12 ths, 16 ths and 24 ths.

Sol :

Quarters $=\frac{1}{2} \times \frac{2}{2}=\frac{2}{4}$

Sixths $=\frac{1}{2} \times \frac{3}{3}=\frac{3}{6}$

Eights $=\frac{1}{2} \times \frac{4}{4}=\frac{4}{8}$

12 ths $=\frac{1}{2} \times \frac{6}{6}=\frac{6}{12}$

16 ths $=\frac{1}{2} \times \frac{8}{8}=\frac{8}{16}$

24 ths $=\frac{1}{2} \times \frac{12}{12}=\frac{12}{24}$

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Question 3

Express $\frac{3}{8}$ as fraction with

(a) numerator 15

(b) denominator 72

Sol :

(a) $\frac{3}{8} \times \frac{5}{5}=\frac{15}{40}$

(b) $\frac{3}{8} \times \frac{9}{9}=\frac{27}{72}$

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Question 4

Reduce each of the following fractions to its lowest terms.

(a) $\frac{18}{48}$

(b) $\frac{105}{120}$

(c) $\frac{210}{315}$

Sol :

(a) $=\frac{18\div 2}{48 \div 2}=\frac{9\div 3}{24\div 3}=\frac{3}{8}$

(b) $=\frac{105\div 5}{120\div 5}=\frac{21\div3}{24\div 3}=\frac{7}{8}$

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Question 5

Express each of the following mixed number as improper fraction

(a) $9 \frac{7}{10}$

$=\frac{(9 \times 10)+7}{10}$

$=\frac{97}{10}$

(b) $3 \frac{15}{22}$

$=\frac{(3 \times 22)+15}{22}$

$=\frac{81}{22}$

(c) $18 \frac{11}{30}$

$=\frac{(18 \times 30)+11}{30}$

$=\frac{551}{30}$

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Question 6

Express each of the following as mixed number

(a) $\frac{19}{5}=3 \frac{4}{5}$

(b) $\frac{77}{24}=3 \frac{5}{24}$

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Question 7

In each of the following write down the largest value and smallest value

(a) $\frac{2}{11}, \frac{8}{11}, \frac{5}{11}, \frac{9}{11}$

Sol :

Largest value$=\frac{9}{11}$

Smallest value$=\frac{2}{11}$

(b) $\frac{2}{3}, \frac{2}{7}, \frac{2}{5}, \frac{2}{9}$

Sol :

LCM of 3,7,5,9=315

$\frac{2 \times 105}{3 \times 105}=\frac{210}{315}$

$\frac{2 \times 45}{7 \times 45}=\frac{90}{315}$

$\frac{2 \times 63}{5 \times 63}=\frac{126}{315}$

$\frac{2 \times 35}{9 \times 35}=\frac{70}{315}$

Largest value $=\frac{2}{3}$

Smallest value $=\frac{2}{9}$

(c) $\frac{9}{16}, \frac{3}{5}, \frac{11}{20}, \frac{23}{40}$

Sol :

LCM of 16,5,20,40 is 80

$\frac{9 \times 5}{16 \times 5}=\frac{45}{80}$

$\frac{3 \times 16}{5 \times 16}=\frac{48}{80}$

$\frac{11 \times 4}{20 \times 4}=\frac{44}{80}$

$\frac{23 \times 2}{40 \times 2}=\frac{46}{80}$

Largest value $=\frac{3}{5}$

Smallest value $=\frac{11}{20}$

(d) $\frac{5}{6}, \frac{13}{15}, \frac{23}{30}, \frac{14}{18}$

Sol :

LCM of 6, 15, 30, 18 is 90

$\frac{5 \times 15}{6 \times 15}=\frac{75}{90}$

$\frac{13 \times 6}{15 \times 6}=\frac{78}{90}$

$\frac{23 \times 3}{30 \times 3}=\frac{69}{90}$

$\frac{14 \times 5}{18 \times 5}=\frac{70}{90}$

$\begin{aligned} \text { Largest } \text { value } &=\frac{13}{15} \\ \text { Smallest value} &=\frac{23}{30} \end{aligned}$

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Question 8

Insert < = or >

(a) $\frac{4}{9} \square \frac{5}{12}$

Sol :

LCM of 9, 12 is 36

$\frac{4 \times 4}{9 \times 4}=\frac{16}{36}$

$\frac{5 \times 3}{12 \times 3}=\frac{15}{36}$

∴$\frac{4}{9}>\frac{5}{12}$

(b) $\frac{7}{24} \square \frac{11}{36}$

Sol :

LCM of 24,36 is 72

$\begin{aligned}&\frac{7 \times 3}{24 \times 3}=\frac{21}{72} \\&\frac{11 \times 2}{36 \times 2}=\frac{22}{72}\end{aligned}$

∴$\frac{7}{24}<\frac{11}{36}$

(c) $\frac{4}{5} \square \frac{12}{15}$

Sol :

LCM of 5, 15 is 15

$\frac{4 \times 3}{5 \times 3}=\frac{12}{15}$

$\frac{12 \times 1}{15 \times 1}=\frac{12}{15}$

∴$\frac{4}{5}=\frac{12}{15}$

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Question 9

Arrange in descending order

(a) $\frac{3}{10}, \frac{2}{5}, \frac{1}{3}$

Sol :

(a) LCM of 10, 5, 3 is 30

$\frac{3 \times 3}{10 \times 3}=\frac{9}{30}$

$\frac{2 \times 6}{5 \times 6}=\frac{12}{30}$

$\frac{1 \times 10}{3 \times 10}=\frac{10}{30}$

∴$\frac{2}{5}, \frac{1}{3}, \frac{3}{10}$

(b) $\frac{7}{12}, \frac{5}{9}, \frac{9}{16}$

Sol :

LCM of 12, 9, 16 is 144

$\frac{7 \times 12}{12 \times 12}=\frac{84}{144}$

$\frac{5 \times 16}{9 \times 16}=\frac{80}{144}$

$\frac{9 \times 9}{16 \times 9}=\frac{81}{144}$

∴$\frac{7}{12},\frac{9}{16}, \frac{5}{9}$

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Question 10

Arrange in ascending order

(a) $\frac{11}{15} , \frac{3}{4}, \frac{13}{20}$

Sol :

LCM of 15, 4, 20 is 60

$\frac{11 \times 4}{15 \times 4}=\frac{44}{60}$

$\frac{3 \times 15}{4 \times 15}=\frac{45}{60}$

$\frac{13 \times 3}{20 \times 3}=\frac{39}{60}$

$\frac{39}{60}<\frac{44}{60} <\frac{45}{60} $

∴$\frac{13}{20}< \frac{11}{15}< \frac{3}{4}$

(b) $\frac{5}{12}, \frac{7}{18}, \frac{11}{27}$

Sol :

LCM of 12, 8, 27 is 108

$\frac{5 \times 9}{12 \times 9}=\frac{45}{108}$

$\frac{7 \times 6}{18 \times 6}=\frac{42}{108}$

$\frac{11 \times 4}{27 \times 4}=\frac{44}{108}$

∴$\frac{7}{18}, \frac{11}{27}, \frac{5}{12}$

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Question 11

Simplify the following, expressing your answer in the simplest form

(a) $\frac{17}{24}+\frac{1}{24}$

Sol :

$\begin{aligned} =& \frac{17}{24}+\frac{1}{24} \\=& \frac{17+1}{24} \\=& \frac{18}{24} \\=& \frac{3}{4} \end{aligned}$

(b) $\frac{14}{15}+\frac{11}{15}+1 \frac{1}{15}$

Sol :

$\frac{14}{15}+\frac{11}{15}+1 \frac{1}{15}$

$=\frac{14}{15}+\frac{11}{15}+\frac{16}{15}$

$=\frac{14+11+16}{15}$

$=\frac{41}{15}=2 \frac{11}{15}$

(c) $\frac{5}{6}-\frac{1}{6}$

Sol :

$=\frac{5}{6}-\frac{1}{6}$

$=\frac{5-1}{6}$

$=\frac{4}{6}=\frac{2}{3}$

(d) $12 \frac{6}{7}-9 \frac{1}{7}$

Sol :

$\begin{aligned} =& 12 \frac{6}{7}-9 \frac{1}{7} \\=& \frac{90}{7}-\frac{64}{7} \\=& \frac{90-64}{7} \\=& \frac{26}{7} \\=& 3 \frac{5}{7} \end{aligned}$

(e) $18 \frac{12}{19}+23 \frac{18}{19}-15 \frac{14}{19}$

Sol :

$18 \frac{12}{19}+23 \frac{18}{19}-15 \frac{14}{19}$

$\begin{aligned}&=(18+23-15)+\frac{12}{19}+\frac{18}{19}-\frac{14}{19} \\&=26+\frac{12+18-14}{19} \\&=26+\frac{16}{19} \\&=\frac{494+16}{19} \\&=\frac{510}{19} \\&=26 \frac{16}{19}\end{aligned}$

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Question 12

(a) $\frac{15}{1}+4 \frac{1}{4}$

Sol :

$\begin{aligned}=& 15+4 \frac{1}{4} \\=& 15+\frac{17}{4} \\=& \frac{60+17}{4} \\=& \frac{77}{4} \\=& 19 \frac{1}{4}\end{aligned}$

(b) $\frac{27}{1}-3 \frac{1}{5}$

Sol :

$\begin{aligned}=&27-3 \frac{1}{5} \\=&27-\frac{16}{5} \\=&\frac{135-16}{5} \\=&\frac{119}{5} \\=&23 \frac{4}{5}\end{aligned}$

(c) $61-2 \frac{7}{8}$

Sol :

$\begin{aligned}&=61-2 \frac{7}{8} \\&=61-\frac{23}{8} \\&=\frac{488-23}{8} \\&=\frac{465}{8} \\&=58 \frac{1}{8}\end{aligned}$

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Question 13

(a) $1 \frac{2}{5}+3 \frac{1}{4}+\frac{7}{10}$

$\begin{aligned}&=\frac{7}{5}+\frac{13}{4}+\frac{7}{10} \\&=\frac{28+65+14}{20} \\&=\frac{107}{20} \\&=5 \frac{7}{20}\end{aligned}$

(b) $7 \frac{6}{15}+4 \frac{11}{12}+3 \frac{7}{30}$

$=\frac{111}{15}+\frac{59}{12}+\frac{27}{30}$

$=\frac{444+295+194}{60}$

$=\frac{933}{60}=15\frac{11}{20}$

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Question 14

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

$=\frac{17}{3}-\frac{31}{6}+\frac{17}{6}$

$=\frac{34-31+17}{6}$

$=\frac{20}{6}$

$=3 \frac{1}{3}$

(b) $3 \frac{5}{24}-1 \frac{7}{36}+\frac{11}{16}$

$=\frac{77}{24}-\frac{43}{36}+\frac{11}{16}$

$=\frac{462-172+99}{144}$

$=\frac{389}{144}$

$=2 \frac{101}{144}$

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Question 15

(a) $6 \frac{1}{5}-\left(4 \frac{3}{10}-1 \frac{1}{2}\right)$

$=\frac{31}{5}-\left(\frac{43}{10}-\frac{3}{2}\right)$

$=\frac{31}{5}-\frac{43-15}{10}$

$=\frac{31}{5}-\frac{28}{10}$

$=\frac{62-28}{10}=\frac{34}{10}$

$=3 \frac{2}{5}$

(b) $3 \frac{5}{9}-\left(2 \frac{1}{3}-1 \frac{5}{12}\right)+1 \frac{5}{6}$

$=\frac{32}{9}-\left(\frac{7}{3}-\frac{17}{12}\right)+\frac{11}{6}$

$=\frac{32}{9}-\frac{28-17}{12}+\frac{11}{6}$

$=\frac{32}{9}-\frac{11}{12}+\frac{11}{6}$

$=\frac{128-33+66}{36}$

$=\frac{161}{36}$

$=4 \frac{17}{36}$

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Question 16

If in a mushroom $\frac{19}{20}$ is water, what fraction of it is solid matter?

Sol :

The fraction of mushroom in solid matter

$\begin{aligned}&=1-\frac{19}{20} \\&=\frac{20-19}{20} \\&=\frac{1}{20}\end{aligned}$

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Question 17

During a campaign an army loses $\frac{1}{10}$ of its member in battle and $\frac{1}{5}$ by sickness what fraction survive?

Sol :

The fraction of campaign survives

$\begin{aligned}&=1-\left(\frac{1}{10}+\frac{1}{5}\right) \\&=1-\frac{3}{10} \\&=\frac{10-3}{10} \\&=\frac{7}{10}\end{aligned}$

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Question 18

In a certain magazine $\frac{11}{27}$ consists of advertisements and $\frac{1}{3}$ of illustrations, what fraction is readable matter

Sol :

The fraction in readable matter

$\begin{aligned}&=1-\left(\frac{11}{27}+\frac{1}{3}\right) \\&=1-\frac{11+9}{27} \\&=1-\frac{20}{27} \\&=\frac{27-20}{27} \\&=\frac{7}{27}\end{aligned}$

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