Selina solutions

Selina solutions

Grade 6

Ratio | Exercise 11(A)

Question 1

Q1) Express each of the following ratios in its simplest form :

(a) (i) 4 : 6

(ii) 48 : 54

(iii) 200 : 250

(b) (i) 5 kg : 800 gm

(ii) 30 cm : 2 m

(iii) 3 m : 90 cm

(iv) 2 years : 9 months

(v) 1 hour : 45 minutes

(vi) 4 min : 45 sec

(c) \left(i\right)\ 1\frac{1}{2}:2\frac{1}{2}\ \ \ \left(ii\right)\ 3\frac{1}{2}:7\ \ \ \ \ \left(iii\right)\ 2\frac{1}{3}:3\frac{1}{2}:1\frac{1}{4}\ \ \ \left(iv\right)\ x^2:4x\ \ \ \ \left(v\right)\ 2.5:1.5\ \ \ \ \left(vi\right)\ 2.5:5

Solution:

(a) (i)4:6=\frac{4}{6}=\frac{2}{3}=2:3

(ii)48:54=\frac{48}{54}=\frac{8}{9}=8:9

(iii)200:250=\frac{200}{250}=\frac{4}{5}=4:5

(b) (i) 5kg:800gm = 5000:800

(5 x 1000gm = 5000gm)

=\frac{5000}{800}=\frac{50}{8}=25:4

(ii) 30cm : 2m = 30 cm : 200 cm

(3 x 100 cm = 300 cm)

=\frac{30}{200}=\frac{3}{20}=3:20

(iii) 3 m : 90 cm = 300 cm : 90 cm

( 3 x 100cm = 300 cm)

=\frac{300}{90}=\frac{10}{3}=10:3

(iv) 2 years : 9 months = 24 months : 9 months

(2 years = 2 x 12 = 24 months)

=\frac{24}{9}=\frac{8}{3}=8:3

(v) 1 hour : 45 minutes = 60 minutes : 45 minutes

( 1 hour = 60 minutes)

\frac{60}{45}=\frac{4}{3}=4:3

(vi) 4 min : 45 sec = 240 sec : 45 sec

(1 minutes = 60 sec , 4 x 60 = 240 sec)

=\frac{240}{45}=\frac{16}{3}=16:3

(c)\ (i)\ 1\frac{1}{2}:2\frac{1}{2}=\frac{3}{2}:\frac{5}{2}=\frac{3}{2}\div\frac{5}{2}

=\frac{3}{2}\times\frac{2}{5}=\frac{3}{5}=3:5

(ii)\ 3\frac{1}{2}:7=\frac{7}{2}:\frac{7}{1}=\frac{7}{2}\div\frac{7}{1}

=\frac{7}{2}\times\frac{1}{7}=\frac{1}{2}=1:2

(iii)\ 2\frac{1}{3}:3\frac{1}{2}:1\frac{1}{4}=\frac{7}{3}:\frac{7}{2}:\frac{5}{4}

=\frac{7}{3}\times12:\frac{7}{2}\times12::\frac{5}{4}\times12

(L.C.M of 2,3 and 4 = 12)

= 28 : 42 : 15

(iv)x^2:4x=\frac{x^2}{4x}=\frac{x\times x}{4\times x}=\frac{x}{4}=x:4

(v)\ 2.5:1.5=\frac{25}{15}=\frac{5}{3}=5:3

OR,2.5:1.5=\frac{25}{10}:\frac{15}{10}=\frac{25}{10}\div\frac{15}{10}

=\frac{25}{10}\times\frac{10}{15}=\frac{25}{15}=\frac{5}{3}=5:3

(vi)\ 2.5:5=\frac{25}{10}:\frac{15}{10}=\frac{25}{10}\div\frac{15}{10}

=\frac{25}{10}\times\frac{10}{15}=\frac{25}{15}=\frac{5}{3}=5:3

(vi)\ 2.5:5=\frac{25}{10}:\frac{5}{1}=\frac{25}{10}\div\frac{5}{1}=\frac{25}{10}\times\frac{1}{5}

=\frac{5}{10}=1:2

OR, 2.5 : 5 = 2.5 : 5.0 = \frac{2.5}{5.0}=\frac{25}{50}=\frac{1}{2}=1:2

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Question 1

Q1) Express each of the following ratios in its simplest form :

(a) (i) 4 : 6

(ii) 48 : 54

(iii) 200 : 250

(b) (i) 5 kg : 800 gm

(ii) 30 cm : 2 m

(iii) 3 m : 90 cm

(iv) 2 years : 9 months

(v) 1 hour : 45 minutes

(vi) 4 min : 45 sec

(c) \left(i\right)\ 1\frac{1}{2}:2\frac{1}{2}\ \ \ \left(ii\right)\ 3\frac{1}{2}:7\ \ \ \ \ \left(iii\right)\ 2\frac{1}{3}:3\frac{1}{2}:1\frac{1}{4}\ \ \ \left(iv\right)\ x^2:4x\ \ \ \ \left(v\right)\ 2.5:1.5\ \ \ \ \left(vi\right)\ 2.5:5

Solution:

(a) (i)4:6=\frac{4}{6}=\frac{2}{3}=2:3

(ii)48:54=\frac{48}{54}=\frac{8}{9}=8:9

(iii)200:250=\frac{200}{250}=\frac{4}{5}=4:5

(b) (i) 5kg:800gm = 5000:800

(5 x 1000gm = 5000gm)

=\frac{5000}{800}=\frac{50}{8}=25:4

(ii) 30cm : 2m = 30 cm : 200 cm

(3 x 100 cm = 300 cm)

=\frac{30}{200}=\frac{3}{20}=3:20

(iii) 3 m : 90 cm = 300 cm : 90 cm

( 3 x 100cm = 300 cm)

=\frac{300}{90}=\frac{10}{3}=10:3

(iv) 2 years : 9 months = 24 months : 9 months

(2 years = 2 x 12 = 24 months)

=\frac{24}{9}=\frac{8}{3}=8:3

(v) 1 hour : 45 minutes = 60 minutes : 45 minutes

( 1 hour = 60 minutes)

\frac{60}{45}=\frac{4}{3}=4:3

(vi) 4 min : 45 sec = 240 sec : 45 sec

(1 minutes = 60 sec , 4 x 60 = 240 sec)

=\frac{240}{45}=\frac{16}{3}=16:3

(c)\ (i)\ 1\frac{1}{2}:2\frac{1}{2}=\frac{3}{2}:\frac{5}{2}=\frac{3}{2}\div\frac{5}{2}

=\frac{3}{2}\times\frac{2}{5}=\frac{3}{5}=3:5

(ii)\ 3\frac{1}{2}:7=\frac{7}{2}:\frac{7}{1}=\frac{7}{2}\div\frac{7}{1}

=\frac{7}{2}\times\frac{1}{7}=\frac{1}{2}=1:2

(iii)\ 2\frac{1}{3}:3\frac{1}{2}:1\frac{1}{4}=\frac{7}{3}:\frac{7}{2}:\frac{5}{4}

=\frac{7}{3}\times12:\frac{7}{2}\times12::\frac{5}{4}\times12

(L.C.M of 2,3 and 4 = 12)

= 28 : 42 : 15

(iv)x^2:4x=\frac{x^2}{4x}=\frac{x\times x}{4\times x}=\frac{x}{4}=x:4

(v)\ 2.5:1.5=\frac{25}{15}=\frac{5}{3}=5:3

OR,2.5:1.5=\frac{25}{10}:\frac{15}{10}=\frac{25}{10}\div\frac{15}{10}

=\frac{25}{10}\times\frac{10}{15}=\frac{25}{15}=\frac{5}{3}=5:3

(vi)\ 2.5:5=\frac{25}{10}:\frac{15}{10}=\frac{25}{10}\div\frac{15}{10}

=\frac{25}{10}\times\frac{10}{15}=\frac{25}{15}=\frac{5}{3}=5:3

(vi)\ 2.5:5=\frac{25}{10}:\frac{5}{1}=\frac{25}{10}\div\frac{5}{1}=\frac{25}{10}\times\frac{1}{5}

=\frac{5}{10}=1:2

OR, 2.5 : 5 = 2.5 : 5.0 = \frac{2.5}{5.0}=\frac{25}{50}=\frac{1}{2}=1:2

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