Selina solutions

Selina solutions

Grade 7

Ratio and Proportion (Including Sharing in a Ratio) | Exercise 6(A)

Question 1

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

(i) 22:66

(ii) 1.5:2.5

(iii) 6\frac{1}{4}:12\frac{1}{2}

(iv) 40 kg: 1 quintal

(v) 10 paisa: 1 rupee

(vi) 200m:5km

(vii) 3hours:1day

(viii) 6\ months:1\frac{1}{3}\ year

(ix) 1\frac{1}{3}:2\frac{1}{4}:2\frac{1}{2}

Solution:

(i) 22:66=\frac{22}{66}=\ \frac{22\div22}{66\div22}=\frac{1}{3}

(HCF OF 22 AND 66 = 22)

= 1:3

(ii) 1.5:2.5=\frac{1.5}{2.5}=\frac{15\div5}{25\div5}=\frac{3}{5}

(HCF OF 15 AND 25 = 5)

= 3:5

(iii) 6\frac{1}{4}:12\frac{1}{2}=\frac{25}{4}:\frac{25}{2}=\frac{25}{4}\times\frac{2}{25}=\frac{2}{4}=\frac{1}{2}=1:2

(iv) 40Kg:1 quintal = 40kg:100kg

(1 quintal = 100 kg)

=\frac{40}{100}=\frac{40\div20}{100\div20}=\frac{2}{5}

(HCF OF 40 AND 100 = 20)

= 2:5

(v) 10 paise:1 rupee = 10 paise:100 paise

(1 rupee= 100 paise)

\frac{10}{100}=\frac{1}{10}=1:10

(vi) 200m:5km = 200m:5000m

(1KM = 1000M)

\frac{200}{5000}=\frac{200\div200}{1000\div200}=\frac{1}{25}=1:25

(HCF OF 200 AND 5000=200)

(vii) 3 hours: 1 day = 3hours: 24hours

(1day = 24hours)

=\frac{3}{24}=\frac{1}{8}=1:8

(viii) 6\ months:1\frac{1}{3}\ year

=\frac{4}{3}\times12=16\ months=6:16=\frac{6\div2}{16\div2}=\frac{3}{8}

(ix) 1\frac{1}{3}:2\frac{1}{4}:2\frac{1}{2}=\frac{4}{3}:\frac{9}{4}:\frac{5}{2}

(LCM OF 3,4,2 = 12)

=\frac{16:27:30}{12}=16:27:30

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Question 1

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

(i) 22:66

(ii) 1.5:2.5

(iii) 6\frac{1}{4}:12\frac{1}{2}

(iv) 40 kg: 1 quintal

(v) 10 paisa: 1 rupee

(vi) 200m:5km

(vii) 3hours:1day

(viii) 6\ months:1\frac{1}{3}\ year

(ix) 1\frac{1}{3}:2\frac{1}{4}:2\frac{1}{2}

Solution:

(i) 22:66=\frac{22}{66}=\ \frac{22\div22}{66\div22}=\frac{1}{3}

(HCF OF 22 AND 66 = 22)

= 1:3

(ii) 1.5:2.5=\frac{1.5}{2.5}=\frac{15\div5}{25\div5}=\frac{3}{5}

(HCF OF 15 AND 25 = 5)

= 3:5

(iii) 6\frac{1}{4}:12\frac{1}{2}=\frac{25}{4}:\frac{25}{2}=\frac{25}{4}\times\frac{2}{25}=\frac{2}{4}=\frac{1}{2}=1:2

(iv) 40Kg:1 quintal = 40kg:100kg

(1 quintal = 100 kg)

=\frac{40}{100}=\frac{40\div20}{100\div20}=\frac{2}{5}

(HCF OF 40 AND 100 = 20)

= 2:5

(v) 10 paise:1 rupee = 10 paise:100 paise

(1 rupee= 100 paise)

\frac{10}{100}=\frac{1}{10}=1:10

(vi) 200m:5km = 200m:5000m

(1KM = 1000M)

\frac{200}{5000}=\frac{200\div200}{1000\div200}=\frac{1}{25}=1:25

(HCF OF 200 AND 5000=200)

(vii) 3 hours: 1 day = 3hours: 24hours

(1day = 24hours)

=\frac{3}{24}=\frac{1}{8}=1:8

(viii) 6\ months:1\frac{1}{3}\ year

=\frac{4}{3}\times12=16\ months=6:16=\frac{6\div2}{16\div2}=\frac{3}{8}

(ix) 1\frac{1}{3}:2\frac{1}{4}:2\frac{1}{2}=\frac{4}{3}:\frac{9}{4}:\frac{5}{2}

(LCM OF 3,4,2 = 12)

=\frac{16:27:30}{12}=16:27:30

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