Selina solutions

Selina solutions

Grade 6

Proportion (Including Word Problems) | Exercise 12(A)

Question 1

Q1)

In each of the following, check whether or not the given ratios form a proportion :

(i) 8 : 16 and 12 : 15

(ii) 16 : 28 and 24 : 42

(iii) 12 ÷ 3 and 8 ÷ 2

(iv) 25 : 40 and 20 : 32

(v)\frac{15}{18}and\frac{10}{12}

(vi)\frac{7}{8}and\ 14:16

Solution:

(i) 8:16 and 12:15

Since 8:16 = \frac{8}{16}=\frac{1}{2}

And 12 :15 = \frac{12}{15}=\frac{4}{5}

Ratio 8:16\neRatio 12:15 , they are not in a proportion.

(ii) 16:28 and 24:42

Since 16:28 = \frac{16}{28}=\frac{4}{7}

And 24:42 = \frac{24}{42}=\frac{4}{7}

Ratio 16:28 and 24:42 are equal, so they form a proportion

(iii)12\div3\ and\ 8\div2

Since \frac{12}{3}=4\ and\ \frac{8}{2}=4

Ratio 12\div3\ and\ 8\div2 re equal , so they form a proportion

(iv) 25:40 and 20:32

Since 25:40 = \frac{25}{40}=\frac{5}{8}

Ratio 25:20 and 20:32 are equal , so they form a proportion

(v)\ \frac{15}{18}and\ \frac{10}{12}

Since \frac{15}{18}=\frac{5}{6}\ and\ \frac{10}{12}=\frac{5}{6}

Ratio \frac{15}{18}\ and\ \frac{10}{12} are equal, so they form a proportion

(vi)\ \frac{7}{8}\ and\ 14:16

Since \frac{7}{8}=\frac{7}{8}\ and\ 14:16=\frac{14}{16}=\frac{7}{8}

Ratio 7/8 and 14:16 are equal, so they form a proportion

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Question 1

Q1)

In each of the following, check whether or not the given ratios form a proportion :

(i) 8 : 16 and 12 : 15

(ii) 16 : 28 and 24 : 42

(iii) 12 ÷ 3 and 8 ÷ 2

(iv) 25 : 40 and 20 : 32

(v)\frac{15}{18}and\frac{10}{12}

(vi)\frac{7}{8}and\ 14:16

Solution:

(i) 8:16 and 12:15

Since 8:16 = \frac{8}{16}=\frac{1}{2}

And 12 :15 = \frac{12}{15}=\frac{4}{5}

Ratio 8:16\neRatio 12:15 , they are not in a proportion.

(ii) 16:28 and 24:42

Since 16:28 = \frac{16}{28}=\frac{4}{7}

And 24:42 = \frac{24}{42}=\frac{4}{7}

Ratio 16:28 and 24:42 are equal, so they form a proportion

(iii)12\div3\ and\ 8\div2

Since \frac{12}{3}=4\ and\ \frac{8}{2}=4

Ratio 12\div3\ and\ 8\div2 re equal , so they form a proportion

(iv) 25:40 and 20:32

Since 25:40 = \frac{25}{40}=\frac{5}{8}

Ratio 25:20 and 20:32 are equal , so they form a proportion

(v)\ \frac{15}{18}and\ \frac{10}{12}

Since \frac{15}{18}=\frac{5}{6}\ and\ \frac{10}{12}=\frac{5}{6}

Ratio \frac{15}{18}\ and\ \frac{10}{12} are equal, so they form a proportion

(vi)\ \frac{7}{8}\ and\ 14:16

Since \frac{7}{8}=\frac{7}{8}\ and\ 14:16=\frac{14}{16}=\frac{7}{8}

Ratio 7/8 and 14:16 are equal, so they form a proportion

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