question_answer 14)

Write the fractions and pair up the equivalent fractions from each row.

Answer:

(a) Here, total number of equal parts = 2; Number of shaded parts = 1 \[=12\] Fraction represented by the shaded portion \[\frac{3}{5}=\frac{}{20}\][simplest form] (b) Here, total number of equal parts = 6 Number of shaded parts = 4 \[\frac{45}{60}=\frac{15}{}\] Fraction represented by the shaded portion \[\therefore \] \[45\times =15\times 60\] [\[45\times =15\times 20\times 3\]HCF of 4 and 6 is 2] \[=\frac{2}{3}\] [simplest form] (c) Here, total number of equal parts = 9 Number of shaded parts = 3 \[[\because 60=20\times 3]\] Fraction represented by the shaded portion \[45\times =45\times 20\] \[=20\] [\[\frac{45}{60}=\frac{15}{}\] HCF of 3 and 9 is 3] \[=\frac{1}{3}\] [simplest form] (d) Here, total number of equal parts = 8 Number of shaded parts = 2 \[\frac{18}{24}=\frac{}{4}\] Fraction represented by the shaded portion \[\therefore \] [\[24\times =18\times 4\]HCF of 2 and 8 is 2] \[6\times 4\times =6\times 3\times 4\] [simplest form] (e) Here, total number of equal parts = 4 Number of shaded parts = 3 \[[\because 24=6\times 4\,\text{and}\,18=6\times 3]\] Fraction represented by the shaded portion \[=\frac{3}{4}\] [simplest form] Now, taking second row (i) Here, total number of equal parts = 18 Number of shaded parts = 6 \[24\times =24\times 3\] Fraction represented by the shaded portion \[=3\] \[\frac{18}{24}=\frac{}{4}\] [\[\frac{3}{5}\]HCF of 6 and 18 is 6 ] \[\therefore \] [simplest form] (ii) Here, total number of equal parts = 8 Number of shaded parts = 4 \[\frac{N}{20}=\frac{3}{5}\Rightarrow N\times 5=20\times 3\] Fraction represented by the shaded portion \[N\times 5=4\times 5\times 3\] \[20=4\times 5\] [\[\Rightarrow \] HCF of 6 and 18 is 6] \[N\times 5=12\times 5\] [simplest form] (iii) Here, total number of equal parts = 16 Number of shaded parts = 12 \[\therefore \] Fraction represented by the shaded portion \[\frac{3}{5}=\frac{N}{D}=\frac{12}{20}\] \[\therefore \] [\[\frac{9}{D}=\frac{3}{5}\]HCF of 12 and 16 is 4] \[\Rightarrow \] [simplest form] (iv) Here, total number of equal parts = 12 Number of shaded parts = 8 \[D\times 3=9\times 5\] Fraction represented by the shaded portion \[D\times 3=3\times 3\times 5\] \[9=3\times 3\] [\[\Rightarrow \]HCF of 8 and 12 is 4] \[D\times 3=15\times 3\] [simplest form] (v) Here, total number of equal parts = 16 Number of shaded parts = 4 \[\therefore \]Fraction represented by the shaded portion\[\frac{3}{5}=\frac{N}{D}=\frac{9}{15}\] \[\therefore \] [\[\frac{N}{30}=\frac{3}{5}\Rightarrow N\times 5=30\times 3\] HCF of 4 and 16 is 4] \[N\times 5=6\times 5\times 3\] [simplest form] Now, the equivalent fractions are (a) \[30=6\times 5\] (ii) \[\Rightarrow \] (b) \[N\times 5=18\times 5\] (iv) \[\therefore \] (c) \[\frac{3}{5}=\frac{N}{D}=\frac{18}{30}\] (i) \[\therefore \] (d) \[\frac{27}{D}=\frac{3}{5}\] (v) \[\Rightarrow \] (e) \[D\times 3=27\times 5\] (iii) \[D\times 3=3\times 9\times 5\]