question_answer 1)

Write the fractions. Are all these fractions equivalent? (a) (b) TIPS To write the fractions, firstly find number of equal parts and number shaded parts, then \[\left[ \because \frac{1}{4}=\frac{1}{4} \right]\] Now, convert all these fractions in simplest form. If simplest form is same, then these fractions will be equivalent otherwise not.

Answer:

(a) (i) Total number of equal parts = 2; Number of shaded parts = 1 \[\to \] Fraction for shaded portion \[\left[ \because \frac{3}{4}=\frac{3}{4} \right]\] (ii) Total number of equal parts = 4; Number of shaded parts = 2 \[\] Fraction for shaded portion = 2/4 (iii) Total number of equal parts = 6; Number of shaded parts = 3 \[\frac{2}{7}=\frac{8}{}\] Fraction for shaded portion = 3/6 (iv) Total number of equal parts = 8; Number of shaded parts = 4 \[\frac{5}{8}=\frac{10}{}\] Fraction for shaded portion = 4/8 Now, \[\frac{3}{5}=\frac{}{20}\] [\[\frac{45}{60}=\frac{15}{}\]HCF of 2 and 4 is 2] \[\frac{18}{24}=\frac{}{4}\] [\[\frac{2}{7}=\frac{8}{}\]HCF of 3 and 6 is 3] \[\therefore \] [\[2\times =7\times 8\]HCF of 4 and 8 is 4] Since, all fractions in simplest form are same. \[2\times =7\times 2\times 4=28\times 2\]\[[\because 8=2\times 4]\]i.e. the fractions are equivalent. (b) (i) Total number of equal parts = 12 Number of shaded parts = 4 \[2\times =2\times 28\] Fraction for shaded portion\[=28\] (ii) Total number of equal parts = 9 Number of shaded parts = 3 \[\frac{2}{7}=\frac{8}{}\] Fraction for shaded portion = 3/9 (iii) Total number of equal parts = 6; Number of shaded parts = 2 \[\frac{5}{8}=\frac{10}{}\] Fraction for shaded portion = 2/6 (iv) Total number of equal parts = 3; Number of shaded parts = 1 \[\therefore \] Fraction for shaded portion = 1/3 (v) Total number of equal parts =15; Number of shaded parts = 6 \[5\times =8\times 10\] Fraction for shaded portion \[5\times =8\times 2\times 5=16\times 5\] Now, \[[\because 10=2\times 5]\] [\[5\times =5\times 16\]HCF of 4 and 12 is 4] \[=16\] [\[\frac{5}{8}=\frac{10}{}\]HCF of 3 and 9 is 3] \[\frac{3}{5}=\frac{}{20}\] [\[\therefore \]HCF of 2 and 6 is 2] \[3\times 20=5\times \] [\[3\times 5\times 4=5\times \]HCF of 6 and 15 is 3] Here, except \[[\because 20=5\times 4]\] all the fractions in simplest form are same. So, \[5\times 12=5\times \] Hence, these fraction are not equivalent.