Question

Write each fraction. Arrange them in ascending and descending order using the correct sign ‘>’, ‘=’, ‘<’ between the fractions.

Answer 1

Hint: Here, find the fraction of shaded area in each figure. Then compare the fractions and arrange them in ascending and descending order.

Complete step-by-step answer:
 Each circle is divided in 8 equal parts. Some parts are shaded and some are unshaded.
First find the fraction of shaded parts in each circle.
(i)

In this circle no part is shaded.
Hence, shaded part = 0 and total parts = 8
Fraction of shaded part = ${\displaystyle \frac{0}{8}}=0$
(ii)

In this circle three parts are shaded.
Hence, shaded part = 3 and total parts = 8
Fraction of shaded part = ${\displaystyle \frac{3}{8}}$
(iii)

In this circle six parts are shaded.
Hence, shaded parts = 6 and total parts = 8
Fraction of shaded part = ${\displaystyle \frac{6}{8}}={\displaystyle \frac{3}{4}}$
(iv)

In this circle four parts are shaded.
Hence, shaded parts = 4 and total parts = 8
Fraction of shaded part = ${\displaystyle \frac{4}{8}}={\displaystyle \frac{1}{2}}$
Ascending order: 0 < ${\displaystyle \frac{3}{8}}$ < ${\displaystyle \frac{1}{2}}$ < ${\displaystyle \frac{3}{4}}$
Descending order: ${\displaystyle \frac{3}{4}}$ > ${\displaystyle \frac{1}{2}}$ > ${\displaystyle \frac{3}{8}}$ > 0

Note: In these types of questions, always compare whether all regions whether shaded or unshaded are equal or not, if not then draw lines inside the given figure to make all areas equal.
Ascending order: Ascending order arrangement or fractions or number means first write the smallest number/fraction then write the numbers/fractions with increasing values and at last the largest number, and put ‘<’ sign between the numbers/fractions.
Descending order: Descending order arrangement or fractions or number means first write largest number/fraction then write the numbers/fractions with decreasing values and at last the smallest number, and put ‘>’ sign between the numbers/fractions.