Question

Arrange the following in ascending order:
\[\dfrac{5}{8},\dfrac{5}{6},\dfrac{1}{2}\]
(a) \[\dfrac{1}{2},\dfrac{5}{8},\dfrac{5}{6}\]
(b) \[\dfrac{5}{6},\dfrac{5}{8},\dfrac{1}{2}\]
(c) \[\dfrac{5}{8},\dfrac{1}{2},\dfrac{5}{6}\]
(d) \[\dfrac{1}{2},\dfrac{5}{6},\dfrac{5}{8}\]

Answer 1

Hint: First make the denominators of fractions equal by first calculating the L.C.M and then multiply with a number to both numerator and denominator. So, that the denominator becomes equal. Hence, for the applied fact that if the denominator is equal then greater the numerator greater the fraction is.

Complete step-by-step answer:
In the question three fractions are given \[\dfrac{5}{8},\dfrac{5}{6},\dfrac{1}{2}\] and we have to arrange it in ascending order.
Before proceeding we will first learn briefly about fractions.
A fraction represents a part of a whole or more generally any number of equal parts. When spoken in English, a fraction describes how many parts of a certain size there are, for example, one – half, eight – fifths, three – quarters. A common, or simple fraction for example: \[\dfrac{1}{2}\], \[\dfrac{17}{2}\] consists of a numerator displayed below or after the line. Numerators and denominators are also used in fractions that are not in common, including compound fractions and mixed numerals.
Arranging in ascending order means writing the given quantities from smallest to largest.
To make the denominator the same we have to first take L.C.M of all denominators of the fractions and then take all the fractions and multiply with the numbers such that denominators are the same. Here denominators are 8, 6, 2 and their L.C.M is 24.
Now we will compare all the fractions but before that we will make all the denominators of fractions the same.
Let us consider the first fraction \[\dfrac{5}{8}\] and we will multiply by 3 to both numerator and denominator to make the fraction as \[\dfrac{15}{24}\].
Now let’s go for second fraction \[\dfrac{5}{6}\] and we will multiply by 4 to both the numerator and denominator to make the fraction as \[\dfrac{20}{24}\].
And now for the last fraction \[\dfrac{1}{2}\] we will multiply it with 12 to both the numerator and denominator we get \[\dfrac{12}{24}\].
So, the transformed fractions are \[\dfrac{15}{24},\dfrac{20}{24}\] and \[\dfrac{12}{24}\].
Now, as the denominators are the same we can say that smaller the numerator smaller the fraction and greater the numerator greater is the fraction.
So, \[\dfrac{12}{24}<\dfrac{15}{24}<\dfrac{20}{24}\]
Or, \[\dfrac{1}{2}<\dfrac{5}{8}<\dfrac{5}{6}\].
Hence, the correct option is ‘(a)’.

Note: We can also compare fractions by another method. Let's suppose two fractions be \[\dfrac{a}{b},\dfrac{c}{d}\].
We can say that, \[\dfrac{a}{b}>\dfrac{c}{d}\] if and only if \[ad>bc\]. In this way we can compare and find out.