Question

Arrange the fractions in ascending order.

$\frac{3}{4}$, $\frac{7}{20}$, $\frac{9}{15}$, $\frac{14}{30}$

Answer 1

Step 1 : Given data

Here, the given fractions are $\frac{3}{4}$, $\frac{7}{20}$, $\frac{9}{15}$, $\frac{14}{30}$. Since the denominator of all the fractions is not same, therefore the given fractions are unlike fractions. The unlike fractions are compared by converting them into like fractions. They are converted into like fractions by taking their equivalent forms with denominator as the LCM of denominators of unlike fractions.

Two or more fractions are said to be like fractions if they have same denominator. For like fraction, the fraction with greater numerator is greater.

Here, the LCM of denominators i.e. $4$, $20$, $15$ and $30$ is $60$. Therefore, the equivalent forms of $\frac{3}{4}$, $\frac{7}{20}$, $\frac{9}{15}$, $\frac{14}{30}$ must have denominator $60$.

Step 2 : Finding the equivalent fractions

Equivalent fraction of $\frac{3}{4}$ :

To obtain an equivalent form of $\frac{3}{4}$ with denominator $60$, we have

$\frac{3}{4}=\frac{3\times 15}{4\times 15}=\frac{45}{60}$ [Multiplying numerator and denominator by $15$]

Equivalent fraction of $\frac{7}{20}$.

To obtain an equivalent form of $\frac{7}{20}$ with denominator $60$, we have

$\frac{7}{20}=\frac{7\times 3}{20\times 3}$$=$$\frac{21}{60}$ [Multiplying numerator and denominator by $3$]

Equivalent fraction of $\frac{9}{15}$.

To obtain an equivalent form of $\frac{9}{15}$ with denominator $60$, we have

$\frac{9}{15}=\frac{9\times 4}{15\times 4}$$=$$\frac{36}{60}$ [Multiplying numerator and denominator by $4$]

Equivalent fraction of $\frac{14}{30}$.

To obtain an equivalent form of $\frac{14}{30}$ with denominator $60$, we have

$\frac{14}{30}=\frac{14\times 2}{30\times 2}$$=$$\frac{28}{60}$ [Multiplying numerator and denominator by $2$ ]

Step 3 : Arranging the fractions in ascending order

From the above steps the equivalent fractions for $\frac{3}{4}$, $\frac{7}{20}$, $\frac{9}{15}$, $\frac{14}{30}$ are $\frac{45}{60}$, $\frac{21}{60}$, $\frac{36}{60}$ and $\frac{28}{60}$ respectively.

Since, all the fractions now have same denominator, therefore, the fraction with greater numerator is greater. i.e., $21<28<36<45$

So, $\frac{21}{60}$$<$$\frac{28}{60}$$<$$\frac{36}{60}$$<$$\frac{45}{60}$

Hence, fractions in asending order $\frac{7}{20}$, $\frac{14}{30}$,$\frac{9}{15}$, $\frac{3}{4}$.