Question

Which of the following is greater: $\dfrac{5}{9}$ or $\dfrac{3}{7}$

Answer 1

Hint: In this question we have been given two numbers and we have to compare and accordingly we can check which one is greater and put the symbol between them. This symbol $' > '$ is known as greater than a symbol. It means that the value on the left side is greater than the value on the right side. And the symbol $ < $ is known as the less than sign, it means that the value on the left side is greater than the value on the right side.

Complete step-by-step solution:
Here we have $\dfrac{5}{9}\_\_\_\dfrac{3}{7}$.
Since we can see that these are unlike fractions, we have to convert the denominator into the same of both these fractions. For this, we will take the LCM of the denominator and then solve it further.
We have the LCM of $9,7$ and it is $63$. So now we can convert the fractions with the same denominator.
The first fraction can be written as $\dfrac{{5 \times 7}}{{9 \times 7}} = \dfrac{{35}}{{63}}$ and the second fraction can be written as $\dfrac{{3 \times 9}}{{7 \times 9}} = \dfrac{{27}}{{63}}$.
We know that if the denominators of the fractions are the same then the fraction with a greater numerator is the greater fraction. So on comparing the numerator of the first fraction is greater than the second. It can be written as $\dfrac{{35}}{{63}} > \dfrac{{27}}{{63}}$ or $\dfrac{5}{9} > \dfrac{3}{7}$.

Hence $\dfrac{5}{9}$ is greater than $\dfrac{3}{7}$.

Note: We should note that the factors of $9$ is $3 \times 3$ and the factors of $7 = 7 \times 1$, so from this we get our least common multiple or LCM$ = 3 \times 3 \times 7 = 63$. We should always try to convert the unlike fractions into like fractions and then solve them. We should know that whenever we compare numbers, we generally talk about the sizes of the numbers. There is a trick to remember the less than sign i.e. $ < $. This sign looks like the English letter $L$, so starts with less than sign.