Question

How quickly can you do this? Fill with appropriate sign. \[\left( {' < ',' = ',' > '} \right)\]

$\dfrac{6}{10}$ $\square$ $\dfrac{6}{10}$

Answer 1

Hint:First, check the denominator of both the fraction if they are equal then compare the numerator and if the denominator is different then make the common denominator then compare the numerator.

Complete step by step solution:
Two fractions are equivalent fractions when they represent the same part of a whole.
We cannot compare the fractions directly because they have different denominators. First, find a common denominator for the two fractions.
Since \[10\] is a factor of \[5\], we can use \[10\] as the common denominator.
Multiply the numerator and denominator by \[2\] to create an equivalent fraction with a denominator of \[10\].
\[\begin{aligned}
  \dfrac{3}{5} = \dfrac{{3 \cdot 2}}{{5 \cdot 2}} \\
   = \dfrac{6}{{10}} \\
\end{aligned} \]
Now that the denominators are the same, compare the numerators.
Since \[6\] is the value of the numerator for both fractions, the two fractions are equal.
Here, \[\dfrac{6}{{10}}\] and \[\dfrac{3}{5}\] are equivalent fractions.

Therefore, \[\dfrac{6}{{10}}\boxed = \dfrac{3}{5}\].

Note:
Since equivalent fractions do not always have the same numerator and denominator, one way to determine if two fractions are equivalent is to find a common denominator and rewrite each fraction with that denominator. Once the two fractions have the same denominator, you can check to see if the numerators are equal. If they are equal, then the two fractions are equal as well.