Question

Convert the following fractions into equivalent like fractions:
A.$\dfrac{7}{8},\dfrac{5}{14}$
B.$\dfrac{5}{6},\dfrac{7}{16}$
C.$\dfrac{3}{4},\dfrac{5}{6},\dfrac{7}{8}$

Answer 1

Hint: Here just identify the least common denominator and then make them the same. When two or more fractions which have different numerator and denominator but result in the same value after simplification are said to be equivalent fractions.

Complete step-by-step answer:
To convert the fraction into equivalent fractions we have to identify the least common denominator.
Now we are given $\dfrac{7}{8},\dfrac{5}{14}$.
We can say that the common factor between $8$ and $14$ is $56$.
Now to convert $8$ to $56$, let us multiply numerator and denominator of $\dfrac{7}{8}$ by $7$.
$\dfrac{7\times 7}{8\times 7}=\dfrac{49}{56}$.
Similarly, the same goes for $\dfrac{5}{14}$.
To convert $14$ to $56$, multiply numerator and denominator of $\dfrac{5}{14}$ by $4$.
$\dfrac{5\times 4}{14\times 4}=\dfrac{20}{56}$.
Therefore, $\dfrac{7}{8}$ and $\dfrac{5}{14}$ can be written as $\dfrac{49}{56}$ and $\dfrac{20}{56}$ respectively which are equivalent fraction.
Now we are given $\dfrac{5}{6},\dfrac{7}{16}$.
So, the common factor between $6$ and $16$ is $48$.
To convert the fraction $\dfrac{5}{6}$ multiply numerator and denominator by $8$.
$\dfrac{5\times 8}{6\times 8}=\dfrac{40}{48}$.
Also, for $\dfrac{7}{16}$ multiply numerator and denominator by $3$.
$\dfrac{7\times 3}{16\times 3}=\dfrac{21}{48}$.
Therefore, $\dfrac{5}{6}$ and $\dfrac{7}{16}$ can be written as $\dfrac{40}{48}$ and $\dfrac{21}{48}$ respectively which are equivalent fraction.
Here we are given $\dfrac{3}{4},\dfrac{5}{6},\dfrac{7}{8}$.
The common factor between $4$, $6$ and $8$ is $24$.
Now for $\dfrac{3}{4}$ multiply numerator and denominator by $6$.
$\dfrac{3\times 6}{4\times 6}=\dfrac{18}{24}$.
For $\dfrac{5}{6}$ multiply numerator and denominator by $4$.
$\dfrac{5\times 4}{6\times 4}=\dfrac{20}{24}$.
Also, for $\dfrac{7}{8}$ multiply numerator and denominator by $3$.
$\dfrac{7\times 3}{8\times 3}=\dfrac{21}{24}$.
Therefore, $\dfrac{3}{4},\dfrac{5}{6}$ and $\dfrac{7}{8}$ can be written as $\dfrac{18}{24}$, $\dfrac{20}{24}$ and $\dfrac{21}{24}$ respectively which are equivalent fractions.

Additional information:
The least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators. To find the LCD of two fractions, we will find the LCM of their denominators. We follow the procedure we used earlier to find the LCM of two numbers. We only use the denominators of the fractions, not the numerators, when finding the LCD.

Note: To convert a fraction to equivalent fraction, first Identify the least common denominator of two fractions, then Use the LCD of two fractions to convert them to equivalent fractions. Here we can see that the LCD between $\dfrac{7}{8}$ and $\dfrac{5}{14}$ is $56$.