Question

What is the value of \[\dfrac{5}{7}+\dfrac{3}{4}\]?

Answer 1

Hint: From the question we have been asked to add two fractions. We will use the concept of least common denominator and the basic mathematical operations like multiplication and addition etc.., next we have to simplify the question using a mixed fraction concept and find the answer to the question.

Complete step by step solution:
In order to add or subtract fractions, they must have the same denominator. We can determine the least common denominator (LCD) by listing the multiples of each denominator, and finding the lowest multiple they have in common.
\[\begin{align}
  & \Rightarrow 7:7,14,21,28,35,42.... \\
 & \Rightarrow 4:4,8,12,16,20,24...... \\
\end{align}\]
The LCD is \[28\].
Multiply each fraction by a fractional form of \[1\], such as \[\dfrac{3}{3}\], that will give each fraction the denominator \[28\]. This will change the numbers, but not the value of each fraction.
\[\Rightarrow \dfrac{5}{7}\times \dfrac{4}{4}+\dfrac{3}{4}\times \dfrac{7}{7}\]
\[\Rightarrow \dfrac{20}{28}+\dfrac{21}{28}\]
\[\Rightarrow \dfrac{41}{28}\]
Since \[41\] is a prime number, the fraction cannot be reduced. However, we can convert it to a mixed number: \[ a\dfrac{b}{c}\]
Divide \[41\] by \[28\] using long division to get a whole number quotient and a remainder. The whole number quotient is the whole number in the mixed number, the remainder is the numerator, and the divisor is the denominator.
\[\Rightarrow \dfrac{41}{28}\]
\[\Rightarrow 1\dfrac{13}{28}\]

Note: Students must be very careful in doing the calculations. Students should be able to convert fractions into mixed fractions to solve this question completely. If we leave the solution as \[ \dfrac{41}{28}\] instead of \[1\dfrac{13}{28}\] then our solution will be incomplete.