Question

Pinku has 5 red marbles and 6 blue marbles, Jitu has 6 red marbles and 8 marbles. Rinku has as many red marbles as equal to the sum of Pinku and Jitu's red marbles and 20 blue marbles. Express the number of red marbles to blue marbles as fractions. Also, convert these fractions into like fractions.

Answer 1

Hint: In this question, we are given number of red and blue marbles for three children Pinku, Jitu and Rinku and we have to write them in the form of fractions for this we will take number of red marbles in numerator for every child and number of blue marbles in denominator, hence, we will get our required fraction. After that we will convert them into like fractions by making denominators of these fractions the same. For this, we will take LCM of all three denominators and convert the denominator of these fractions into that LCM by suitable multiplication in numerator and denominator.

Complete step-by-step answer:
We are given a number of red and blue marbles that Pinku, Rinku and Jitu have.
Number of red marbles with Pinku are equal to 5 and the number of blue marbles with Pinku are equal to 6. We have to find the fraction of the number of red marbles to the number of blue marbles. So, we will take number of red marbles in numerator and number of blue marbles in denominator, we get fraction for Pinku's marbles as below:
\[\begin{align}
  & \text{Fraction for Pinku}'\text{s marble}=\dfrac{\text{Number of red marbles}}{\text{Number of blue marbles}} \\
 & \text{Fraction for Pinku}'\text{s marble}=\dfrac{\text{5}}{\text{6}} \\
\end{align}\]
Number of red marbles with Jitu are equal to 6 and the number of blue marbles with Jitu are equal to 8. To find fraction of number of red marbles to number of blue marbles, we will take number of red marble in numerator and number of blue marbles in denominator, we get:
\[\begin{align}
  & \text{Fraction for Jitu}'\text{s marble}=\dfrac{\text{Number of red marbles}}{\text{Number of blue marbles}} \\
 & \text{Fraction for Jitu}'\text{s marble}=\dfrac{\text{6}}{\text{8}}=\dfrac{3}{4} \\
\end{align}\]
Number of red marbles with Rinku are equal to the sum of red marbles with Pinku and Jitu. Therefore, the number of red marble with Rinku becomes equal to 5+6 = 11. Number of blue marbles with Rinku are 20.
\[\begin{align}
  & \text{Fraction for Rinku}'\text{s marble}=\dfrac{\text{Number of red marbles}}{\text{Number of blue marbles}} \\
 & \text{Fraction for Rinku}'\text{s marble}=\dfrac{\text{11}}{20} \\
\end{align}\]
Now, we have to convert all these fractions into like fractions.
Denominators of all these fractions are 6, 4 and 20.
Let us take the least common multiple of them using prime factorization.
Prime factors of $6=2\times 3$.
Prime factors of $4=2\times 2$.
Prime factors of $20=2\times 2\times 5$.
Hence, \[LCM=2\times 3\times 2\times 5=60\]
For changing denominator of $\dfrac{5}{6}$ to 60, multiply by 10 in numerator and denominator, we get:
\[\begin{align}
  & \dfrac{5\times 10}{6\times 10}=\dfrac{50}{60} \\
 & \text{Pinku}'\text{s marbles}=\dfrac{50}{60} \\
\end{align}\]
For changing denominator of $\dfrac{3}{4}$ to 60, multiply by 15 in numerator and denominator, we get:
\[\begin{align}
  & \dfrac{3\times 15}{4\times 15}=\dfrac{45}{60} \\
 & \text{Jitu}'\text{s marbles}=\dfrac{45}{60} \\
\end{align}\]
For changing denominator of $\dfrac{11}{20}$ to 60, multiply by 3 in numerator and denominator, we get:
\[\begin{align}
  & \dfrac{11\times 3}{20\times 3}=\dfrac{33}{60} \\
 & \text{Rinku}'\text{s marbles}=\dfrac{33}{60} \\
\end{align}\]
Hence, like fraction becomes $\dfrac{50}{60},\dfrac{45}{60}\text{ and }\dfrac{33}{60}$.

Note: Students should note that fractions are the fraction whose denominators are the same. Try to simplify the fraction first before converting them to like fraction. For taking fractions as red marbles to blue marbles, always take red marbles in numerator and blue marbles in denominator. Don't make mistakes while taking LCM, every denominator should be able to convert into LCM by simply multiplying with a number. Don't forget to change the numerator also.