Question

The product of a fraction and the sum of 5 1/3 and 6 1/3 is 3. What is the fraction?

Answer 1

Concept:

Fraction is ratio or comparison between two mathematical quantities or numbers or values.

Replace the unknown quantity by variable and then form a mathematical equation using the given condition and variable. On solving which we can find the required value or quantity.  

Given:

The product of a fraction and the sum of 5 1/3 and 6 1/3 is 3.

Find:

The unknown fraction.

Solution:

Let the fraction be = x

$5\frac{1}{3}=\frac{3\times5+1}{3}=\frac{16}{3}\\6\frac{1}{3}=\frac{3\times6+1}{3}=\frac{19}{3}$

The sum of 16/3 and 19/3 is = 16/3 + 19/3 = (16+19)/3 = 35/3

The product of the fraction and 35/3 = x*(35/3) = 35x/3

According to the information of the problem, the mathematical equation is given by,

35x/3 = 3

35x = 3*3

35x = 9

x = 9/35

Hence the required fraction is given by 9/35.

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Answer 2

Answer:

The required fraction is $\frac{9}{35}$.

Step-by-step explanation:

Step 1 of 2

Consider the given numbers as follows:

$5\frac{1}{3}$ and $6\frac{1}{3}$

Convert the mixed fraction into the proper fraction as follows:

$5\frac{1}{3}=\frac{16}{3}$

$6\frac{1}{3}=\frac{19}{3}$

Also,

It is given that the sum $of$ numbers $5\frac{1}{3}$ and $6\frac{1}{3}$ is 3.

⇒ $\frac{16}{3}+\frac{19}{3}$

⇒ $\frac{35}{3}$

Let the required fraction be $x$.

According to the question,

The product of $a$ fraction and the sum of numbers $5\frac{1}{3}$ and $6\frac{1}{3}$ is 3, i.e.,

⇒ $x\times\frac{35}{3}=3$ ____ (1)

Step 2 of 2

Find the value of $x$.

Multiply both the sides of expression (1) by $\frac{3}{35}$, we get

⇒ $x\times\frac{35}{3}\times\frac{3}{35} =3\times\frac{3}{35}$

On simplifying, we get

⇒ $x=\frac{9}{35}$

Final answer: The required fraction is $\frac{9}{35}$.

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