Question

find the number if 7/3 of it is 5 5/6

Answer 1

Answer: $\dfrac{5}{2}.$

Step-by-step explanation:

To find: The number if  $\dfrac{7}{3}$ of it is $5\dfrac{5}{6}$.

Let x be the number.

Then, as per the statement, we have

$\dfrac{7}{3}x=5\dfrac{5}{6}$

Simplify $5\dfrac{5}{6}$ as $\dfrac{5\times6+5}{6}=\dfrac{35}{6}$

Then, $\dfrac{7}{3}x=\dfrac{35}{6}$

Multiply 3 on both sides, we get

$7x=\dfrac{35}{2}$

Divide both sides by 7, we get

$x=\dfrac{35}{2\times7}\\\\\Rightarrow\ x=\dfrac{5}{2}$

Hence, the number is $\dfrac{5}{2}.$

Answer 2

We will see that the mixed number is:

N = 2 + 1/2

How to find the number?

We want to find a number N such that 7/3 times N is equal to 5 + 5/6.

So we just need to solve:

(7/3)*N = (5 + 5/6)

If we multiply both sides by 3/7, we get:

(3/7)*(7/3)*N = (3/7)*(5 + 5/6)

N = 15/7 + 15/42

If we multiply and divide the first fraction by 6, we get:

N = (6/6)*15/7 + 15/42 = 90/42 + 15/42

N = 105/42

Now we can write:

105 = 42 + 42 + 21

Replacing that in the fraction we would get:

N = 105/42 = (42 + 42 + 21)/42 = 42/42 + 42/42 + 21/42 = 2 + 21/42

N = 2 + 1/2

If you want to learn more about mixed numbers, you can read:

https://brainly.com/question/1746829