Question

I have a math sentence. I have a photo can I send the question to you with the photo?

Answer 1

3/10

Step-by-step explanation

Let x be the fraction of the barrel of apples that were leftover. We know that Emma collected 5/6 of a barrel of apples, and she used 1/3 of that barrel to make apple dumplings and also 1/5 of that barrel to make apple crisp. The leftover fraction of the barrel is,

`x=(5)/(6)-(1)/(3)-(1)/(5)`

To do this subtraction we have to find the least common denominator. Write some multiples of each denominator,

`\begin{cases}6\colon6,12,18,24,30,36\ldots \\ 3\colon3,6,9,12,15,18,21,24,27,30,\ldots \\ 5\colon5,10,15,20,25,30,35,\ldots\end{cases}`

As we can see, the least common multiple for the three numbers is 30. Now, we have to multiply and divide each fraction by the same number (in each fraction) to make each denominator 30. The first one must be multiplied and divided by 5, the second by 10 and the third by 6,

`x=(5)/(6)\cdot(5)/(5)-(1)/(3)\cdot(10)/(10)-(1)/(5)\cdot(6)/(6)=(25)/(30)-(10)/(30)-(6)/(30)`

Next, subtract the numerators,

`x=(25-10-6)/(30)=(9)/(30)`

And simplify the fraction. Both numerator and denominator can be divided by 3,

`x=(9/3)/(30/3)=(3)/(10)`

Hence, 3/10 of the barrel was left over.