Question

What is the value of the expression?

2/5+3/10
________
−7/9
Enter your answer in simplest form.

Answer 1

-9/10 is the simplest form of the given expression.

Explanation:

We are given the following complex fraction:

`((2)/(5)+(3)/(10)  )/((-7)/(9) )`

To solve it, we will first take LCM of the fractions in the numerator and change it to a single fraction to get:

`((2)/(5) +(3)/(10) )/((-7)/(9) )`

`=((4+3)/(10) )/((-7)/(9) )`

`=((7)/(10) )/((-7)/(9) )`

Taking inverse of the fraction in the denominatot:

`=(7)/(10)` ×
`-(9)/(7)`

`= -(9)/(10)`

Therefore, the simplest form of the given expression is -9/10.

Answer 2

-
`(9)/(10)`

Explanation:

Step 1: Add the numerator fractions.

2/5 + 3/10

Here we have to find LCD, the LCD of 5 and 10 is 10

(2*2) + 3 4 + 3

Therefore, 2/5 + 3/10 = --------------- = ------------------

10 10

= 7/10

Step 2: Now substitute 2/5 + 3/10 = 7/10 in the given fraction, we get

7/10

= ----------

-7/9

If we have fraction over fraction, we have to find the reciprocal of denominator fraction and multiply.

The reciprocal of -7/9 is -9/7

Step 3: Now multiply 13/10 and -9/7

= (7/10) x (-9/7)

= -9/10

=-9/10

The answer is -
`(9)/(10)`