Question

What is the value of the expression?
2/5+3/10
________
−7/9
Enter your answer in simplest form.

Answer 1

Answer:

- $\frac{9}{10}$

Step-by-step 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  -$\frac{9}{10}$

Answer 2

Answer:

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

Step-by-step explanation:

We are given the following complex fraction:

$\frac{\frac{2}{5}+\frac{3}{10}  }{\frac{-7}{9} }$

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

$\frac{\frac{2}{5} +\frac{3}{10} }{\frac{-7}{9} }$

$=\frac{\frac{4+3}{10} }{\frac{-7}{9} }$

$=\frac{\frac{7}{10} }{\frac{-7}{9} }$

Taking inverse of the fraction in the denominatot:

$=\frac{7}{10}$ × $-\frac{9}{7}$

$= -\frac{9}{10}$

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