Question

What is the value of the expression
Picture above
Thanks

Answer 1

First, we want the fractions in the numerator to have the same denominator.

Find the LCM (least common multiple) of 5 and 10:

Multiples of 5: 5, 10, 15, 20

Multiples of 10: 10, 20

10 < 20

The LCM is 10. Divide the LCM by the smaller denominator for 2/5:

$10 \div 5 = 2$

Multiply the numerator and denominator of the fraction by this number:

$\frac{2}{5} \cdot \frac{2}{2} = \frac{4}{10}$

We can now solve for the overall numerator:

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

The expression should now look like this:

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

We can multiply the numerator by the fraction's denominator within the expression's denominator:

$\frac{\frac{7}{10}}{-\frac{7}{9}} = \frac{\frac{7}{10} \cdot 9}{-7} = \frac{\frac{63}{10}}{-7}$

We can eliminate the denominator of the expression's numerator fraction by multiplying it by the expression's denominator:

$\frac{\frac{63}{10}}{-7} = \frac{63}{-7 \cdot 10} = \frac{63}{-70}$

Find the GCF (greatest common factor) between 63 and 70:

Factors of 63: 1, 3, 7, 9, 21, 63

Factors of 70: 1, 2, 5, 7, 10, 14, 35, 70

7 > 1

GCF : 7

Divide the numerator and denominator by the GCF:

$\frac{63}{-70} \div \frac{7}{7} = \frac{9}{-10}$

There is a negative sign in the denominator. Move this negative sign outside of the fraction:

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

The answer in simplest form will be -9/10.