Use the properties of operations and rules for multiplying and dividing to solve: (8/9) x (-3/4) divide (1/9) x (-4/5) divide (3/5)

1 answer

To solve this expression, we will simplify each part separately and then divide the results.

First, we simplify (8/9) x (-3/4).

To multiply fractions, we multiply the numerators together and the denominators together.

(8/9) x (-3/4) = (8 x -3) / (9 x 4) = -24/36

The fraction -24/36 can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 12.

-24/36 = (-24 ÷ 12) / (36 ÷ 12) = -2/3

Now, we simplify (1/9) x (-4/5).

(1/9) x (-4/5) = (1 x -4) / (9 x 5) = -4/45

Finally, we divide (-2/3) by (-4/45).

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.

(-2/3) ÷ (-4/45) = (-2/3) x (45/-4)

We can simplify before multiplying by dividing the numerator and denominator by their greatest common divisor, which is 1.

(-2/3) x (45/-4) = (-2 x 45) / (3 x -4) = -90/-12

Again, we simplify by dividing the numerator and denominator by their greatest common divisor, which is 6.

-90/-12 = (-90 ÷ 6) / (-12 ÷ 6) = 15/2

So, (8/9) x (-3/4) ÷ (1/9) x (-4/5) ÷ (3/5) simplifies to 15/2.