Question

Evaluate : 2/15-17/9+3/5-20/3​

Answer 1

So, to add and subtract fractions we need to find a common denominator. This needs to be a number divisble by all denominators present in the term, so it has to be divisible by 15, 9, 5, and 3.

As 5 and 3 are divisors of 15 (and therefore of every multiple of 15), we only really need to find a common multiple of 15 and 9. As 15=5*3 and 9=3*3 we see that 45=5*3*3 would be the smalles common multiple.

So, now we need to adjust each of the fractions to the denominator 45.

2/15 = 2*3/15*3=6/45

-17/9= -17*5/9*5 = -85/45

3/5 = 3*9/5*9 = 27/45

-20/3 = -20*15/3*15 = - 300/45

In total we now have

(6-85+27-300)/45 = -352/45

As -352 and 45 have no common divisors, we are done :)

Answer 2

Explanation:

To evaluate the expression:

2/15 - 17/9 + 3/5 - 20/3

First, we need to find a common denominator for the fractions involved.

The least common denominator (LCD) for 15, 9, 5, and 3 is 45.

Now, we can rewrite each fraction with the LCD:

2/15 = (2 * 3)/(15 * 3) = 6/45

17/9 = (17 * 5)/(9 * 5) = 85/45

3/5 = (3 * 9)/(5 * 9) = 27/45

20/3 = (20 * 15)/(3 * 15) = 300/45

Now, we can substitute these values back into the original expression:

6/45 - 85/45 + 27/45 - 300/45

To combine the fractions, we can add or subtract the numerators while keeping the common denominator:

(6 - 85 + 27 - 300)/45

Simplifying the numerator:

-352/45

Therefore, the evaluated expression is -352/45.