Expressing -3/5 as a rational number with different denominators:

To express -3/5 as a rational number with different denominators, we need to find a common multiple of the given denominator and the required denominator. Then, we can multiply both the numerator and denominator by the same number to get an equivalent fraction with the required denominator.

1. With denominator 20:

To find a common multiple of 5 and 20, we can use the LCM (Least Common Multiple) method.

5 = 5 x 1
20 = 5 x 4

LCM = 5 x 4 = 20

So, we can multiply the numerator and denominator of -3/5 by 4 to get an equivalent fraction with denominator 20.

-3/5 x 4/4 = -12/20

Therefore, -3/5 as a rational number with denominator 20 is -12/20.

2. With denominator -30:

To find a common multiple of 5 and -30, we can use the LCM method again.

5 = 5 x 1
-30 = -5 x 6

LCM = 5 x 6 = 30

However, since the required denominator is negative, we need to multiply both the numerator and denominator by -6 to get an equivalent fraction with denominator -30.

-3/5 x (-6)/(-6) = 18/30

Therefore, -3/5 as a rational number with denominator -30 is 18/-30 or -6/10.

3. With denominator 35:

To find a common multiple of 5 and 35, we can use the LCM method again.

5 = 5 x 1
35 = 5 x 7

LCM = 5 x 7 = 35

So, we can multiply the numerator and denominator of -3/5 by 7 to get an equivalent fraction with denominator 35.

-3/5 x 7/7 = -21/35

Therefore, -3/5 as a rational number with denominator 35 is -21/35.

4. With denominator -40:

To find a common multiple of 5 and -40, we can use the LCM method again.

5 = 5 x 1
-40 = -5 x 8

LCM = 5 x 8 = 40

However, since the required denominator is negative, we need to multiply both the numerator and denominator by -8 to get an equivalent fraction with denominator -40.

-3/5 x (-8)/(-8) = 24/40

Therefore, -3/5 as a rational number with denominator -40 is 24/-40 or -6/10.

Represent following number on number line -3/4