Question

verify commutativity of addition of rational number— 2/-7 and 12/-35​

Answer 1

Answer:

Step-by-step explanation:

Firstly we need to convert the denominators to positive numbers.

2/-7 = (2 × -1)/ (-7 × -1) = -2/7

12/-35 = (12 × -1)/ (-35 × -1) = -12/35

By using the commutativity law, the addition of rational numbers is commutative.

∴ a/b + c/d = c/d + a/b

In order to verify the above property let us consider the given fraction

-2/7 and -12/35 as

-2/7 + -12/35 and -12/35 + -2/7

The denominators are 7 and 35

By taking LCM for 7 and 35 is 35

We rewrite the given fraction in order to get the same denominator

Now, -2/7 = (-2 × 5) / (7 ×5) = -10/35

-12/35 = (-12 ×1) / (35 ×1) = -12/35

Since the denominators are same we can add them directly

-10/35 + (-12)/35 = (-10 + (-12))/35 = (-10-12)/35 = -22/35

-12/35 + -2/7

The denominators are 35 and 7

By taking LCM for 35 and 7 is 35

We rewrite the given fraction in order to get the same denominator

Now, -12/35 = (-12 ×1) / (35 ×1) = -12/35

-2/7 = (-2 × 5) / (7 ×5) = -10/35

Since the denominators are same we can add them directly

-12/35 + -10/35 = (-12 + (-10))/35 = (-12-10)/35 = -22/35

∴ -2/7 + -12/35 = -12/35 + -2/7 is satisfied.

(v) 4 and -3/5

Solution: By using the commutativity law, the addition of rational numbers is commutative.

∴ a/b + c/d = c/d + a/b

In order to verify the above property let us consider the given fraction

4/1 and -3/5 as