Question

IV.Verify commutativity of addition of rational numbers for each of the following pairs of : rational numbers 16)-11/5 and 4/7 17) 4/9 and 7/-12 18) "-3/5" and "-2/-15" 19) 2/-7 and 12/-35​

Answer 1

Answer:

Verify commutativity of addition of rational numbers for each of the following pairs of ... - 11/5 and 4/7 as ... 4/9 + -7/12 = -7/12 + 4/9 is satisfied. ... -3/5 + -2/-15 = -2/-15 + -3/5 is satisfied. (iv) ...

Answer 2

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

-11/5 and 4/7 as

-11/5 + 4/7 and 4/7 + -11/5

The denominators are 5 and 7

By taking LCM for 5 and 7 is 35

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

Now, -11/5 = (-11 × 7) / (5 ×7) = -77/35

4/7 = (4 ×5) / (7 ×5) = 20/35

Since the denominators are same we can add them directly

-77/35 + 20/35 = (-77+20)/35 = -57/35

4/7 + -11/5

The denominators are 7 and 5

By taking LCM for 7 and 5 is 35

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

Now, 4/7 = (4 × 5) / (7 ×5) = 20/35

-11/5 = (-11 ×7) / (5 ×7) = -77/35

Since the denominators are same we can add them directly

20/35 + -77/35 = (20 + (-77))/35 = (20-77)/35 = -57/35

∴ -11/5 + 4/7 = 4/7 + -11/5 is satisfied.