Question

Verify commutativity of addition and multiplication of the rational number for the following pairs of number s -11/5 and 4/7

Answer 1

addition

lhs

-11/5 + 4/7

= -11 + 4 / 35 (lcm)

= -7/35 = -1/35

rhs=

4/7 + (-11)/5

=4+(-11)/ 35

= -7/35

= -1/35

thus proved commutative under addition

Multiplication

lhs =

-11 /5 × 4/7

= -44/35

rhs=

4/7 × (-11)/5

= -44/35

thus lhs= rhs

this proved

multiplication under commutative

Answer 2

$\fbox \red{Required Solution:}$

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

-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)

= (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.

Thank you!

@itzshivani