 # Verify the property x × y = y × z

Question:

Verify the property x × y = y × z of rational numbers by using

Solution:

(a) x = 7 and y = ½

In the question is given to verify the property = x × y = y × x

Where, x = 7, y = ½

Then, 7 × ½ = ½ × 7

LHS = 7 × ½

= 7/2

RHS = ½ × 7

= 7/2

By comparing LHS and RHS

LHS = RHS

∴ 7/2 = 7/2

Hence x × y = y × x

(b) x = 2/3 and y = 9/4

Solution:-

In the question is given to verify the property = x × y = y × x

Where, x = 2/3, y = 9/4

Then, (2/3) × (9/4) = (9/4) × (2/3)

LHS = (2/3) × (9/4)

= (1/1) × (3/2)

= 3/2

RHS = (9/4) × (2/3)

= (3/2) × (1/1)

= 3/2

By comparing LHS and RHS

LHS = RHS

∴ 3/2 = 3/2

Hence x × y = y × x

(c) x = -5/7 and y = 14/15

Solution:-

In the question is given to verify the property = x × y = y × x

Where, x = -5/7, y = 14/15

Then, (-5/7) × (14/15) = (14/15) × (-5/7)

LHS = (-5/7) × (14/15)

= (-1/1) × (2/3)

= -2/3

RHS = (14/15) × (-5/7)

= (2/3) × (-1/1)

= -2/3

By comparing LHS and RHS

LHS = RHS

∴ -2/3 = -2/3

Hence x × y = y × x

(d) x = -3/8 and y = -4/9

Solution:-

In the question is given to verify the property = x × y = y × x

Where, x = -3/8, y = -4/9

Then, (-3/8) × (-4/9) = (-4/9) × (-3/8)

LHS = (-3/8) × (-4/9)

= (-1/2) × (-1/3)

= 1/6

RHS = (-4/9) × (-3/8)

= (-1/3) × (-1/2)

= 1/6

By comparing LHS and RHS

LHS = RHS

∴ 1/6 = 1/6

Hence x × y = y × x