Verify the property: \(x\times(y+z)=x\times y+x\times z\) by taking \(x=\frac{-3}{7},y=\frac{12}{13},z=\frac{-5}{6}\)

Question

Verify the property: \(x\times(y+z)=x\times y+x\times z\)  by taking

i) \(x=\frac{-3}{7},y=\frac{12}{13},z=\frac{-5}{6}\)

ii) \(x=\frac{-12}{5},y=\frac{-15}{4},z=\frac{8}{3}\)

Answer 1

By using the property 

x × (y + z) = x × y + x × z

i) -3/7 × (12/13 + -5/6) = -3/7 × 12/13 + -3/7 × -5/6

-3/7 × ((12×6) + (-5×13))/78 = (-3×12)/(7×13) + (-3×-5)/(7×6)

-3/7 × (72-65)/78 = -36/91 + 15/42

-3/7 × 7/78 = (-36×6 + 15×13)/546

-1/26 = (196-216)/546

= -21/546

= -1/26

Hence, the property is verified.

ii) By using property,

-12/5 × (-15/4 + 8/3) = -12/5 × -15/4 + -12/5 × 8/3

-12/5 × ((-15×3) + (8×4))/12 = (-12×-15)/(5×4) + (-12×8)/(5×3)

-12/5 × (-45+32)/12 = 180/20 – 96/15

-12/5 × -13/12 = 9 – 32/5

13/5 = (9×5 – 32×1)/5

= (45-32)/5

= 13/5

Hence, the property is verified.