Verify the property $ x \times(y+z)=(x \times y)+(x \times z) $ for the given values of $ x,\ y $ and $ z $.$ x=\frac{-5}{2}, y=\frac{1}{2} $ and $ z=-\frac{10}{7} $>
Given: $x=\frac{-5}{2},\ y=\frac{1}{2}$ and $z=-\frac{10}{7}$.
To do: To verify the property $x\times(y+z)=( x\times y)+( x\times z)$ for the given values of $x,\ y$ and $z$.
Solution:
$L.H.S.=x\times( y+z)$
$=\frac{-5}{2}\times( \frac{1}{2}-\frac{10}{7})$ [On substituting values of $x,\ y$ and $z$]
$=-\frac{5}{2}\times\frac{-13}{14}$
$=\frac{65}{28}$
$R.H.S.=( x\times y)+( x\times z)$
$=( \frac{-5}{2}\times\frac{1}{2})+( \frac{-5}{2}\times-\frac{10}{7})$
$=-\frac{5}{4}+\frac{50}{14}$
$=-\frac{5}{4}\times\frac{7}{7}+\frac{50}{14}$
$=-\frac{35}{28}+\frac{100}{28}$
$=\frac{65}{28}$
Thus $L.H.S.=R.H.S.$
Related Articles
- Verify: $x\times(y\times z)=(x\times y)\times z$, where $x=\frac{1}{2},\ y=\frac{1}{3}$ and $z=\frac{1}{4}$.
- Verify the property: $x \times (y \times z) = (x \times y) \times z$ by taking:(i) \( x=\frac{-7}{3}, y=\frac{12}{5}, z=\frac{4}{9} \)(ii) \( x=0, y=\frac{-3}{5}, z=\frac{-9}{4} \)(iii) \( x=\frac{1}{2}, y=\frac{5}{-4}, z=\frac{-7}{5} \)(iv) \( x=\frac{5}{7}, y=\frac{-12}{13}, z=\frac{-7}{18} \)
- 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) \( x=\frac{-12}{5}, y=\frac{-15}{4}, z=\frac{8}{3} \)(iii) \( x=\frac{-8}{3}, y=\frac{5}{6}, z=\frac{-13}{12} \)(iv) \( x=\frac{-3}{4}, y=\frac{-5}{2}, z=\frac{7}{6} \)
- Verify that \( x^{3}+y^{3}+z^{3}-3 x y z=\frac{1}{2}(x+y+z)\left[(x-y)^{2}+(y-z)^{2}+(z-x)^{2}\right] \)
- Subtract $3 x y+5 y z-7 z x$ from $5 x y-2 y z-2 z x+10 x y z$.
- Verify associativity of addition of rational numbers i.e., $(x + y) + z = x + (y + z)$, when:(i) \( x=\frac{1}{2}, y=\frac{2}{3}, z=-\frac{1}{5} \)(ii) \( x=\frac{-2}{5}, y=\frac{4}{3}, z=\frac{-7}{10} \)(iii) \( x=\frac{-7}{11}, y=\frac{2}{-5}, z=\frac{-3}{22} \)(iv) \( x=-2, y=\frac{3}{5}, z=\frac{-4}{3} \)
- If $2^x \times 3^y \times 5^z = 2160$, find $x, y$ and $z$. Hence, compute the value of $3^x \times 2^{-y} \times 5^{-z}$.
- Find the product of $(-3 x y z)(\frac{4}{9} x^{2} z)(-\frac{27}{2} x y^{2} z)$ and verify the result for ; $x=2, y=3$ and $z=-1$
- Find the following product.$\frac{1}{2} x y \times \frac{2}{3} x^{2} y z^{2}$
- Find the following product.\( \left(\frac{-7}{5} x y^{2} z\right) \times\left(\frac{13}{3} x^{2} y z^{2}\right) \)
- If \( 3^{x}=5^{y}=(75)^{z} \), show that \( z=\frac{x y}{2 x+y} \).
- Find the following product.\( (-7 x y) \times\left(\frac{1}{4} x^{2} y z\right) \)
- Find the following product.\( (0.5 x) \times\left(\frac{1}{3} x y^{2} z^{4}\right) \times\left(-24 x^{2} y z\right) \)
- If \( 2^{x}=3^{y}=12^{z} \), show that \( \frac{1}{z}=\frac{1}{y}+\frac{2}{x} \).
- Find the following products:\( \frac{-4}{27} x y z\left[\frac{9}{2} x^{2} y z-\frac{3}{4} x y z^{2}\right] \)
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies