Advertisements
Advertisements
प्रश्न
Verify the property: x × (y + z) = x × y + x × z by taking:
Advertisements
उत्तर
\[\text{We have to verify that} x \times (y + z) = x \times y + x \times z . \]
\[x = \frac{- 12}{5}, y = \frac{- 15}{4}, z = \frac{8}{3}\]
\[x \times (y + z) = \frac{- 12}{5} \times (\frac{- 15}{4} + \frac{8}{3}) = \frac{- 12}{5} \times \frac{- 45 + 32}{12} = \frac{- 12}{5} \times \frac{- 13}{12} = \frac{13}{5}\]
\[x \times y + x \times z = \frac{- 12}{5} \times \frac{- 15}{4} + \frac{- 12}{5} \times \frac{8}{3}\]
\[ = \frac{9}{1} + \frac{- 32}{5}\]
\[ = \frac{45 - 32}{5}\]
\[ = \frac{13}{5}\]
\[ \therefore \frac{- 12}{5} \times (\frac{- 15}{4} + \frac{8}{3}) = \frac{- 12}{5} \times \frac{- 15}{4} + \frac{- 12}{5} \times \frac{8}{3}\]
\[\text{Hence verified .} \]
APPEARS IN
संबंधित प्रश्न
Use the distributivity of multiplication of rational numbers over their addition to simplify:
Name the property of multiplication of rational numbers illustrated by the following statements:
By what number should we multiply \[\frac{- 15}{28}\] so that the product may be\[\frac{- 5}{7}?\]
By what number should we multiply \[\frac{- 8}{13}\]
so that the product may be 24?
Verify the property x + y = y + x of rational numbers by taking
`x = 1/2, y = 1/2`
Verify the property x + y = y + x of rational numbers by taking
`x = (-3)/7, y = 20/21`
Verify the property x + y = y + x of rational numbers by taking
`x = (-2)/5, y = (-9)/10`
Simplify the following by using suitable property. Also name the property.
`[1/2 xx 1/4] + [1/2 xx 6]`
Verify the property x × (y + z) = x × y + x × z of rational numbers by taking.
`x = (-1)/2, y = 3/4, z = 1/4`
Name the property used in the following.
`-2/3 xx [3/4 + (-1)/2] = [(-2)/3 xx 3/4] + [(-2)/3 xx (-1)/2]`
