Distributive Property of Rational Numbers

Q.

Verify the following :

(i) $\frac{3}{7}\times (\frac{5}{6}+\frac{12}{13})=(\frac{3}{7}\times \frac{5}{6})+(\frac{3}{7}\times \frac{12}{13})$
(ii) $\frac{-15}{4}\times (\frac{3}{7}+\frac{-12}{5})=(\frac{-15}{4}\times \frac{3}{7})+(\frac{-15}{4}\times \frac{-12}{5})$
(iii) $(\frac{-8}{3}+\frac{-13}{12})\times \frac{5}{6}=(\frac{-8}{3}\times \frac{5}{6})+(\frac{-13}{12}\times \frac{5}{6})$
(iv) $\frac{-16}{7}\times (\frac{-8}{9}+\frac{-7}{6})=(\frac{-16}{7}\times \frac{-8}{9})+(\frac{-16}{7}\times \frac{-7}{6})$

Q. Find the value of
$\frac{3}{5}\times (\frac{35}{24}+\frac{10}{1})$

1. $\frac{55}{8}$
2. $\frac{55}{4}$
3. $\frac{-55}{8}$
4. $\frac{-55}{4}$

Q. Calculate the following:
$\frac{-4}{5}\times \frac{3}{7}+\frac{4}{5}\times \frac{3}{7}=$ ____

1. 0
2. 1
3. $\frac{4}{5}$
4. $\frac{3}{7}$

Q. Question 1(i)
Using appropriate properties find:
\(-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}\)

Q.

For the rational numbers a, b and c, which of the following is true?

1. a $\times$ (b + c) = (a + b)$\times$(a + c)

2. a $\times$ (b + c) = (a + b)$\times$(a + c) = 1

3. a $\times$ (b + c) = (a $\times$ b) + (a $\times$ c)

4. a $\times$ (b + c) = (a $\times$ b) - (a $\times$ c)

Q.

Name the property used in the following: $\left(\frac{-2}{3}\right)\times \left[\left(\frac{3}{4}\right)+\left(\frac{-1}{2}\right)\right]=\left[\left(\frac{-2}{3}\right)\times \left(\frac{3}{4}\right)\right]+\left[\left(\frac{-2}{3}\right)\times \left(\frac{-1}{2}\right)\right]$

Q. Question 124(ii)
Name the property used in each of the following:
$\frac{-2}{3}\times [\frac{3}{4}+\frac{-1}{2}]=[\frac{-2}{3}\times \frac{3}{4}]+[\frac{-2}{3}\times \frac{-1}{2}]$

Q.

Verify: $-(-\mathrm{x})=\mathrm{x}$ for $\mathrm{x}=\frac{3}{5}$.

Q.

Question 22

Which of the following is an example of distributive property of multiplication over addition for rational numbers.
(a) $-\frac{1}{4}\times \{\frac{2}{3}+\left(\frac{-4}{7}\right)\}=[-\frac{1}{4}\times \frac{2}{3}]+[-\frac{1}{4}\times \left(\frac{-4}{7}\right)]$
(b) $-\frac{1}{4}\times \{\frac{2}{3}+\left(\frac{-4}{7}\right)\}=[\frac{1}{4}\times \frac{2}{3}]-\left(\frac{-4}{7}\right)$
(c) $-\frac{1}{4}\times \{\frac{2}{3}+\left(\frac{-4}{7}\right)\}=\frac{2}{3}+(-\frac{1}{4})\times \frac{-4}{7}$
(d) $-\frac{1}{4}\times \{\frac{2}{3}+\left(\frac{-4}{7}\right)\}=\{\frac{2}{3}+\left(\frac{-4}{7}\right)\}-\frac{1}{4}$

Q.

$\text{Verify that}(x+y)\times z=x\times z+y\times z,if\left(i\right)x=\frac{4}{5},y=\frac{-2}{3}\text{~}andz=-4\left(ii\right)x=2,y=\frac{4}{5}\text{~}andz=\frac{3}{-10}$

Q. Question 106(iii)
Simplify each of the following by using suitable property. Also, name the property
$\frac{-3}{5}\times \{\frac{3}{7}+\left(\frac{-5}{6}\right)\}$

Q. Question 106(ii)
Simplify each of the following by using suitable property. Also, name the property
$[\frac{1}{5}\times \frac{2}{15}]-[\frac{1}{5}\times \frac{2}{5}]$

Q.

Verify the property $x+y=y+x$ of rational numbers by using $x=\frac{1}{2}$and $y=\frac{1}{2}$.

Q. Question 111(i)
Use the distributivity of multiplication of rational numbers over addition to simplify.
$\frac{3}{5}\times [\frac{35}{24}+\frac{10}{1}]$

Q. Question 111(ii)
Use the distributivity of multiplication of rational numbers over addition to simplify.
$\frac{-5}{4}\times [\frac{8}{5}+\frac{16}{15}]$

Q. Question 1(ii)
Using appropriate properties find:
$\frac{2}{5}\times \left(\frac{-3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

Q. 6. Rationalise the denominator of 12÷ root 2+root 3+root5

Q.

Divide the sum of $\frac{3}{5}$ and $\frac{-1}{2}$ by the product of $\frac{-1}{7}$ and $-1$.

1. 1

2. 0.7

3. 2

4. 8

Q.

Question 37
For rational numbers $\frac{a}{b},\frac{c}{d}$ and $\frac{e}{f}$, we have $\frac{a}{b}\times (\frac{c}{d}+\frac{e}{f})=$ ___ + ____

Q. Question 70
For all rational numbers a, b and c, a (b + c) = ab + bc

Q. Question 1(ii)
Using appropriate properties find:
$\frac{2}{5}\times \left(\frac{-3}{7}\right)-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

Q. Question 106(i)
Simplify each of the following by using suitable property. Also, name the property
$[\frac{1}{2}\times \frac{1}{4}]+[\frac{1}{2}\times 6]$

Q. Question 69
For every rational numbers x, y and z, $x+(y\times z)=(x+y)\times (x+z)$

Q.

Find the product by suitable rearrangement: $285\times 5\times 60$

Q.

The cost of 15 metres of a cloth is Rs. 981. What length of this cloth can be purchased for Rs. 1308 ?

Q. Question 111(iv)
Use the distributivity of multiplication of rational numbers over addition to simplify.
$\frac{3}{4}\times [\frac{8}{9}-40]$

Q. Question 111(iii)
Use the distributivity of multiplication of rational numbers over addition to simplify.
$\frac{2}{7}\times [\frac{7}{16}-\frac{21}{4}]$

Q.

Use the distributivity of multiplication of rational numbers over their addition to simplify:

(i) $\frac{3}{5}\times (\frac{35}{24}+\frac{10}{1})$

(ii)$\frac{-5}{4}\times (\frac{8}{5}+\frac{16}{5})$

(iii)$\frac{2}{7}\times (\frac{7}{16}-\frac{21}{4})$

(iv)$\frac{3}{4}\times (\frac{8}{9}-40)$

Q. Question 106(iii)
Simplify each of the following by using suitable property. Also, name the property
$\frac{-3}{5}\times \{\frac{3}{7}+\left(\frac{-5}{6}\right)\}$

Q. Question 111(i)
Use the distributivity of multiplication of rational numbers over addition to simplify.
$\frac{3}{5}\times [\frac{35}{24}+\frac{10}{1}]$