Distributive Property

Q.

Verify the property $x\times (y+z)=\left(x\times y\right)+\left(x\times z\right)$ of rational numbers by using $x=\frac{-2}{3}$, $y=\frac{-4}{6}$and $z=\frac{-7}{9}$.

Q. Find using distributivity.
$\frac{8}{5}\times (\frac{15}{24}+\frac{10}{8})=?$

1. $5\frac{7}{8}$
2. $1\frac{2}{8}$
3. 3
4. 4

Q.

Subtraction of integer is commutative.

1. True

2. False

Q.

What is rearrangement property ?

Q. Find the value of $(\frac{8}{25}\times \frac{7}{3})\times \frac{15}{14}$.

1. $\frac{4}{5}$
   
2. $\frac{5}{4}$
   
3. $\frac{15}{2}$
   
4. $\frac{5}{8}$
   

Q. $a\times (b+c)=(a\times b)+(a\times c)$ represents which of the following property?

1. Distributive property
2. Associative property of addition
3. Commutative property
4. Associative property of multiplication

Q. For rational numbers $\frac{a}{b},\frac{c}{d}$ and $\frac{e}{f}$, what is $\frac{a}{b}\times (\frac{c}{d}+\frac{e}{f})$?

Q. Using suitable rearrangement, find the sum.
$-5+\frac{7}{10}+\frac{3}{7}+(-3)+\frac{5}{14}+\left(\frac{-4}{5}\right)$

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.

Find the product of the following using properties:

$7909\times 991$

Q. How can we understand commutative property, closure property, associative property, distributive property

Q.

Find using distributive property:

(a) 728 ×101 (b) 5437 × 1001

(c) 824 ×25 (d) 4275 × 125

(e) 504 ×35

Q. Match the following properties.

1. a + b = b + a
2. a+(b+c)=(a+b)+c
3. a(b+c)=ab+ac

Q.

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

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

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

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

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

Q.

Question 6

Which of the following expressions show that rational numbers are associative under multiplication.
(a) $\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=(\frac{2}{3}\times \frac{-6}{7})\times \frac{3}{5}$
(b) $\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=\frac{2}{3}\times (\frac{3}{5}\times \frac{-6}{7})$
(c) $\frac{2}{3}\times (\frac{-6}{7}\times \frac{3}{5})=(\frac{3}{5}\times \frac{2}{3})\times \frac{-6}{7}$
(d) $(\frac{2}{3}\times \frac{-6}{7})\times \frac{3}{5}=(\frac{-6}{7}\times \frac{2}{3})\times \frac{3}{5}$

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. Question 5(ii)
Name the property under multiplication used in each of the following:

$-\frac{13}{17}\times \frac{-2}{7}=\frac{-2}{7}\times \frac{-13}{17}$

Q.

The product 108 x 109 can be written as 10000 + ____ x 100 + 72.

1. 19

2. 18

3. 17

4. 15

Q.

Using the pattern,

2² = 4

20² = 400

We get 2000² =

1. 40000

2. 40000000

3. 4000000

4. 400000

Q. Find the value of $(\frac{8}{25}\times \frac{7}{3})\times \frac{15}{14}$.

1. $\frac{4}{5}$
   
2. $\frac{5}{4}$
   
3. $\frac{15}{2}$
   
4. $\frac{5}{8}$
   

Q.

Solve using appropriate proper properties.

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}$

Q.

Question 5
$-\frac{3}{8}+\frac{1}{7}=\frac{1}{7}+\left(\frac{-3}{8}\right)$ is an example to show that
(a) addition of rational numbers is commutative.
(b) rational numbers are closed under addition.
(c) addition of rational number is associative.
(d) rational numbers are distributive under addition

Q.

Find the product using suitable properties.

(a) 738 × 103 (b) 854 × 102

(c) 258 × 1008 (d) 1005 × 168

Q. Using appropriate properties find:
$-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$

Q.

Question 127(i)

An insect is on the 0 point of a number line, hopping towards 1. It covers half the distance from its current location to 1 with each hop.
So, it will be at $\frac{1}{2}$ after one hop, $\frac{3}{4}$ after two hops and so on.



Make a table showing the insects location for the first 10 hops.

Q.

Solve using appropriate proper properties [3 MARKS]

$\frac{2}{5}\times \frac{-3}{7}-\frac{1}{14}-\frac{3}{7}\times \frac{3}{5}$

Q.

(1) 1.0001 × 10⁹

(2) 5.8 × 10¹²

Q. $\frac{1}{5}\times [\frac{2}{7}+\frac{3}{8}]=[\frac{1}{5}\times \frac{2}{7}]+$ ______

Q.

Verify the associative property for the multiplication of the following whole numbers :

$4,5,0$

Q. The property $x\times (y+z)=x\times y+x\times z$ represents property .

1. Commutative
2. Closure
3. Associative
4. Distributive