Associative Property of Rational Numbers

Q.

Tell what property allows you to compute $\frac{1}{3}\times (6\times \frac{4}{3})$ as $(\frac{1}{3}\times 6)\times \frac{4}{3}$

Q.

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) $x=-2,y=\frac{3}{5},z=\frac{-4}{3}$

Q.

For each set of rational numbers, given below, verify the associative property of addition of rational numbers:
$\left(i\right)\frac{1}{2},\frac{2}{3}\text{and}-\frac{1}{6}\left(ii\right)\frac{-2}{5},\frac{4}{15}\text{and}\frac{-7}{10}\left(iii\right)\frac{-7}{9},\frac{2}{-3}\text{and}\frac{-5}{18}\left(iv\right)-1,\frac{5}{6}\text{~}and\frac{-2}{3}$

Q.

Tell what property allows you to compute $\frac{1}{3}\times \left(6\times \frac{4}{3}\right)$as$\left(\frac{1}{3}\times 6\right)\times \frac{4}{3}$

Q.

Verify the property: $x\times (y\times z)=(x\times y)\times zbytaking:$

(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)$x=\frac{5}{7},y=\frac{-12}{13},z=\frac{-7}{18}$

Q.

Key to represent a relationship between tables is called?

Q.

Which of the following expressions shows that rational numbers are associative under multiplication.

1. $\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{-6}{7}\right)\times \left(\frac{3}{5}\right)\right)\right]=\left[\left(\left(\frac{2}{3}\right)\times \left(\frac{-6}{7}\right)\right)\times \left(\frac{3}{5}\right)\right]$

2. $\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{-6}{7}\right)\times \left(\frac{3}{5}\right)\right)\right]=\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{3}{5}\right)\times \left(\frac{-6}{7}\right)\right)\right]$

3. $\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{-6}{7}\right)\times \left(\frac{3}{5}\right)\right)\right]=\left[\left(\left(\frac{3}{5}\right)\times \left(\frac{2}{3}\right)\right)\times \left(\frac{-6}{7}\right)\right]$

4. $\left[\left(\frac{2}{3}\right)\times \left(\left(\frac{-6}{7}\right)\times \left(\frac{3}{5}\right)\right)\right]=\left[\left(\left(\frac{-6}{7}\right)\times \left(\frac{2}{3}\right)\right)\times \left(\frac{3}{5}\right)\right]$

Q.

Verify whether the given statement is true or false :

(i) $(\frac{5}{9}÷\frac{1}{3})÷\frac{5}{2}=\frac{5}{9}÷(\frac{1}{3}÷\frac{5}{2})$

(ii) $\left\{\right(-16)÷\frac{6}{5}\}÷\frac{-9}{10}=(-16)÷\{\frac{6}{5}÷\frac{-9}{10}\}$

(iii) $(\frac{-3}{5}÷\frac{-12}{35})÷\frac{1}{14}=\frac{-3}{5}÷(\frac{-12}{35}÷\frac{1}{14})$

Q.

Find using distributivity.

{7/5*(-3/12)} + {7/5*5/12}

Q.

The numbers $\frac{-1}{2}$ , $\frac{2}{3}$ and $\frac{1}{6}$ follow the Associative property of addition.

1. True

2. False

Q.

Prove that :

5/4×(54/48+105/75)=(5/4×54/48)+(5/4×105/75)

Q.

Name the property used in the following: $\left(\frac{1}{3}\right)+\left[\left(\frac{4}{9}\right)+\left(-\frac{4}{3}\right)\right]=\left[\left(\frac{1}{3}\right)+\left(\frac{4}{9}\right)\right]+\left(-\frac{4}{3}\right)$

Q.

Check the following rational numbers for distributive property of multiplication over addition

$\frac{1}{4},\frac{1}{3}$ and $\frac{3}{2}$

Q.

Question 109(i)
Verify the property $x\times (y\times z)=(x\times y)\times z$ of rational numbers by using
$x=1,y=\frac{-1}{2}$ and $z=\frac{1}{4}$
and what is the name of this property?

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. In a class of 40 students, $\frac{1}{5}$ of the total number of students like to study english, $\frac{2}{5}$ of the total number like to study mathematics and the remaining students like to study science. What fractions of the total number of students like to study science?

1. 
2. 
3. 
4. 

Q.

Name the property used in each of the following:
$\frac{1}{3}+[\frac{4}{9}+\left(\frac{-4}{3}\right)]=[\frac{1}{3}+\frac{4}{9}]+\left[\frac{-4}{3}\right]$

Q.

What Is the Use of the Keyword Import in Java Programming?

Q.

Tell which property allows you to compute $\frac{1}{5}\times \left(\frac{5}{6}\times \frac{7}{9}\right)as\left(\frac{1}{5}\times \frac{5}{6}\right)\times \frac{7}{9}$

Q. Verify associativity of addition of rational numbers i.e.,
$(x+y)+z=x+(y+z)$

iv) $x=-2,y=\frac{3}{5},z=\frac{-4}{3}$

Q.

Tell which property allows you to compare $\left(\frac{2}{3}\right)\times \left[\left(\frac{3}{4}\times \frac{5}{7}\right)\right]and\left[\left(\frac{2}{3}\times \frac{5}{7}\right)\right]\times \left(\frac{3}{4}\right)$

Q.

Is multiplication associative for rational numbers?

Q. Question 107
Tell which property allows you to compute $\frac{1}{5}\times [\frac{5}{6}\times \frac{7}{9}]as[\frac{1}{5}\times \frac{5}{6}]\times \frac{7}{9}$

Q. Tell what property allows you to compute $\frac{1}{3}\times \left(6\times \frac{4}{3}\right)$ as $\left(\frac{1}{3}\times 6\right)\times \frac{1}{4}$

Q. Question 123
Tell which property allows you to compare $\frac{2}{3}\times [\frac{3}{4}\times \frac{5}{7}]$ and $[\frac{2}{3}\times \frac{5}{7}]\times \frac{3}{4}$

Q.

Identify the property in the following statements:

(i) 2 + (3 + 4) = (2 + 3) + 4; (ii) 2.8 = 8.2; (iii) 8. (6 + 5) = (8.6) + (8.5).

Q.

What should be added to thrice the rational number $\frac{3}{5}$ to get $\frac{1}{2}$? [1 MARK]

Q.

Compare the following rational numbers and choose the correct option(s):
$\frac{4}{-9}$, $\frac{5}{-12}$, $\frac{7}{-18}$, $\frac{2}{-3}$

1. -4/9

2. 5/-12

3. 7/-18

4. 2/-3

Q.

Question 109(ii)
Verify the property $x\times (y\times z)=(x\times y)\times z$ of rational numbers by using
$x=\frac{2}{3},y=\frac{-3}{7}$ and $z=\frac{1}{2}$
and what is the name of this property?

Q.

Question 109(iv)
Verify the property $x\times (y\times z)=(x\times y)\times z$ of rational numbers by using
$x=0,y=\frac{1}{2}$ and $z=\frac{1}{4}$
and what is the name of this property?