Commutative Property of Rational Numbers

Q.

Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers: (i) $\frac{-11}{5}and\frac{4}{7}$ (ii)$\frac{4}{9}and\frac{7}{-12}$ (iii) $\frac{-3}{5}and\frac{-2}{-15}$ (iv) $\frac{2}{-7}and\frac{12}{-35}$ (v) $4and\frac{-3}{5}$ (vi) $-4and\frac{4}{-7}$

Q. Question 102(ii)
Using suitable rearrangement, find the sum.
$-5+\frac{7}{10}+\frac{3}{7}+(-3)+\frac{5}{14}+\left(\frac{-4}{5}\right)$

Q.

Verify the following

(i) $\frac{-12}{5}+\frac{2}{7}=\frac{2}{7}+\frac{-12}{5}$

(ii) $\frac{-5}{8}+\frac{-9}{13}=\frac{-9}{13}+\frac{-5}{8}$

(iii) $3+\frac{-7}{12}=\frac{-7}{12}+3$

(iv) $\frac{2}{-7}+\frac{12}{-35}=\frac{12}{-35}+\frac{2}{-7}$

Q.

Using commutativity and associativity of addition of rational numbers, express each of the following as a rational number:

(i) $\frac{2}{5}+\frac{7}{3}+\frac{-4}{5}+\frac{-1}{3}$

(ii) $\frac{3}{7}+\frac{-4}{9}+\frac{-11}{7}+\frac{7}{9}$

(iii) $\frac{2}{5}+\frac{8}{3}+\frac{-11}{15}+\frac{4}{5}+\frac{-2}{3}$

(iv) $\frac{4}{7}+0+\frac{-8}{9}+\frac{-13}{7}+\frac{17}{21}$

Q.

The cost of $3\frac{2}{5}$ meters of cloth is ₹ $63\frac{3}{4}$ . Find the cost of 1 meter of cloth

1. Irrational

2. Rational

3. Integer

4. Can't say

Q.

Verify each of the following :

(i) $(\frac{5}{7}\times \frac{12}{13})\times \frac{7}{18}=\frac{5}{7}\times (\frac{12}{13}\times \frac{7}{18})$
(ii) $\frac{-13}{24}\times (\frac{-12}{5}\times \frac{35}{36})=(\frac{-13}{24}\times \frac{-12}{5})\times \frac{35}{36}$
(iii) $(\frac{-9}{5}\times \frac{-10}{3})\times \frac{21}{-4}=\frac{-9}{5}\times (\frac{-10}{3}\times \frac{21}{-4})$

Q.

Assembler is used as a translator for?

1. C

2. COBOL

3. high level language

4. low level language

Q.

Simplify: $\left(\frac{32}{5}\right)+\left(\frac{23}{11}\right)\times \left(\frac{22}{15}\right)$

Q.

Rational numbers are closed under addition and multiplication but not under subtraction.

1. True
2. False

Q.

Name the property of multiplication illustrated by each of the following statements :

(i) $\frac{-15}{8}\times \frac{-12}{7}=\frac{-12}{7}\times \frac{-15}{8}$

(ii) $(\frac{-2}{3}\times \frac{7}{9})\times \frac{-9}{5}=\frac{-2}{3}\times (\frac{7}{9}\times \frac{-9}{5})$

(iii) $\frac{-3}{4}\times (\frac{-3}{4}\times \frac{-5}{6})+(\frac{-3}{4}\times \frac{7}{8})$

(iv) $\frac{-16}{9}\times 1=1\times \frac{-16}{9}=\frac{-16}{9}$

(v) $\frac{-11}{15}\times \frac{15}{-11}=\frac{15}{-11}\times \frac{-11}{15}=1$

(vi) $\frac{-7}{5}\times 0=0$

Q.

The sum of the series $\frac{1}{3\times 7}+\frac{1}{7\times 11}+\frac{1}{11\times 15}+........$ is

1. $\frac{1}{3}$

2. $\frac{1}{6}$

3. $\frac{1}{9}$

4. $\frac{1}{12}$

Q.

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 $z=\frac{1}{4}$.

Q.

Using appropriate properties find:

(i) $-\frac{2}{3}\times \frac{3}{5}+\frac{5}{2}-\frac{3}{5}\times \frac{1}{6}$

(ii) $\frac{2}{5}\times [-\frac{3}{7}]-\frac{1}{6}\times \frac{3}{2}+\frac{1}{14}\times \frac{2}{5}$

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.

$\frac{-3}{8}+\frac{1}{7}=\frac{1}{7}+\frac{-3}{8}$ is an example to show that

1. addition of rational numbers is commutative.

2. rational numbers are closed under addition.

3. addition of rational numbers is associative.

4. rational numbers are distributive under addition.

Q.

Verify the property : $x+y=y\times x$ by taking:

(i) $x=-\frac{1}{3},y=\frac{2}{7}$

(ii) $x=\frac{-3}{5},y=\frac{-11}{13}$

(iii) $x=2,y=\frac{7}{-8}$

(iv) $x=0,y=\frac{-15}{8}$

Q. Question 105(ii)
Verify the property x + y = y + x of rational number by taking
$x=\frac{-2}{3}$ and $y=\frac{-5}{6}$

Q.

Verify the following and also name the property: $\frac{3}{5}\times \left(\frac{\left(-4\right)}{7}\times \frac{(-8)}{9}\right)=\left(\frac{3}{5}\times \frac{(-4)}{7}\right)\times \left(\frac{-8}{9}\right)$

Q.

Simplify: $\left(\frac{3}{7}\right)+\left(\frac{-2}{21}\right)\times \left(\frac{-5}{6}\right)$

Q.

Solve: $8\frac{1}{2}-3\frac{5}{8}$

Q.

Fill in the blanks.

(i) $\left(\frac{-3}{17}\right)+\left(\frac{-12}{5}\right)=\left(\frac{-12}{5}\right)+(.....)$

(ii) $-9+\frac{-21}{8}=(......)+(-9)$

(iii) $(\frac{-8}{13}+\frac{3}{7})+\left(\frac{-13}{4}\right)=(......)+[\frac{3}{7}+(\frac{-13}{4}\left)\right]$

(iv) $-12+(\frac{7}{12}+\frac{-9}{11})=(-12+\frac{7}{12})+(.....)$

(v) $\frac{19}{-5}+(\frac{-3}{11}+\frac{-7}{8})=\{\frac{19}{-5}+(.....\left)\right\}+\frac{-7}{8}$

(vi) $\frac{-16}{7}+.....=......+\frac{-16}{7}=\frac{-16}{7}$

Q. Question 105(i)
Verify the property x + y = y + x of rational number by taking
$x=\frac{1}{2}$ and $y=\frac{1}{2}$

Q.

What should be subtracted from $\frac{-7}{9}$ to get $\frac{5}{6}$ ?

1. $\frac{-29}{18}$

2. $\frac{-26}{18}$

3. $\frac{-19}{18}$

4. $\frac{-13}{18}$

Q.

Sum of two rational numbers is not a rational number.

1. True

2. False

Q. a(b + c) = ab + ac is an example of ________ property.

1. closure
2. distributive
3. associative
4. commutative

Q.

What Does A Cross-Platform Language Mean?

Q.

Choose the rational numbers whose numerator is $(-5)\times 6$, and the denominator is $(34-23)\times (7-5)$.

1. $\frac{20}{11}$

2. $\frac{40}{22}$

3. $\frac{-15}{11}$

4. $\frac{-30}{22}$

Q. Is $\frac{8}{9}$ the multiplicative inverse of $-1\frac{1}{8}$? Why or why not?

Q. Verify the commutative property of multiplication $x\times y=y\times x$, for the following pairs of rational numbers:
[4 MARKS]

$i)x=\frac{-1}{5},y=\frac{2}{7}$ $ii)x=0,y=\frac{3}{4}$

Q.

$\text{For each pair of rational numbers, given below, verify that the multiplicatin is commutative :}\left(i\right)\frac{-1}{5}\text{and}\frac{2}{9}\left(ii\right)\frac{5}{-3}\text{and}\frac{13}{-11}\left(iii\right)3\text{and}\frac{-8}{9}\left(iv\right)0\text{and}\frac{-12}{17}$