Commutative Property

Q. The numerical expression $(\frac{3}{8}-\frac{5}{7})$ equal to $-\frac{19}{56}$ states that:

1. rational numbers are not closed under subtraction
2. subtraction of rational numbers is not commutative.
3. rational numbers are closed under subtraction
4. subtraction of rational numbers is commutative

Q.

Solve using appropriate proper properties.

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

Q.

Prove that multiplication is commutative for rational numbers.

Q. The commutative property for rational numbers does not hold for which of the following mathematical operations?

1. Subtraction and division.
2. Addition and subtraction.
3. Multiplication and addition.
4. Division and multiplication.

Q. The order in which we add rational numbers does not affect its sum. This is known as property.

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

Q. Commutative law of addition is

1. $a+b=b-a$
2. $a+b=b+a$
3. $ab=ba$
4. $a-b=b+a$

Q. The ____ property states that we can add rational numbers in any order and this does not affect the result of addition.

1. commutative
2. associative
3. additive inverse
4. multiplicative inverse

Q.

State whether true or false
Division of whole numbers follows the commutative law.

1. True

2. False

Q.

Addition of whole number follows commutative law.

1. True

2. False

Q. Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers:

(v) $4\text{and}\frac{-3}{5}$

Q.

Question 31

In the given question, fill in the blanks to make the statement true.

If A x 3 = 1A, then A = ___.

Q.

Which of the following holds true?

1. $\frac{3}{5}$ $÷$ $\frac{7}{5}$ = $\frac{7}{5}$ $÷$$\frac{3}{5}$

2. $\frac{3}{5}$ + $\frac{7}{5}$ = $\frac{7}{5}$ + $\frac{3}{5}$

3. $\frac{3}{5}$ - $\frac{7}{5}$ = $\frac{7}{5}$ - $\frac{3}{5}$

4. $\frac{3}{5}$ - $\frac{7}{5}$ = $\frac{7}{5}$ $÷$ $\frac{3}{5}$

Q. Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers:

(iv) $\frac{2}{-7}\text{and}\frac{12}{-35}$

Q. Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers:

(iii) $\frac{-3}{5}\text{and}\frac{-2}{-15}$

Q. Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers:

(i) $\frac{-11}{5}\text{and}\frac{4}{7}$

Q. of whole numbers does not follow the commutative law.

1. Division
2. Addition
3. Subtraction
4. Multiplication

Q.

Commutative law of rational numbers is ____ .

1. applicable to addition and multiplication

2. applicable to addition only

3. applicable to addition and division

4. applicable to division only

Q.

Which of the following shows the commutative property of multiplication?

1. $4\times 4=4+4+4$

2. $9\times 5-7\times 5=(9-7)\times 5$

3. $9\times 1=9$

4. $23\times 4=4\times 23$

Q.

Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers:​

vi. $-4\text{and}\frac{4}{-7}$

Q. Find $\frac{3}{7}+\left(\frac{-6}{11}\right)+\left(\frac{-8}{21}\right)+\left(\frac{5}{22}\right)$.

Q.

The ___ property states that we can add rational numbers in any order.

Q. What should be multiplied $156\times$_____ to get $0$?

1. $156$
2. $1$
3. $-1$
4. $0$

Q. The multiple inverse of $\frac{3}{4}+(\frac{5}{4}+\frac{1}{2})$ is .

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

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.

Evaluate the following :
1. -5/18 - 7/24 + 5/12.
2. -5/36 + 3/8 - -2/9.

Q. Correct matching of the statements with the property illustrated are -

1. $(7+3)+6=(3+7)+6$ : Commutative property of multiplication
2. $(2+9)+4=2+(9+4)$ : Commutative property of addition
3. $(2+9)+4=2+(9+4)$ : Associative property of addition
4. $0.3+(-0.3)=0$ : Inverse (opposite) property for addition

Q. Given here is an algorithm to swap two numbers. Which of the following line will replace'?" to complete the algorithm?
Step 1: Read two numbers $X$ and $Y$.
Step 2: ?
Step 3: $Y=X-Y$
Step 4: $X=X-Y$

1. $X=X+Y$
2. $X=X\times Y$
3. $X=\frac{X}{Y}$
4. $X=X-Y$

Q. Which among the following represents the commutative property under multiplication?

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

Q. Verify commutativity of addition of rational numbers for each of the following pairs of rational numbers:

(ii) $\frac{4}{9}\text{and}\frac{7}{-12}$

Q.

Fill in the blanks to make each of the following a true statement :

$458\times 85=\_\_\_\_\_\_\_\_\times 458$