Additive inverse of x - 1 x is

Additive inverse for a rational number is the same number with the opposite sign. Also, adding its additive inverse to a number results in zero. Additive inverse of a number is a number which when added to the given number gives zero. Let additive inverse of x - 1 x is f x . So, x - 1 x + f x = 0 ⇒ f x = 1 x - x Therefore, Additive inverse of x - 1 x is 1 x - x .

Find the product, using suitable property: 26 × ( - 48 ) + ( - 48 ) × ( - 36 )

The Distributive Property of Multiplication over Addition of Integers states that: For any three integers a , b and c , a × b + a × c = a × b + c Here, a = - 48 , b = 26 , c = - 36 ∴ 26 × ( - 48 ) + ( - 48 ) × ( - 36 ) = - 48 × 26 + ( - 36 ) = - 48 × ( - 10 ) = 480 Hence, the required product is 480 .

Find the missing entries in the following table: Fraction in standard form Numerator Denominator Sign of the rational number 1. - 3 × 3 8 × 3 -------- 24 --------- 2. 6 7 84 --------- Positive 3. --------- - 5 - 8 --------- 4. - 2 1 × - 2 7 1 × - 2 -------- - 142 Negative

- 9 , negative, 98 , positive, 42

-9, negative, 108, positive, 44

Find the value of the following: 81265 × 169 - 81265 × 69

Given, 81265 × 169 - 81265 × 69 We know that when a, b and c are whole numbers then by distributive property, a × b - c = a × b - a × c Here a = 81 , 265 ; b = 169 ; c = 69 81265 × 169 - 81265 × 69 = 81265 169 - 69 = 81265 × 100 Hence, 81265 × 169 - 81265 × 69 = 81 , 26 , 500 .

If a = − 8 , b = − 7 , c = 6 , verify that ( a + b ) + c = a + ( b + c ) .

Given, a = − 8 , b = − 7 , c = 6 , To verify that ( a + b ) + c = a + ( b + c ) . Consider LHS, ( a + b ) + c Now, put the values, we get: = ( − 8 + ( − 7 ) ) + 6 = − 15 + 6 = − 9 Similarly, Consider RHS: a + ( b + c ) Now, put the values, we get: = − 8 + ( − 7 + 6 ) = − 8 + ( − 1 ) = − 9 Therefore, LHS = - 9 = RHS Hence, verified. This also satisfies the property of associativity of addition.

Verify: 18 × [ 7 + ( - 3 ) ] = [ 18 × 7 ] + 18 × - 3

Given statement is : 18 × [ 7 + ( - 3 ) ] = [ 18 × 7 ] + [ 18 × ( - 3 ) ] Simplifying the LHS: 18 × [ 7 + ( - 3 ) ] = 18 × 4 = 72 Simplifying the RHS: [ 18 × 7 ] + [ 18 × ( - 3 ) ] = 126 + ( - 54 ) = 72 Since, L H S = R H S . Hence, the given statement is verified.

Write five pairs of integers ( a , b ) such that a ÷ b = - 3 . One such pair is ( 6 , - 2 ) because 6 ÷ ( - 2 ) = ( - 3 ) .

Five pairs of integers ( a , b ) such that a ÷ b = - 3 can be: (i) - 9 , 3 because - 9 ÷ 3 = - 3 (ii) 12 , - 4 because 12 ÷ - 4 = - 3 (iii) - 21 , 7 because - 21 ÷ 7 = - 3 (iv) 3 , - 1 because 3 ÷ - 1 = - 3 (v) - 15 , 5 because - 15 ÷ 5 = - 3

Find the following products: 9 × ( - 3 ) × ( - 6 )

Given: 9 × ( - 3 ) × ( - 6 ) We know that, The product of two integers of opposite signs is equal to the additive inverse of the product of their absolute values. The product of two integers with like signs is equal to the product of their absolute values. So, 9 × ( 3 ) = - 27 Therefore, - 27 × ( - 6 ) = + 162 Therefore, 9 × ( - 3 ) × ( - 6 ) = 162

Complete the following multiplication table: × - 3 - 2 - 1 0 1 2 3 - 3 - 2 - 1 0 1 2 3

Using the rule for multiplcation of integers, we get The multiplication table is as follows × - 3 - 2 - 1 0 1 2 3 - 3 9 6 3 0 - 3 - 6 - 9 - 2 6 4 2 0 - 2 - 4 - 6 - 1 3 2 1 0 - 1 - 2 - 3 0 0 0 0 0 0 0 0 1 - 3 - 2 - 1 0 1 2 3 2 - 6 - 4 - 2 0 2 4 6 3 - 9 - 6 - 3 0 3 6 9 When a positive number is multiplied with negative number then the result is also negative number.When a negative number is multiplied with another negative number then the product is positive

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Prove that subtraction of integers is not associative.

Important Questions on Number System

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Mathematics>Arithmetic>Number System>Algebraic Operations on Integers

Solve the following by using 'Sutra Paravartya'.

$14885 \div 123$

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Mathematics>Arithmetic>Number System>Algebraic Operations on Integers

Additive inverse of $x - \frac{1}{x}$ is

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Mathematics>Arithmetic>Number System>Algebraic Operations on Integers

$\{(- 5) \times 3\} \times (- 6) =$ (_____) $\times \{3 \times (- 6)\}$

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Mathematics>Arithmetic>Number System>Algebraic Operations on Integers

Find the product, using suitable property: $26 \times (- 48) + (- 48) \times (- 36)$

EASY

Mathematics>Arithmetic>Number System>Algebraic Operations on Integers

Find the missing entries in the following table:

Fraction in standard form	Numerator	Denominator	Sign of the rational number
1. $\frac{- 3 \times 3}{8 \times 3}$	--------	$24$	---------
2. $\frac{6}{7}$	$84$	---------	Positive
3. ---------	$- 5$	$- 8$	---------
4. $\frac{- 21 \times - 2}{71 \times - 2}$	--------	$- 142$	Negative