Firstly we need to convert the denominators to positive numbers.
\(\dfrac{ 2}{-7} =\dfrac{ (2 × -1)}{ (-7 × -1)} = \dfrac{ 2}{-7}\)
\(\dfrac{ 12}{-35} = \dfrac{(12 × -1)}{ (-35 × -1) }= \dfrac{ -12}{35}\)
By using the commutativity law, the addition of rational numbers is commutative.
\(\dfrac{ a}{b} + \dfrac{c}{d} =\dfrac{c}{d} + \dfrac{ a}{b}\)
In order to verify the above property let us consider the given fraction
\(\dfrac{ -2}{7} and -\dfrac{12}{35}\) as
\( \dfrac{ -2}{7} + -\dfrac{12}{35}\)and \(\dfrac{-12}{35}+ \dfrac{ -2}{7} \)
The denominators are 7 and 35
By taking LCM for 7 and 35 is 35
We rewrite the given fraction in order to get the same denominator
Now, \( \dfrac{ -2}{7} = \dfrac{(-2 × 5) }{ (7 ×5) }= \dfrac{-10}{35}\)
\(\dfrac{ -12}{35} = \dfrac{(-12 ×1) } {(35 ×1) }= \dfrac{ -12}{35} \)
Since the denominators are same we can add them directly
\(\dfrac{ -10}{35} +\dfrac{ (-12)}{35} = \dfrac{(-10 + (-12))}{35 }\)
\( = \dfrac{(-10-12)}{35} = \dfrac{-22}{35}\)
\( \dfrac{-12}{35 }+ \dfrac{-2}{7}\)
The denominators are 35 and 7
By taking LCM for 35 and 7 is 35
We rewrite the given fraction in order to get the same denominator
Now, \(\dfrac{ -12}{35} =\dfrac{ (-12 ×1) }{ (35 ×1)} = \dfrac{-12}{35}\)
\(\dfrac{ -2}{7} =\dfrac{ (-2 × 5) }{ (7 ×5)} = \dfrac{-10}{35}\)
Since the denominators are same we can add them directly
\( \dfrac{-12}{35} + \dfrac{-10}{35} = \dfrac{(-12 + (-10))}{35} \)
\( = \dfrac{(-12-10)}{35} = \dfrac{-22}{35}\)
\(\dfrac{ -2}{7} +\dfrac{ -12}{35} = \dfrac{-12}{35} +\dfrac{ -2}{7}\) is satisfied.
Answered by Sakshi | 1 year agoBy what number should 1365 be divided to get 31 as quotient and 32 as remainder?
Which of the following statement is true / false?
(i) \(\dfrac{ 2 }{ 3} – \dfrac{4 }{ 5}\) is not a rational number.
(ii) \( \dfrac{ -5 }{ 7}\) is the additive inverse of \( \dfrac{ 5 }{ 7}\)
(iii) 0 is the additive inverse of its own.
(iv) Commutative property holds for subtraction of rational numbers.
(v) Associative property does not hold for subtraction of rational numbers.
(vi) 0 is the identity element for subtraction of rational numbers.
If x = \( \dfrac{4 }{ 9}\), y =\( \dfrac{-7 }{ 12}\) and z = \( \dfrac{-2 }{ 3}\), then verify that x – (y – z) ≠ (x – y) – z
If x = \(\dfrac{ – 4 }{ 7}\) and y = \( \dfrac{2 }{ 5}\), then verify that x – y ≠ y – x
Subtract the sum of \(\dfrac{ – 5 }{ 7} and\dfrac{ – 8 }{ 3}\) from the sum of \(\dfrac{5 }{ 2} and \dfrac{– 11 }{ 12}\)