Question

Questions

Find, the answer whether the given numbers are equal :

$\frac{3}{7} \frac{ - 3 }{7}$
1.

2.
$\frac{5}{9 } \frac{100}{180}$

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Answer 1

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$\star\textsf{We are provided with numbers}$

$\sf{1. \dfrac{3}{7} \:and\: \dfrac{-3}{7} }$

Now we have to say wether these two numbers are equal or not .

Let the numbers be equal

$\sf{\dfrac{3}{7} =\dfrac{-3}{7}}$

So as denominators are equal hence we can cancel it out

$\sf{\dfrac{3}{\cancel{7}} = \dfrac{-3}{\cancel{7}}}$

$\sf{ 3 = -3 }$

But as we know

$\mathsf{ 3 \neq -3 }$

So we have got a contradiction

So the we came to say that

$\mathsf{ \dfrac{3}{7} \neq \dfrac{-3}{7}}$

Or $\sf{\dfrac{3}{7} \: and \: \dfrac{-3}{7}}$ are not equal.

$\sf{ 2. \dfrac{5}{9}\: and\: \dfrac{100}{180} }$

$\sf{ By \:reducing\: \dfrac{100}{180} \:into\: standard\: form}$

$\sf{= \dfrac{100}{180}}$

$\sf{=\dfrac{10\cancel{0}}{18\cancel{0}}}$

$\sf{=\dfrac{5 \times 2}{9 \times 2}}$

$\sf{=\dfrac{5 \times\cancel{2}}{9 \times\cancel{2}}}$

So via comparing both numbers

$\sf{\dfrac{5}{9} = \dfrac{5}{9}}$

Or

$\sf{\dfrac{5}{9} = \dfrac{100}{180} }$

So both numbers are equal.

Answer 2

Answer:

1.)

Whether 3/7 and -3/7 are equal or not.

Putting them equal to each other we get ;

3/7 = (-3)/7

By cross multiplication :

21 = -21

Which isn't equal for sure!

Therefore, 3/7 and (-3)/7 are not equal.

2.)

5/9 and 100/180

Again, putting no. as equal ;

5/9 = 100/180

By cross multiplication ;

180×5 = 9×100

900 = 900

Thus, These no. are equal!