Question

Divide the sum of 25/9 and 4/9 by their differences

Answer 1

Answer :-

• The required fraction is 29/21.

What to do?

• Divide the sum of 25/9 and 4/9 by their difference.

Step-by-step explanation :-

• Here, we are asked to divide the sum of 25/9 and 4/9 by their differences. For this, we will first find out the sum of 25/9 and 4/9. Then we will find out the difference of 25/9 and 4/9. Finally, we will divide their sum by their difference.

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Finding the sum of 25/9 and 4/9 :-

$\longmapsto\tt \dfrac{25}{9} + \dfrac{4}{9}$

Here, the denominator of both the fractions are same, so we will add them just like normal numbers and give them the denominator 9.

$\longmapsto\tt \dfrac{25 + 4}{9}$

Adding 4 to 25,

$\longmapsto\underline{\boxed{\tt\dfrac{29}{9}}}$

Finding the difference of 25/9 and 4/9 :-

$\longmapsto\tt\dfrac{25}{9} - \dfrac{4}{9}$

Here, the denominator of both the fractions are same, so we will subtract them just like normal numbers and give them the denominator 9.

$\longmapsto \tt\dfrac{25 - 4}{9}$

Subtracting 4 from 25,

$\longmapsto\underline{\boxed{\tt\dfrac{21}{9}}}$

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Dividing the sum of 25/9 and 4/9 by their difference :-

Now, we have :-

• The sum of 25/9 and 4/9 is 29/9.
• The difference of 25/9 and 4/9 is 21/9.

So let's divide them now!

$\tt \dfrac{29}{9} \div \dfrac{21}{9}$

We know that, to divide two fractions, we multiply the fraction on the LHS by the reciprocal of the fraction on the RHS.

Here,

• Fraction on the RHS = 21/9.
• It's reciprocal is 9/21.

Therefore, we will multiply 29/9 and 9/21 now.

$\longmapsto\rm \dfrac{29}{ \not9} \times \dfrac{ \not9}{21}$

Reducing the numbers,

$\longmapsto\rm \dfrac{29}{1} \times \dfrac{1}{21}$

Now let's multiply the remaining numbers since we can't reduce them anymore.

$\longmapsto\rm \dfrac{29 \times 1}{1 \times 21}$

Multiplying the numbers,

$\longmapsto\rm\dfrac{29}{21}$

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$\underline{\overline{\boxed{\rm Hence, \: the \: required \: \: fraction \: is \: \dfrac{29}{21}}}}$

Answer 2

Sum of the given fractions
25/9 + 4/9
=29/9
Difference between the two fractions
25/9 - 4/9
=21/9
=7/3
Now, according to the question

29/9
————
7/3

= 29/9 X 3/7
=29/21