Question

write a pair of fractions whose sum is 13/ 7​

Answer 1

Answer:

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Answer 2

ǫᴜᴇsᴛɪᴏɴ →

write a pair of fractions whose sum iis

$\longmapsto\tt{\dfrac{13}{17}}$

ᴀɴsᴡᴇʀ →

Let the fractions be a and b.

$\longmapsto\tt{a + b =\dfrac{13}{17}}$

or

$\longmapsto\tt{17a + 17b = 13 …(1)}$

$\longmapsto\tt{a - b=\dfrac{2}{5}}$

or

$\longmapsto\tt{5a - 5b = 2 …(2)}$

Multiply (1) by 5 to get

$\longmapsto\tt{85a + 85b = 65 …(1a)}$

Multiply (2) by 17 to get

$\longmapsto\tt{85a - 85b = 34 …(2a)}$

Add (1a) and (2a) to get

$\longmapsto\tt{170a = 65+34 = 99,}$

or

$\longmapsto\tt{a=\dfrac{99}{170}}$

We have

$\longmapsto\tt{a + b=\dfrac{13}{17}}$

so

$\longmapsto\tt{b=(\dfrac{13}{17}) - a = (\dfrac{13}{17}) - (\dfrac{99}{170})}$

$\longmapsto\tt{(\dfrac{130}{170}) - (\dfrac{99}{170})}$

$\longmapsto\tt{\dfrac{31}{170}}$

So the two fractions are (99/170) and (31/170). Answer