Question

Find 3/7 plus 6/-11 plus -8/21 plus 5/22

Answer 1

To find the sum of fractions, we need to have a common denominator. In this case, the common denominator is 7 * (-11) * 21 * 22 = -230,514.

Now we can add the fractions:

`\displaystyle (3)/(7) + (6)/(-11) + (-8)/(21) + (5)/(22) = (3 \cdot (-11) \cdot 21 \cdot 22)/(7 \cdot (-11) \cdot 21 \cdot 22) + (6 \cdot 7 \cdot (-21) \cdot 22)/(-11 \cdot 7 \cdot (-21) \cdot 22) + (-8 \cdot 7 \cdot (-11) \cdot 22)/(21 \cdot 7 \cdot (-11) \cdot 22) + (5 \cdot 7 \cdot (-11) \cdot 21)/(22 \cdot 7 \cdot (-11) \cdot 21)`

Simplifying the fractions:

`\displaystyle (-1386)/(-230514) + (1848)/(-230514) + (-1936)/(-230514) + (1155)/(-230514)`

Combining the fractions:

`\displaystyle (-1386 + 1848 - 1936 + 1155)/(-230514)`

Simplifying the numerator:

`\displaystyle (-319)/(-230514)`

Dividing the numerator and denominator:

`\displaystyle (319)/(230514)`

Therefore, the sum of the fractions 3/7, 6/-11, -8/21, and 5/22 is 319/230514.

`\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}`

♥️
`\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}`