Question

Multiple 7/9 to the sum of 8 3/7 and 5 11/14

Answer 1

`(7)/(9) * (8 (3)/(7) + 5 (11)/(14)) = \\`

`(7)/(9) * (8 (6)/(14) + 5 (11)/(14) ) = \\`

`(7)/(9) * (13 (6 + 11)/(14)) = \\`

`(7)/(9) * (13 (17)/(14)) = \\`

`(7)/(9) * (14 (3)/(14)) = \\`

`(7)/(9) * ( (14 * 3 + 3)/(14)) = \\`

`(7)/(9) * ( (42 + 3)/(14)) = \\`

`(7)/(9) * ( (45)/(14)) = (7 * 45)/(9 * 14) = (5)/(2) \\`

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And we're done.

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Answer 2

`\displaystyle (199)/(18)`

Explanation:

Fraction Operations

Before attempting to operate with the given fractions, we need to express all of them in the form a/b, because the last 2 fractions are in mixed form.

`\displaystyle 8(3)/(7)=8+(3)/(7)=(8*7+3)/(7)=(59)/(7)`

`\displaystyle 5(11)/(14)=5+(11)/(14)=(5*14+11)/(14)=(81)/(14)`

Now for the sum of the last two fractions:

`\displaystyle (59)/(7)+(81)/(14)`

Make both denominators equal by multiplying by 2 both parts of the first fraction:

`\displaystyle (59)/(7)+(81)/(14)=(118)/(14)+(81)/(14)`

`\displaystyle =(118+81)/(14)=(199)/(14)`

Now multiply by 7/9:

`\displaystyle (199)/(14)*(7)/(9)=(199)/(18)`