[tex]14 \times \frac{3}{8} + 7 \times \frac{5}{6} + 2 \times \frac{5}{12} [/tex]

[tex]
14 \times \frac{3}{8} + 7 \times \frac{5}{6} + 2 \times \frac{5}{12} \\\\=7\times\dfrac{3}{4}+\dfrac{35}{6}+\dfrac{5}{6}=\dfrac{21}{4}+\dfrac{40}{6}=\dfrac{21\cdot3}{4\cdot3}+\dfrac{40\cdot2}{6\cdot2}=\dfrac{63}{12}+\dfrac{80}{12}\\\\=\dfrac{143}{12}=11\dfrac{11}{12} [/tex]

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GoddessofDork GoddessofDork · Answer 2 · 2018-08-12T22:02:29+02:00

So firstly, do the multiplications: [tex] \frac{42}{8}+\frac{35}{6}+\frac{10}{12} [/tex]

Next, we want to find the LCM, or lowest common multiple, between the 3 denominators. In this case, it is 24. Multiply 42/8 by 3/3, 35/6 by 4/4, and 10/12 by 2/2:

[tex] \frac{42}{8}*\frac{3}{3}=\frac{126}{24}\\ \\ \frac{35}{6}*\frac{4}{4}=\frac{140}{24}\\ \\ \frac{10}{12}*\frac{2}{2}=\frac{20}{24}\\ \\ \frac{126}{24}+\frac{140}{24}+\frac{20}{24} [/tex]

Now add up all the numerators together to get 286/24, which can be simplified to 143/12 when divided by 2 on the numerator and denominator.

In short, 143/12 is the answer.