Question

Which is the best estimate for …14 1/5 - 2 5/6 A) I0B) 11 C) 12 D) 13

Answer 1

To get the best estimate, let's perform subtraction of the fractions

`\begin{gathered} 14(1)/(5)-2(5)/(6) \\ \end{gathered}`

First, let us change the mixed fractions to improper fractions, we have

`\begin{gathered} \text{Now, }14(1)/(5),\text{ we say 5}*14\text{ = 70, 71 + 1 = 71,} \\ \text{this becomes } \\ (71)/(5) \\ \text{Now, 2}(5)/(6),\text{ we say 6}*2\text{ = 12, 12 + 5 = 17,} \\ \text{this becomes } \\ (17)/(6) \end{gathered}`

Subtracting the improper fractions we have

`\begin{gathered} (71)/(5)-(17)/(6) \\ Now\text{ multiply the denominators} \\ 5*6=30,\text{ this becomes the least common multiple } \\ \text{place the 30 as the common denominator } \\ (\square)/(30) \\ \text{cross multiply and place the result as the numera}tor\text{ } \\ 71*6=426 \\ 17*5=85 \\ we\text{ have } \\ (426-85)/(30) \\ =(341)/(30) \end{gathered}`

Breaking the fraction we have

`\begin{gathered} (341)/(30) \\ =11(11)/(30) \end{gathered}`

Looking at the options, the closest to this is 11, option B