Question

Find the mixed number halfway between 6.4 and 6and 1/3. Give
your answer in its simplest form.

Answer 1

The mixed number halfway between 6.4 and 6 and 1/3 is 6 and 3/10 in its simplest form.

Step-by-step explanation:

To find the mixed number halfway between 6.4 (which is 6 and 2/5 in mixed number form) and 6 and 1/3, we first convert both numbers to improper fractions with a common denominator. In this case, the common denominator is 15. Therefore, 6 and 2/5 becomes 97/15 (because 6*15 + 2*3 = 90 + 7 = 97), and 6 and 1/3 becomes 95/15 (because 6*15 + 1*5 = 90 + 5 = 95).

To find the number halfway between these two fractions, we take the average by adding them together and dividing by 2, which gives us (97/15 + 95/15) / 2 = 192/30 / 2 = 96/30, which simplifies to 3 and 3/10 or 3.2 as a mixed number. Thus, 6 and 3/10 is the mixed number halfway between 6.4 and 6 and 1/3.

Answer 2

`6(1)/(3)\rule[0.35em]{10em}{0.25pt}M\rule[0.35em]{10em}{0.25pt}6.4`

so, let's find their difference, take half of it and give it to 6⅓.

`\stackrel{mixed}{6(1)/(3)}\implies \cfrac{6\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{19}{3}} ~\hfill 6.4\implies \cfrac{64}{10}\implies \cfrac{32}{5} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{32}{5}~~ - ~~\cfrac{19}{3}\implies \cfrac{(3)32~~ - ~~5(19)}{\underset{\textit{using this LCD}}{15}}\implies \cfrac{96-95}{15}\implies \cfrac{1}{15}`

`\stackrel{\textit{now let's take half of that}}{\cfrac{1}{15}/ 2\implies \cfrac{1}{15}/ \cfrac{2}{1}}\implies \cfrac{1}{15}\cdot \cfrac{1}{2}\implies \cfrac{1}{30} \\\\\\ \stackrel{\textit{now let's add it to }6(1)/(3)}{\cfrac{19}{3}+\cfrac{1}{30}}\implies \cfrac{10(19)~~ + ~~(1)1}{\underset{\textit{using this LCD}}{30}}\implies \cfrac{191}{30}\implies {\Large \begin{array}{llll} 6(11)/(30) =M\end{array}}`