Question

Subtract, write your answer as a mixed number in simplest form 6 1/6 - 3 1/4

Answer 1

$\large\begin{array}{l} \mathsf{6\,\dfrac{1}{6}-3\,\dfrac{1}{4}}\\\\ =\mathsf{\left(6+\dfrac{1}{6}\right)-\left(3+\dfrac{1}{4}\right)}\\\\ =\mathsf{\left(\dfrac{6\cdot 6}{6}+\dfrac{1}{6}\right)-\left(\dfrac{4\cdot 3}{4}+\dfrac{1}{4}\right)}\\\\ =\mathsf{\left(\dfrac{36}{6}+\dfrac{1}{6}\right)-\left(\dfrac{12}{4}+\dfrac{1}{4}\right)}\\\\ =\mathsf{\dfrac{36+1}{6}-\dfrac{12+1}{4}} \end{array}$

$\large\begin{array}{l} =\mathsf{\dfrac{37}{6}-\dfrac{13}{4}\qquad(i)} \end{array}$


$\large\begin{array}{l} \textsf{The LCM of 6 and 4 is 12. Now rewrite those fractions}\\\textsf{properly, so that its denominators are the same:}\\\\ =\mathsf{\dfrac{37}{6}\cdot\dfrac{2}{2}-\dfrac{13}{4}\cdot \dfrac{3}{3}}\\\\ =\mathsf{\dfrac{37\cdot 2}{6\cdot 2}-\dfrac{13\cdot 3}{4\cdot 3}}\\\\ =\mathsf{\dfrac{74}{12}-\dfrac{39}{12}}\\\\ =\mathsf{\dfrac{74-39}{12}}\\\\ =\mathsf{\dfrac{35}{12}} \end{array}$


$\large\begin{array}{l} \textsf{Writing the result in the mixed form:}\\\\ =\mathsf{\dfrac{24+11}{12}}\\\\ =\mathsf{\dfrac{24}{12}+\dfrac{11}{12}}\\\\ =\mathsf{\dfrac{2\cdot \diagup\!\!\!\!\! 12}{\diagup\!\!\!\!\! 12}+\dfrac{11}{12}}\\\\ =\mathsf{2+\dfrac{11}{12}}\\\\ =\mathsf{2\,\dfrac{11}{12}}\qquad\quad\checkmark \end{array}$


$\large\textsf{which already is in its simplest form.}$


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$\large\textsf{I hope it helps. :-)}$


Tags: fraction mixed form subtract rational arithmetic

Answer 2

The answer is 35/12 and simplify that and u get 2 11/12.

To show my work apparently since the mods wont stop deleting my answers, here.

 I first found a common denominator and use it to rewrite each fraction. Then I, subtracted the whole numbers and fractions separately.