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Setler [38]
2 years ago
15

Simplify................................................

Mathematics
2 answers:
ivolga24 [154]2 years ago
6 0
<h3><u>Ⲁⲛ⳽ⲱⲉⲅ</u><u> </u><u>:</u></h3>

\quad\hookrightarrow\quad \sf {\dfrac{19}{12}\: or \: 1\dfrac{7}{12} }

<h3><u>Ⲋⲟⳑⳙⲧⳕⲟⲛ :</u></h3>

We will solve the given mixed fraction in 2 steps :

  • <u>Converting</u><u> </u><u>into </u><u>improper</u><u> </u><u>fraction</u>

\implies\quad \tt {5\dfrac{1}{6}+2\dfrac{1}{3}-5\dfrac{11}{12} }

\implies\quad \tt { \dfrac{(6\times 5)+1}{6}+\dfrac{(3\times 2)+1}{3}-\dfrac{(12\times 5)+11}{12}}

\implies\quad \tt { \dfrac{30+1}{6}+\dfrac{6+1}{3}-\dfrac{60+11}{12}}

\implies\quad \tt { \dfrac{31}{6}+\dfrac{7}{3}-\dfrac{71}{12}}

  • <u>Taking</u><u> </u><u>L.C.M</u>

\implies\quad \tt { \dfrac{(2\times31)+(4\times 7)-(1\times 71)}{12} }

\implies\quad \tt { \dfrac{62+28-71}{12}}

\implies\quad \tt { \dfrac{90-71}{12}}

\implies\quad \tt {\dfrac{19}{12} }

\implies\quad\underline{\underline {\pmb{\tt {1\dfrac{7}{12} }}}}

ololo11 [35]2 years ago
5 0

Answer:

<em><u>see</u></em><em><u> </u></em><em><u>below</u></em><em><u>:</u></em><em><u>-</u></em>

Step-by-step explanation:

Given,

\displaystyle{5 \frac{1}{6} + 2 \frac{1}{3} - 5 \frac{11}{12} }

  • <em><u>Convert</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>mixed</u></em><em><u> </u></em><em><u>fractions</u></em><em><u> </u></em><em><u>into</u></em><em><u> </u></em><em><u>improper</u></em><em><u> </u></em><em><u>fractions.</u></em>

\displaystyle{ \frac{31}{6}  +  \frac{7}{3}  \ -  \frac{71}{12} }

  • <em><u>Take</u></em><em><u> </u></em><em><u>LCM</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>denominators</u></em><em><u>:</u></em><em><u>-</u></em>
<h3><em><u>LCM</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>6</u></em><em><u>,</u></em><em><u>3</u></em><em><u> </u></em><em><u>and</u></em><em><u> </u></em><em><u>1</u></em><em><u>2</u></em><em><u>=</u></em><em><u>3</u></em><em><u>×</u></em><em><u>2</u></em><em><u>×</u></em><em><u>1</u></em><em><u>×</u></em><em><u>1</u></em><em><u>×</u></em><em><u>2</u></em><em><u>=</u></em><em><u>1</u></em><em><u>2</u></em></h3>

<em><u>\therefore{\displaystyle{ \frac{31}{6}  +  \frac{7}{3} -  \frac{71}{12}   =  \frac{31 \times 2 + 7 \times 4 - 71 \times 1}{12} }}</u></em>

<em><u>= \displaystyle{ \frac{62 + 28 - 71}{12} }</u></em>

<em><u>\displaystyle{ =  \frac{90 - 71}{12} }</u></em>

<em><u>\displaystyle{ =  \frac{19}{12} }</u></em>

  • <em><u>Convert</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>improper</u></em><em><u> </u></em><em><u>fractions</u></em><em><u> </u></em><em><u>into</u></em><em><u> </u></em><em><u>mixed</u></em><em><u> </u></em><em><u>fraction</u></em><em><u>:</u></em><em><u>-</u></em>

<em><u>\displaystyle{1 \frac{7}{12} }</u></em>

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