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Simplify................................................
[tex] \displaystyle{5 \frac{1}{6} + 2 \frac{1}{3} - 5 \frac{11}{12} }[/tex]
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Sagot :

Athena8213

Answer:

see below:-

Step-by-step explanation:

Given,

[tex] \displaystyle{5 \frac{1}{6} + 2 \frac{1}{3} - 5 \frac{11}{12} }[/tex]

  • Convert the mixed fractions into improper fractions.

[tex] \displaystyle{ \frac{31}{6} + \frac{7}{3} \ - \frac{71}{12} }[/tex]

  • Take LCM of the denominators:-

LCM of 6,3 and 12=3×2×1×1×2=12

[tex] \therefore{\displaystyle{ \frac{31}{6} + \frac{7}{3} - \frac{71}{12} = \frac{31 \times 2 + 7 \times 4 - 71 \times 1}{12} }}[/tex]

[tex] = \displaystyle{ \frac{62 + 28 - 71}{12} }[/tex]

[tex]\displaystyle{ = \frac{90 - 71}{12} }[/tex]

[tex]\displaystyle{ = \frac{19}{12} }[/tex]

  • Convert the improper fractions into mixed fraction:-

[tex]\displaystyle{1 \frac{7}{12} }[/tex]

ⲊⲧɑⲅⲊⲏɑᴅⲟᏇ

Ⲁⲛ⳽ⲱⲉⲅ :

[tex] \quad\hookrightarrow\quad \sf {\dfrac{19}{12}\: or \: 1\dfrac{7}{12} }[/tex]

Ⲋⲟⳑⳙⲧⳕⲟⲛ :

We will solve the given mixed fraction in 2 steps :

  • Converting into improper fraction

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

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

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

[tex] \implies\quad \tt { \dfrac{31}{6}+\dfrac{7}{3}-\dfrac{71}{12}}[/tex]

  • Taking L.C.M

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

[tex] \implies\quad \tt { \dfrac{62+28-71}{12}}[/tex]

[tex] \implies\quad \tt { \dfrac{90-71}{12}}[/tex]

[tex] \implies\quad \tt {\dfrac{19}{12} }[/tex]

[tex] \implies\quad\underline{\underline {\pmb{\tt {1\dfrac{7}{12} }}}}[/tex]

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