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7 1/3 -2 1/4+(4 1/3)-(2 1/5 - 3/4)

Answers (1)

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We are asked to evaluate:

$7 \tfrac{1}{3} - 2 \tfrac{1}{4} + \left(4 \tfrac{1}{3}\right) - \left(2 \tfrac{1}{5} - \tfrac{3}{4}\right)$

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Step 1: Convert mixed fractions to improper fractions  

$7 \tfrac{1}{3} = \dfrac{22}{3}, \quad 2 \tfrac{1}{4} = \dfrac{9}{4}, \quad 4 \tfrac{1}{3} = \dfrac{13}{3}, \quad 2 \tfrac{1}{5} = \dfrac{11}{5}, \quad \tfrac{3}{4} = \dfrac{3}{4}$  

So expression becomes:  

$\dfrac{22}{3} - \dfrac{9}{4} + \dfrac{13}{3} - \left(\dfrac{11}{5} - \dfrac{3}{4}\right)$

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Step 2: Simplify inside brackets  

$\dfrac{11}{5} - \dfrac{3}{4} = \dfrac{44}{20} - \dfrac{15}{20} = \dfrac{29}{20}$  

So expression becomes:  

$\dfrac{22}{3} - \dfrac{9}{4} + \dfrac{13}{3} - \dfrac{29}{20}$

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Step 3: Combine terms with denominator 3  

$\dfrac{22}{3} + \dfrac{13}{3} = \dfrac{35}{3}$  

So we have:  

$\dfrac{35}{3} - \dfrac{9}{4} - \dfrac{29}{20}$

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Step 4: Take common denominator  

$\dfrac{35}{3} = \dfrac{700}{60}, \quad \dfrac{9}{4} = \dfrac{135}{60}, \quad \dfrac{29}{20} = \dfrac{87}{60}$  

So:  

$\dfrac{700}{60} - \dfrac{135}{60} - \dfrac{87}{60} = \dfrac{700 - 135 - 87}{60}$  

$= \dfrac{478}{60}$

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Step 5: Simplify fraction  

$\dfrac{478}{60} = \dfrac{239}{30}$

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Step 6: Convert to mixed fraction  

$\dfrac{239}{30} = 7 \tfrac{29}{30}$

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Final Answer:  

$\boxed{7 \tfrac{29}{30}}$
 

Posted by

Saumya Singh

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