Question

9/4-[19/4-{2/1+(10/3÷5/3*5/4-4/1)}]​

Answer 1

Answer :-

• The answer is -2.

Step-by-step explanation :-

$\sf \dfrac{9}{4} - \left[\dfrac{19}{4} - \left\{\dfrac{2}{1} + \left(\dfrac{10}{3} \div \dfrac{5}{3} \times \dfrac{5}{4} - \dfrac{4}{1} \right)\right\}\right]$

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Let's solve the round brackets first!

$\sf \left(\dfrac{10}{3} \div \dfrac{5}{3} \times \dfrac{5}{4} - \dfrac{4}{1} \right)$

The reciprocal of 5/3 is 3/5. So we get :-

$\sf \left(\dfrac{\cancel{10}}{\cancel{3}} \times \dfrac{\cancel{3}}{\cancel{5}} \times \dfrac{5}{4} - \dfrac{4}{1} \right)$

Reducing the numbers,

$\sf \left(\dfrac{2}{1} \times \dfrac{1}{1} \times \dfrac{5}{4} - \dfrac{4}{1} \right)$

Multiplying the remaining numbers,

$\sf \left(\dfrac{2}{1} \times \dfrac{5}{4} - \dfrac{4}{1} \right)$

Multiplying 2/1 with 5/4,

$\sf \left(\dfrac{10}{4} - \dfrac{4}{1} \right)$

The LCM of 1 and 4 is 4, so subtracting the fractions using their denominators,

$\sf \left(\dfrac{10 \times 1 - 4 \times 4}{4} \right)$

On simplifying,

$\sf \left(\dfrac{10 - 16}{4} \right)$

Subtracting 16 from 10,

$\sf \left(\dfrac{-6}{\:\:\:4}\right)$

Reducing the fraction to it's simplest form,

$\sf \left( \dfrac{-3}{\:\:\:2} \right)$

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Now let's solve the curly brackets!

$\sf \left\{\dfrac{2}{1} + \dfrac{-3}{\:\:\:2}\right\}$

The LCM of 1 and 2 is 2, so adding the fractions using their denominators,

$\sf \left\{\dfrac{2\times2 + (-3) \times 1}{2} \right\}$

On simplifying,

$\sf \left\{\dfrac{4 + (-3)}{2} \right\}$

Adding -3 to 4,

$\sf \left\{\dfrac{1}{2}\right\}$

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Now at last let's solve the square brackets!

$\sf \left[\dfrac{19}{4} - \dfrac{1}{2} \right]$

The LCM of 4 and 2 is 4, so subtracting the fractions using their denominators,

$\sf \left[\dfrac{19 \times 1 - 1 \times 2}{4} \right]$

On simplifying,

$\sf \left[\dfrac{19 - 2}{4} \right]$

Subtracting 2 from 19,

$\sf \left[\dfrac{17}{4}\right]$

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Finally let's subtract the result from 9/4 to get our answer, since we have solved all the brackets!

$\sf \dfrac{9}{4} - \dfrac{17}{4}$

The denominators of the fractions are same, so let's subtract them like normal numbers.

$\sf \dfrac{9-17}{4}$

Subtracting 17 from 9,

$\sf \dfrac{-8}{\:\:\:4}$

Reducing the fraction to it's simplest form,

$\sf \dfrac{-2}{\:\:\:1}$

Removing the denominator,

$\underline{\boxed{\sf -2}}$

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$\underline{\underline{\bf Know \: more :\!\!-}}$

• We solved the above question using BODMAS.

BODMAS stands for :-

• B - Bracket
• O - Of
• D - Division
• M - Multiplication
• A - Addition
• S - Subtraction

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$\underline{\underline{\bf Order \: of \: Brackets :\!\!-}}$

• First brackets or round brackets :- ()

• Second brackets or curly brackets :- {}

• Third brackets or square brackets :- []

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