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Q.

Evaluate the given expression

$10 - 2 \frac{1}{3} \times 3 + 3 \frac{3}{4} \div 2 \frac{1}{2} = ?$

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a

\frac{3}{2}

b

\frac{3}{5}

c

\frac{1}{2}

d

\frac{7}{2}

answer is A.

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Detailed Solution

Given expression,

10 - 2 \frac{1}{3} \times 3 + 3 \frac{3}{4} \div 2 \frac{1}{2} \dots \dots \dots \dots (1)

First, we have converted the mixed fraction into fraction by this method

= \frac{(quotient \times divisor) + remainder}{divisor}

= 2 \frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3}

= 3 \frac{3}{4} = \frac{(3 \times 4) + 3}{4} = \frac{15}{4}

= 2 \frac{1}{2} = \frac{(2 \times 2) + 1}{2} = \frac{5}{4}

Then, we put the value

2 \frac{1}{3} = \frac{7}{3}, 3 \frac{3}{4} = \frac{15}{4}, 2 \frac{1}{2} = \frac{5}{2}

In the equation (1) we have

10 - \frac{7}{3} \times 3 \frac{15}{4} \div \frac{5}{2}

By using the BODMAS rule we have
1st we can solve division section

(\frac{15}{4} \div \frac{5}{2})

10 - \frac{7}{3} \times 3 + \frac{15}{4} \div \frac{5}{2}

= 10 - \frac{7}{3} \times 3 + \frac{15}{4} \times \frac{2}{5}

= 10 - \frac{7}{3} \times 3 + \frac{3}{2}

2nd we can solve multiplication section

(\frac{7}{3} \times 3)

10 - \frac{7}{3} \times 3 + \frac{3}{2}

= 10 - (\frac{7}{3} \times 3) + \frac{3}{2}

= 10 - 7 + \frac{3}{2}

3rd we can solve the addition section

(7 + \frac{3}{2})

= 10 - (7 + \frac{3}{2})

= 10 - \frac{14 + 3}{2}

= 10 - \frac{17}{2}

4th we can solve the subtraction section

10 - \frac{17}{2}

10 - \frac{17}{2}

= \frac{20 - 17}{2}

= \frac{3}{2}

Hence, the required value of the given expression =

\frac{3}{2}

Correct option is 1.

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