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FOLLOW BODMAS rule to solve this QUESTION, as PER the order given below,

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

Step-2: Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step-4: Last but not LEAST, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

⇒ 87.50 + 1.1 × 2.01 + 45.88

Approximating to the CLOSEST integers

⇒ 88 + 1 × 2 + 46

⇒ 88 + 2 + 46

The GIVEN PROBLEM can be EVALUATED as:

⇒ 315.27 + 858.59 = 1173.86

Hence,

⇒ 315.27 – 527.13 + 858.59

= 1173.86 – 527.13

GIVEN EXPRESSION is,

7.8 + 5.4 × 8.2 = ?

⇒ 7.8 + 44.28 = ?

? % of 950 + 782 = 1200

⇒ ? % of 950 = 1200 – 782

⇒ ? % of 950 = 418

$(\Rightarrow \FRAC{?}{{100}} \times 950 = 418)$

$(\Rightarrow \;?\; = \;\frac{{418\; \times \;100}}{{950}})$

$(\Rightarrow \;?\; = \;\frac{{41800}}{{950}})$

33.33% of 288 + 9.09% of ?1331.22 + 19.12% of ?624 = ?

It can be approximated as

1/3 × 288 + 1/11 × 11 + 20% of ?625 = ?

⇒ 96 + 1 + 1/5 × 5 = ?

⇒ 97 + 1 = ?

$(\begin{ARRAY}{l} \sqrt {23.001 + \sqrt {5931} } \times \sqrt {624.78} = \sqrt {15624} \times ?\\ \Rightarrow \sqrt {23 + \sqrt {5929} } \times \sqrt {625} = \sqrt {15625} \times ?\\ \Rightarrow \sqrt {23 + 77} \times 25 = 125 \times ?\\ \Rightarrow \sqrt {100} = \frac{{125}}{{25}} \times ? \end{array})$

⇒ 10 = 5 × ?

∴ ? = 2

40.93 × 1.012 × 1.210 = ?

Here, 40.93 ≈ 41

1.012 ≈ 1

1.210 ≈ 1.2

Now, the EXPRESSION will become:

41 × 1 × 1.2 ≈ ?

⇒ ? ≈ 49.2 ≈ 50

Given expression:

(755% of 523) ÷ 777

$(\begin{array}{l} = \left( {\FRAC{{755}}{{100}} \times 523} \RIGHT) \div 777\\ = \left( {\frac{{755 \times {\rm{\;}}523}}{{100 \times {\rm{\;}}777}}} \right) \end{array})$

= 5.08

FOLLOW BODMAS rule to solve this question, as per the given order below.

Step 1: Parts of the equation enclosed in ‘Brackets’ must be solved first.

Step 2: An mathematical ‘Of’ or ‘Exponent’ must be solved next.

Step 3: Next, the parts of the equation containing ‘Division’ or ‘Multiplication’ are calculated.

Step 4: Last but not the least, the parts of the equation containing ‘Addition’ or ‘Subtraction’ are calculated.

Given,

$(\BEGIN{array}{l} \frac{{56}}{{135}} \div \left\{ {\left( {\frac{7}{3} + \frac{1}{5}} \right) \div \left( {9 + 3\frac{3}{4}} \right) \times \frac{{17}}{{19}}} \right\} = \frac{1}{?}\\ \Rightarrow \frac{{56}}{{135}} \div \left\{ {\left( {\frac{7}{3} + \frac{1}{5}} \right) \div \left( {9 + \frac{{15}}{4}} \right) \times \frac{{17}}{{19}}} \right\} = \frac{1}{?}\\ \Rightarrow \frac{{56}}{{135}} \div \left\{ {\frac{{38}}{{15}} \div \frac{{51}}{4} \times \frac{{17}}{{19}}} \right\} = \frac{1}{?} \end{array})$

$(\begin{array}{l} \Rightarrow \frac{{56}}{{135}} \div \left\{ {\frac{{38}}{{15}} \times \frac{4}{{51}} \times \frac{{17}}{{19}}} \right\} = \frac{1}{?}\\ \Rightarrow \frac{{56}}{{135}} \div \frac{8}{{45}} = \frac{1}{?}\\ \Rightarrow \frac{{56}}{{135}} \times \frac{{45}}{8} = \frac{1}{?}\\ \Rightarrow \frac{7}{3} = \frac{1}{?} \end{array})$

237.76 × 14.98 + ?³ + 184.54 × 3.98 = 5036.75

Taking their approx. VALUE;

238 × 15 + ?³ + 185 × 4 = 5037

⇒ 3570 + ?³ + 740 = 5037

⇒ 4310 + ?³ = 5037

⇒ ?³ = 5037 – 4310

⇒ ?³ = 727

∴ ? = ?727 ≈ ?729 = 9

GIVEN expression is,

(229.77 ÷ 1.84) ÷ 22.88 = 37.88 - 34.01 + ?

We can write the given VALUES as:

229.77 ≈ 230 and 1.84 ≈ 2

22.88 ≈ 23 and 37.88 ≈ 38 and 34.01 ≈ 34

Then,

⇒ (230 ÷ 2) ÷ 23 = 38 - 34 + ?

⇒ 115 ÷ 23 = 38 - 34 + ?

⇒ 5 = 38 - 34 + ?

⇒ 5 = 4 + ?

⇒ ? = 5 - 4

BODMAS rule to solve this question, as per the order given below,

Step- 1- Parts of an equation enclosed in 'Brackets' must be solved first,

Step- 2- Any mathematical 'Of' or 'Exponent' must be solved NEXT,

Step- 3- Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated,

Step- 4- Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Given expression is,

$(4\FRAC{1}{3} \times 5\frac{1}{3} \div 6\frac{1}{3} \div \frac{1}{3} + 5\frac{1}{3} - 2\frac{1}{3} = ?)$

$(\Rightarrow \;\frac{{13}}{3}\; \times \frac{{16}}{3}\; \div \frac{{19}}{3}\; \div \frac{1}{3} + \frac{{16}}{3} - \frac{7}{3} = \;?)$

$(\Rightarrow \left( {\frac{{13}}{3}\; \times \frac{{16}}{3} \times \frac{3}{{19}} \times 3} \RIGHT) + \frac{{16}}{3} - \frac{7}{3} = \;?)$

$(\Rightarrow \;\frac{{208}}{{\;19}} + \frac{{16}}{3} - \frac{7}{3} = \;?)$

$(\Rightarrow \frac{{624}}{{57}} + \frac{{304}}{{57}} - \frac{{133}}{{57}} = \;?)$

⇒ (795/57) = ?

⇒ ? = 265/19

$(\therefore \;?\; = \;13\frac{{18}}{{19}})$

Laws of Indices:

1. am$ × an $= a{m + n}$

2. am $÷ an $= a{m - n}$

3. (am$)n $= amn$

4. (a)-m $= 1/am$

5. (a)m/n$ = n$√am$

6. (a)0 $= 1

⇒ 65$ × 22$ = 2x$

⇒ 220$ ÷ 2?$ ÷ 214$ = √256

⇒ 2^{20 - ? - 14} = 2⁴

⇒ 2^{6 - ?} = 2⁴

⇒ 6 - ? = 4

⇒ ? = 2

$(\frac{{22 \div 0.5 \TIMES 10 + 6 - 2}}{{30 \div 0.4 \times 4 + 76 - 6}} = ?)$

APPLY BODMAS rule in NUMERATOR and denominator

$(\begin{array}{l} \Rightarrow \frac{{44 \times 10 + 4}}{{75 \times 4\; + 70\;}} = \;?\\ \Rightarrow \frac{{440 + 4}}{{300 + 70}} = \;?\end{array})$

⇒ 444/370 = ?

∴ ? = 1.2

Given EXPRESSION:

⇒ 74% of 2650 + 30% of 320 = ?

⇒ $(\frac{{74}}{{100}}\; \TIMES \;2650\; + \;\frac{{30}}{{100}}\; \times \;320\; = \;?)$

⇒ ? = 1961 + 96

⇒ ? = 2057

⇒ (84/100) × 500 - 25/100 × ? = 350

⇒ 84 × 5 - 350 = 1/4 × ?

⇒ 420 - 350 = 1/4 × ?

⇒ 70 × 4 = ?

⇒ ? = 280

The GIVEN expression,

(4438 – 28 74 – 559) ÷ (269 – 106 – 83) = ?

Consider it to nearest value,

⇒ (4440 – 2875 – 560) ÷ (270 – 110 – 85) = ?

⇒ ? = 1005 ÷ 75

⇒ ? ≈ 13.4

Solve the given question using FOLLOWING LAWS of INDICES.$

1. a$^m$ × a$^n$ = a$^{(m + n)$}

2. a$^m$ ÷ a$^n$ = a$^{(m - n)$}

3. [(a$^m$)$^n$ ] = a$^(mn)$

4. a$^(1/m)$ = $^m$√a$

5. a$^-m$ = 1/a$^m$

6. a$^(m/n)$ = $^n$√a$^m$

7. a$^0 $= 1$

Given expression:

33^8.8 × 33^1.2 ÷ 33⁵ = 33 × 33^?

⇒ 33^{8.8 + 1.2 - 5} = 33^{? + 1}

⇒ 33⁵ = 33^{? + 1}

⇒ 5 = ? + 1

⇒ ? = 4

Follow BODMAS rule to solve this question, as per the order given below.

Step - 1 - steps of an equation ENCLOSED in ‘Brackets’ must be SOLVED first.

Step - 2 - any mathematical ‘Of’ or ‘EXPONENT’ must be solved next.

Step - 3 - Next, the parts of the equation that contain ‘Division’ and ‘Multiplication’ are calculated.

Step - 4 - Last but not least, the parts of the equation that contain ‘Addition’ and ‘Subtraction’ should be calculated.

⇒ ¾ of (470 + 18) + 5/6 of 360 = 111 × √?

⇒ 111 × √? = ¾ of 488 + 5/6 of 360

⇒ 111 × √? = 366 + 300

⇒ 111 × √? = 666

⇒ √? = 666/111

⇒ √? = 6

⇒ ? = 6²

⇒ ? = 36