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,

\(\Rightarrow {\rm{}}\frac{2}{5} \times 3\frac{1}{4} + 5\% \;of\;800 = 6\frac{2}{5} \times \frac{{11}}{4} + ?\% of\;20\)

\( \Rightarrow \frac{2}{5} \times 3\frac{1}{4} + \frac{5}{{100}} \times 800 = 6\frac{2}{5} \times \frac{{11}}{4} + \frac{?}{{100}} \times 20\)

\(\Rightarrow \frac{2}{{5}} \times \frac{{13}}{4} + 40 = \frac{{32}}{5} \times \frac{{11}}{4} + \frac{?}{5}\)

\(\Rightarrow {\rm{}}\frac{{26}}{{20}} + 40 = \frac{{352}}{{20}} + \frac{?}{5}\)

\(\Rightarrow {\rm{}}\frac{{826}}{{20}} - \frac{{352}}{{20}} = \frac{?}{5}\)

\(\Rightarrow \frac{{474}}{{20}} = \frac{?}{5}\)

⇒ ? = 118.5

\({43^2} - 4\;\% \;of\;1030\; + 13\% \;of\;1200 - \;9\% \;of\;\sqrt {196} = ? × 100\)

⇒ \(1849 - \frac{4}{{100}} × 1030 + \frac{{13}}{{100}}\; × 1200 - \frac{9}{{100}}\; × \sqrt {196} = ? × 100\)

⇒ \(1849 - 41.2 + 156 - 1.26 = ?\;× 100\)

⇒ ? × 100 = 1962.54

⇒ ? = 19.62

∴ Answer is 19.62

\(\begin{array}{l} \Rightarrow 1\frac{3}{4} + 1\frac{5}{6} - 2\frac{1}{8} = ? + 1\frac{1}{{12}}\\ \Rightarrow \frac{7}{4} + \frac{{11}}{6} - \frac{{17}}{8} - \frac{{13}}{{12}} = ?\\ \Rightarrow \;? = \;\frac{{7 \times 6 + 11 \times 4 - 17 \times 3 - 13 \times 2}}{{24}}\\ \Rightarrow \;? = \;\frac{{42 + 44 - 51 - 26}}{{24}} \end{array}\)

⇒ ? = 9/24

To solve questions of this type, follow the laws of “Surds and indices’’ given below-

Laws of Indices:

1. a^m × aⁿ = a^{{m + n}}

2. a^m ÷ aⁿ = a^{{m - n}}

3. (a^m)ⁿ = a^mn

4. (a)^-m = 1/a^m

5. (a)^m/n = ⁿ√a^m

6. (a)⁰ = 1

By using this laws:

⇒ 25^? × 5⁶ = 125 × 5⁴ × 625²

⇒ 25^? × 5⁶ = 5³ × 5⁴ × (5⁴)²

⇒ 25^? × 5⁶ = 5³ × 5⁴ × 5⁸

⇒ 5^{(2 × ? + 6)} = 5^{(3 + 4 + 8)}

⇒ 2 × ? + 6 = 3 + 4 + 8

⇒ 2 × ? = 15 – 6

⇒ 2 × ? = 9

∴ ? = 9/2

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,

⇒ 4.5 % of 900 + 8.5 = 8² - ?

\(\Rightarrow \frac{{4.5}}{{100}} \times 900 + 8.5 = {8^2}\:-\:?\)

⇒ 40.5 + 8.5 = 8² - ?

⇒ 49 = 64 - ?

⇒ ? = 64 – 49 = 15

64¹²/4¹⁸ = 4³⁶/4¹⁸

4¹⁸ = 4^{3 × 6} = 64⁶

⇒ 28.314 – 31.427 + 113.928 = ? + 29.114

⇒ 110.815 = ? + 29.114

We use BODMAS to solve certain parts of the question to get a simplified form.

BODMAS stands for:

B – Brackets

O – Of (this simply stands for multiplication)

D – Division

M – Multiplication

A – Addition

S – Subtraction

The above is the standard order in which a given question is simplified.

LHS:

We have OF in the question: 72% of 2000 = \(\frac{{72}}{{100}} \times 2000 = 1440\)

Hence, modified LHS = 1440 – ?

Equating it to RHS,

1440 – ? = 300

⇒ (21.98)² – (25.02)² + (13.03)² = ?

⇒ (22)2 – (25)2 + (13)2 = ?

⇒ 484 - 625 + 169 = ?

Given problem can be re-written as:

(2508 ÷ 15) + (? × 11) = 200

⇒ 167 + (? × 11) = 200

⇒ (? × 11) = (200 - 167)

⇒ ? = (33/11) = 3 (Approximately)

989.001 + 1.00982 × 76.792 = ?

? ≈ 989 + 1 × 77

? = 989 + 77

? = 1066

⇒ 447.75 ÷ 28 × 4.99

\(\begin{array}{l} \frac{{44775}}{{100}} \div 28 \times \frac{{499}}{{100}}\\ \frac{{44775}}{{100}}{\rm{\times}}\frac{1}{{28}}{\rm{\times }}\frac{{499}}{{100}} \end{array}\)

= 79.79

~ 80

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:

⇒ (9.979)³ – (23.99)² + 2⁵

⇒ 10³ - 24² + 2⁵ = 1000 – 576 + 32

⇒ 456 ≈ 450

Given expression:

⇒ ? = 2439.97 – 1234.01 + 401.99 – 989.99

⇒ 2440 – 1234 + 402 – 990 = 618 ≈ 620

In this type of question, we are expected to calculate Approximate value (not exact value), so we can replace the given numbers by their nearest perfect places which makes the calculation easy.

Given expression:

⇒ 38% of 568 + 16% of 1654 – 212 =?

\( \Rightarrow \frac{{38}}{{100}} \times {\rm{\;}}568{\rm{\;}} + \frac{{16}}{{100}}{\rm{\;}} \times {\rm{\;}}1654{\rm{\;}}-{\rm{\;}}212{\rm{\;}} = ?\)

⇒ 215.84 + 264.64 – 212 =?

⇒? = 481 – 212 = 269

⇒? ≈ 270.