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,

⇒ [1496 – 392] /23 × 15 = 213 + ?

⇒ 1104/23 × 15 = 213 + ?

⇒ 1104 ÷ 23 × 15 = 213 + ?

⇒ 720 = 213 + ?

∴ ? = 507

Law of Surds and 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)^(-m) = 1/a^m

5.  (a)⁰ = 1

6.  (a)^1/m = ^m√a

Given expression is,

64² – 36² = ? × 25

⇒ 4096 – 1296 = ? × 25

⇒ 2800 = 25 × ?

∴ ? = 112

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,

\(\frac{{1287}}{{1645}} × \frac{{235}}{{572}} \div 3\frac{{15}}{{16}} = ?\)

⇒ ? = 1287/1645 × 235/572 × 16/63

⇒ ? = (143/1645) × (235/143) × (4/7)

⇒ ? = (1/329) × (47/1) × (4/7)

∴ ? = 4/49

We do not have to simplify the fraction to simplest form.

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,

(5995 + 4874 + 3333) ÷ (713 + 509 + 326) = ?

⇒ 14202 ÷ 1548 = ?

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,

81% of 2300 – 34% of 596 = ?

⇒ ? = (81/100 × 2300) – (34/100 × 596)

⇒ ? = (81 × 2300) – (34 × 5.96)

⇒ ? = 1863 – 202.64

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

3(2/3) × 3(1/3) × 3 = 9(?)

⇒ 3^{(2/3 + 1/3 + 1)} = 9(?)

⇒ 3² = 9(?)

⇒ 9 = 9(?)

∴ ? = 1

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

\(\frac{70}{{4}} + \frac{90}{{4}} + \frac{110}{{4}} + \frac{60}{{4}} + \frac{70}{{4}} =\: ?\)

Taking L.C.M

⇒ ? = (70 + 90 + 110 + 60 + 70)/4

⇒ ? = 400/4

∴ ? = 100

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,

⇒ (684 + 387) ÷ 3 + 163 = 42 × 6 + 164 + ?

⇒ (1071) ÷ 3 + 163 = 42 × 6 + 164 + ?

⇒ 357 + 163 = 42 × 6 + 164 + ?

⇒ 357 + 163 = 252 + 164 + ?

⇒ 520 = 252 + 164 + ?

⇒ 520 = 416 + ?

⇒ ? = 520 - 416

According to the BODMAS rule, the priority in which the operations should be done is:

⇒ √2498 × √626 ÷ √99 = (?)

Approximating the values to the nearest integer:

⇒ √2500 × √625 ÷ √100 = (?)

⇒ 50 × 25 ÷ 10 = (?)

(?) = 125

Given expression is,

⇒ 199.99 - 99.89 ÷ 24.80 = 28.04 × ?

We can write the given values as:

⇒ 199.99 ≈ 200 and 99.89 ≈ 100

⇒ 24.80 ≈ 25 and 28.04 ≈ 28

⇒ 200 - 100 ÷ 25 = 28 × ?

⇒ 200 - 4 = 28 × ?

⇒ 196 = 28 × ?

⇒ ? = 196/28

Given expression is,

⇒ 75.60 × 2.94 ÷ ? = 19.88 × 3.05 - 47.89

We can write the given values as:

⇒ 75.60 ≈ 76 and 2.94 ≈ 3

⇒ 19.88 ≈ 20 and 3.05 ≈ 3 and 47.89 ≈ 48

Then,

⇒ 76 × 3 ÷ ? = 20 × 3 - 48

⇒ 76 × 3 ÷ ? = 60 - 48

⇒ 76 × 3 ÷ ? = 12

⇒ 76 × (3/?) = 12

⇒ 76 ÷ 12 = (?/3)

⇒ (76/12) × 3 = ?

17.977 × 5.123 - 10.02 + 55.999 - 18.2111 ÷ 6.0007

Using BODMAS rule,

⇒ 18 × 5 - 10 + 56 - 18 ÷ 6

Solving it using Approx value,

⇒ 18 × 5 - 10 + 56 - 3, (Simplifying division ‘18 ÷ 6’)

⇒ 90 - 10 + 56 - 3, (Simplifying multiplication ‘18 × 5’)

⇒ 146 - 13, (Simplifying addition)

⇒ 133

Given expression is,

31.87 + 87.80 – 55.11 = 12.84 × ? – 25.88

We can write the given values as:

31.87 ≈ 32 and 87.80 ≈ 88

55.11 ≈ 55 and 12.84 ≈ 13 and 25.88 ≈ 26

Then,

⇒ 32 + 88 – 55 = 13 × ? – 26

⇒ 120 – 55 = 13 × ? – 26

⇒ 65 = 13 × ? – 26

⇒ 65 + 26 = 13 × ?

⇒ 13 × ? = 91

⇒ ? = 91/13

⇒ (4819.01 + 9612.98 + 14423.03) ÷ 5.01 + 5.02 = (?)²

⇒ ?² = 28855 ÷ 5 + 5

⇒ ?² = 5771 + 5

⇒ ?² = 5776

⇒ ?² = 76²

⇒? = 76

We can write following values as :

97.66 ≈ 98, 3.94 ≈ 4 and 4.14 ≈ 4

2.90 ≈ 3, 44.80 ≈ 45 and 185.91 ≈ 186 and 3.01 ≈ 3

Given expression is,

⇒ (97.66 × 3.94 + 4.14) ÷ 2.90 + 44.80 = 185.91 + 3.01 × ?

⇒ (98 × 4 + 4) ÷ 3 + 45 = 186 + 3 × ?

⇒ (392 + 4) ÷ 3 + 45 = 186 + 3 × ?

⇒ 396 ÷ 3+ 45 = 186 + 3 × ?

⇒ 132 + 45 = 186 + 3 × ?

⇒ 177 = 186 + 3 × ?

⇒ ? × 3 = 177 - 186