Approximations Part 1

1)49.6*5.08 + 485.987 +42.6+5.3 = ?

  1. 740      2.780       3.720    4.760   5.800

50 * 5  +  486  +  \frac{40}{5}

250  +  486  +  8 = 746 it is near to 740

2)(64.15)^{2}-(17.90)^{2}-(21.9)^{2}=?

1.3600  2.3900  3.3300  4.4000   5.3000

64^{2}-18^{2}-22^{2}

4096 – 324  – 484 = 3288 it is near to 3300

3)(\sqrt{900.021}-\sqrt{255.989})^{2}\div (\sqrt{575.989}-\sqrt{289.006})^{2}=?

(\sqrt{900}-\sqrt{256})^{2}\div (\sqrt{576}-\sqrt{289})^{2}

(30-16)^{2}\div (24-17)^{2}

\frac{14\times 14}{7\times 7}=4

4)9.09% of 1334 + 14.30% of 2400 =?

1.486  2.465  3.450  4.430  5.418

9.09% of 1334 +14.28% of 2400

\frac{1}{11}\times 1334+\frac{1}{7}\times 2400

121+343 = 464 it is near to 465

5)33\frac{1}{3}% of 768.9 + 25% of 161.2 – 58.12 = ?

1.250  2.220  3.230  4.200  5.240

\frac{1}{3}\times 768+\frac{1}{4}\times 160-58

256 + 40 -58 =238 which is near to 240

Simplifications Part 1

Problem 1: 112\frac{1}{2}% of 12\frac{1}{2}% of 116\frac{2}{3}% of 12.8 = ?

12\frac{1}{2}=\frac{1}{8}

100% = 1

112\frac{1}{2}=1+\frac{1}{8}=\frac{9}{8}

100+16\frac{2}{3}=1+\frac{1}{6}=\frac{7}{6}

\frac{9}{8}\times \frac{1}{8}\times \frac{7}{6}\times 12.8=x

x = 2.1

Problem 2: (81\times 9)^{3}\div (9)^{5}\times (3\times 27)^{2}=(9)^{?}

Convert all terms into 9th power

(81\times 9)^{3}=9^{9}

(3\times 27)^{2}=9^{4}

9 – 5 + 4 = 8

 

Problem 3: \frac{?}{18}of\sqrt{361}=\frac{171}{?}of\sqrt[3]{5832}

\sqrt{361}= 19

Square ends  with 1 is 1 and 9

Delete one’s place and tens place

The number 3 is between 1^{2} and 2^{2}

\sqrt[3]{5832}= 18

Cube ends with 2 is 8

Delete ones, tens, hundred place

5 is between 1^{3} and  2^{3}

Select the least number i.e 1 so answer is 18

\frac{x}{18}\times 9=\frac{171}{x}\times 18

x^{2}=9\times 18\times 18

x= 3\times 18=54

Number Series Part 4

Problem 1: 3   20   88   273   ?   559

3 * 5 + 5 = 20     (5=5*1)

20 * 4 + 8 = 88  (8=4*2)

88 * 3 + 9 = 273 (9=3*3)

273*2 + 2*4 = 554

554*1 + 1*5 = 559

 

Problem 2: ?   48  96   240   720   2520

48 * 2 = 96

96 * 2.5 = 240

240 * 3 = 720

720 * 3.5 = 2520

1.5=\frac{3}{2}

\frac{48\times 2}{3}=32

 

Problem 3: 1   ?   6   21   88   445

6 * 3 +3 = 21

21 * 4 + 4 = 88

88 * 5 + 5 = 445

1 * 1 + 1 = 2

2 * 2 + 2 = 6

 

Problem 4: 6   4   5   11   ?   361

6 * 0.5 + 1 = 4

4 * 1 + 1 = 5

5 * 2 + 1 = 11

11 * 4 + 1 =45

45 * 8 + 1 =361

 

Problem 5: 180   179  183   156   172   ?

180 – 179 = -1 = 1^{3}

179 -183 = +4 = 2^{2}

183 – 156 = -27 = 3^{3}

156 – 172 = +16 = 4^{2}

-5^{3}=125

172 – 125 = 47

Number Series Part 3

Problem 1: 4   6   14   44   ?   892

4 * 1 + 2 = 6

6 * 2 + 2 = 14

14 * 3 + 2 = 44

44 * 4 + 2 = 178

 

Problem 2: 7   3   2   2   4   ?

7 * 0.5 – 0.5 = 3

3 * 1 -1 = 2

2 * 2 – 2 = 2

2 * 4 – 4 = 4

4 * 8 – 8 = 24

 

Problem 3: 5   6   14   23   87   ?

5 – 6 = 1 = 1^{2}

6 – 14 = 8 = 2^{3}

14 – 23 = 9 = 3^{2}

87 – 23 = 64 = 4^{3}

5^{2}=25

87+25 = 112

 

Problem 4: 5   6.2   9   13.4   19.4   ?

5 – 6.2 = 1.2

9 – 6.2 = 2.8

13.4 – 9 = 4.4

Second diference

2.8 – 1.2 = 1.6

4.4 – 2.8 = 1.6

1.6+4.4 = 6

1.6 + 6 + 19.4 = 27

 

Problem 5: 3   2   2   3   8   35   ?

3 * 1 – 1 = 2

2 * 2 – 2 = 2

2 * 3 – 3 = 3

3 * 4 – 4 = 8

8 * 5 – 5 =35

35 * 6 – 6 = 204