Consulting Mental Math

97% of 208

100% of 208 - 3% of 208= 208 - 6.3 = 201.7

23 x 47

1081 Rule of multiplying 2 digit #s 100(2*4) + 10(3*4) + 10(2*7) + 3*7

23% of 60

13.8 ~ 20% of 60 ~ 12, round up ~ 14 20% of 60 + 3% of 60 = 12 + 1.8 = 13.8

20% of 700

140 Find 10%, then double it

288 x 5

1440 Multiply by 10, then divide by 2 2880/2

27% of 54

15 ~ 30% of 55 = ~16.5, round down = 15 20% of 54 + 7% of 54 10.8 + 3.78 = 14.6

38% of 400

152 Same as 400% of 38 = 4 * 38 = 152

10% of 160

16 (divide by 10 or move decimal 1 place)

70% of 24

16.8 Find 10% then multiply by 7

1.7/10

17%

The total widget market is $170mm, our sales are $30mm - what is our market share?

18% 3/15 > 3/17 > 3/20 20% > 2/17 > 15% = 18%

Labor costs are 25% of our $75,000 total cost - how much are labor costs?

18,750 20% of 75,000 + 5% of 75,000 15,000 + 3,750 = 18,750 1/4 of 75,000= 1/4 of 80 = 20, scale down = 18,000

50% of 360

180 50% = 1/2

2% of 980

19.6 Find 1% then double it

.62/31

2% .6/30 6/300 2/100 =2%

.54 / 27

2% x2 = ~1/60 2/120 = 2.4%

14% of 16,000,000

2.2mm 10% of 16mm + 4% of 16mm 1,600,000 + 640,000 = 2,240,000 OR 14% of 16 1.6+.64 = 2.24 mm

25% of 80

20 Same as 1/4; divide by 4

Our cost to make 39,379 widgets is $20mm; what is our cost/unit

20,000,000/40,000 = 2,000/4 = 1,000/2 = 500/1 = $500 / widget

9 x 27

243 10*27 - 27 270-27 243 Multiplying by 9

8 X 27

246 10*27 - 27*2 270-54 Multiplying by 8

13 x 19

247 Multiplying #'s between 11 and 19 (10+a)*(10+b) 100+10(a+b)+a*b 100+120+27 247

30% of 870

261 find 10% then multiply by 3

5,890 / 5

(5,890 / 10) * 2. So in this case, 589 * 2 = 1,178.

1/40

.025, 2.5%

1/40

.025, 2.5% x2 = 2/80 = 2.5/100

1/30

.033 = 3.3%

1/13

.0769, 7.7%

1/11

.099, 9.9%

1/6

.167, 16.7%

1/20

0.05, 5%

1/15

0.066, 6.6%

1/12

0.08333..., 8.3%

1/10

0.1, 10%

What % is 7 of 63

0.11 7/63 10/65 1/6.5 Less than 0.16

1/9

0.111, 11.1%

2% of 6

0.12 Find 1%, then double it

1/8

0.125, 12.5%

1/7

0.142, 14.2%

1/5

0.2, 20%

1/14

0.71 and 71%

35 x 75

2625 Rule of 2 digit #'s ending in 5 Round the smaller number down and the larger up to the nearest multiple of ten. In this case: 35-5=30=X 75+5=80=Y The algorithm reads as follows: (X*Y)+50(t1-t2)+25 Where t1 is the tens unit of the original larger number (75) and t2 is the tens unit of the original smaller number (35). 30*80+50(7-3)+25=2625

16 x 17

272 Multiplying #'s between 11 and 19 (10+a)*(10+b) 100+10(a+b)+a*b =100+130+42 272

40% of 7,890

3,156 find 10% then multiply by 4

670 x 5

3,350 Multiply by 10, then divide by 2

80% of 38

30.4 Find 10% then multiply by 8

25% of 124

31 1/4 of 124 = 1/4 of 100 + 1/4 of 24= 25 + 6 = 31

7*45

315 7*50 - 7*5 350-35 315

60% of 560

336 Find 10% then multiply by 6

78% of 45

35 ~80% of 45 = 36.5, scale down = 35

Your $36 stock increased 6% today - how much is it now worth

38.16 6% of 36 = .36*6 ~.4*6 ~2.4 ~=38.4

45 X 85

3825 Rule of 2 digit #'s ending in 5 Round smaller # down and larger up 45-5 = 40 85+5 = 90 40*90 + 50(4) + 25 3600+200+25 =3825

3/75

4% 1/25

1% of 4,000,000

40,000 (divide by 100 or move decimal 2 places)

60% of 70

42 7*6 OR 50% of 70 + 10% of 70 35+7 = 42

90% of 55

49.5 Also equal to: 100% of 55 - 10% of 55 = 55-5.5 =54.5

10% of 50

5 (divide by 10 or move decimal 1 place)

2.5/50

5%

480mm decrease to 450mm is what % change?

5% 480-450/480 30/480 3/48 ~6%, scale down to 5%

1% of 530

5.3 (divide by 100 or move decimal 2 places)

1% of 550

5.5 (divide by 100 or move decimal 2 places)

75% of 670

504 3/4*670 OR 50% of 670 + 25% of 670 = 335 + 168 = 503

15% of 340

51 10% of 340 + 5% of 340 = 34 + 17 = 51

65% of 80

52 60% of 80 + 5% of 80= 48 + 4 = 52

Shares outstanding = 41,084,000 Investors hold = 25,171,000 What percentage of shares are held by investors?

62.5% 25/40

187% of 350

655 Same as 350% of 187 = 3.5*187 = 655 OR Same as 350% of 187 = (100+100+100+50)% of 187 = 187*3 + 187/2 = 655

1% of 6,800

68 (divide by 100 or move decimal 2 places)

1% of 700

7 (divide by 100 or move decimal 2 places)

78% of 90

70 ~80% of 90 =72, scale down = 70

75% of 1000

750 Same as 3/4

251 x 323

81,073 251*3 + 251*20 + 251*300 753 + 5020 + 75300

2.5% of $3,500,000

87,500 70,000 + 18,000 = 88000

896 x 11

9,856 The ones digit of the multiplier, 6, is copied to the temporary result.: 6 Add 6 + 9 = 15 so 5 is placed on the left side of the result and carry the 1. result: 56 Similarly add 8 + 9 = 17, then add the carried 1 to get 18. Place 8 to the result and carry the 1. result: 856 Add the carried 1 to the highest valued digit in the multiplier, 8 + 1 = 9, and copy to the result to finish.

10% of 900

90 (divide by 10 or move decimal 1 place)

13% of 19

= 2 ~10% of 20 = 2 OR 10% of 19 * 3% of 19= 1.9 + .57 = 2.47

68% of 68

=46 60% of 68% + 8% of 68 6*6.8 + 0.68*8 = 40.8+5.44 =46.24

12% of 83

=9 10% of 83 + 2% of 83= 8.3 + 1.66 9.96

759 x 11

A step-by-step example of 759 × 11: The ones digit of the multiplier, 9, is copied to the temporary result.: 9 Add 5 + 9 = 14 so 4 is placed on the left side of the result and carry the 1. result: 49 Similarly add 7 + 5 = 12, then add the carried 1 to get 13. Place 3 to the result and carry the 1. result: 349 Add the carried 1 to the highest valued digit in the multiplier, 7 + 1 = 8, and copy to the result to finish. Final product of 759 × 11: 8349

90% of 730

Find 10% then multiply by 9

8/256

Step 1: Begin by finding an acceptable range for how many times 8 goes into 256. Because 8 x 10 = 80 and 8 x 100 = 800, we know 8 will go into 256 between 10 and 100 times. So we can safely assume our answer will be a two-digit number. Step 2: Determine what multiple of 10 multiplied with 8 gets you closest to 256. Because 8 x 30 = 240, 8 goes into 256 30-something times. Step 3: Count how many eights are between 240 to 256. Two more eights will do the trick. So our final answer is 256 ÷ 8 = 32.

1% of x is 23

x = 2,300

10% of x is 430

x = 4,300