1 / 10 + 1 / 11 + 1 / 12 + 1 / 13 ····· + 1 / 19 to find the integral part

1 / 10 + 1 / 11 + 1 / 12 + 1 / 13 ····· + 1 / 19 to find the integral part

1 out of 10 = 0.1
One in eleven

What is the integral part of 1 / 10 + 1 / 11 + 1 / 12 +... + 1 / 19?

1

Find 1 △ (1 / 10 + 1 / 11 + 1 / 12 +...) +The integral part of (1 / 19)
With the method of expansion and contraction,

dengdeng~
Hypothesis (1 / 10 + 1 / 11 + 1 / 12 +...) +1 / 19) = t
So t is less than one tenth * 10 = 1
T greater than 1 / 19 * 10 = 10 / 19
So 1 ÷ (1 / 10 + 1 / 11 + 1 / 12 +...) +The integral part of (1 / 19)
Greater than 1 / 1 = 1
Less than 19 / 10 = 1.9
So the integer part is 1

|11 / 12-12 / 13 | + | 12 / 13-13 / 14 | + | 13 / 14-14 / 15 | + | 14 / 15-15 / 16 | simple operation

|11/12-12/13|+|12/13-13/14|+|13/14-14/15|+|14/15-15/16|
=12/13-11/12+13/14-12/13+14/15-13/14+15/16-14/15
=15/16-11/12

Calculation of 11 / 12 × 13 / 16 + 13 / 12 × 1 / 16 by simple method
It must be easy to use,

11/12×13/16+13/12×1/16 = (11*13)/(12*16)+(1*13)/(12*16)=12*13/(12*16)=13/16

How much is 5 / 6 times 1 / 4 plus 1 / 6 divided by 4

What is 5 / 6 times 1 / 4 plus 1 / 6 divided by 4
5/6×1/4+1/6÷4
=5/6×1/4+1/6×1/4
=（5/6+1/6）×1/4
=1×1/4
=1/4

29 times 27 out of 28

29×27/28＝﹙28+1﹚×27/28
＝28×27/28+27/28
＝27+27/28
= 27 and 27 / 28

Simple operation: nine and four fifths multiplied by 4.25 plus four and four quarters / 631 and three eighths multiplied by 72 and nine thirteenth divided by 31 and three eighths
It's 0.25 at six

[ (9+ 4/5) X 4.25 + (4+ 1/4) ] / 6
= [ (9+ 0.8) X 4.25 + 4.25 ] / 6
= [ 4.25 X (9.8 +1) ] / 6
= 4.25 X 10.8 / 6
= 4.25 X 1.8
= 8.5 X 0.9
= 8.5 - 0.85
= 7.5 + 0.15
= 7.65
(31+ 3/8) X (72+ 9/13) / (31+ 6/8) / 0.25
= (248/8 + 3/8) X (72+ 9/13) / (124/4 + 3/4) / (1/4)
= (251/ 8) X 9 X (8+ 1/13) / (127/ 4) / (1/4)
= (251/ 8) X 9 X (105/ 13) X (4/ 127) X 4
= (251 X 9 X 105 X 4 X 4) / (8 X 13 X 127)
There is no mistake. I can't see how to do it

A simple algorithm of (25% plus 3 / 8) multiplication (13 / 17 divided by 13 / 17 divided by 5 / 8)

(13/17*17/13*8/5)*(3/8+25%)=8/5*3/8+8/5*25% =3/5+8/5*1/4 = 3/5+2/5 ...

How to calculate 8.25 times 4.08 plus 0.75 times 4.08 plus 4.08

8.25 times 4.08 plus 0.75 times 4.08 plus 4.08
=4.08*（8.25+0.75+1）
=4.08*10
=40.8