Calculation: (1-half) x (1 + Half) x (1-third) x (1 + Third) x... X (1-tenth) x (1 + tenth)

Calculation: (1-half) x (1 + Half) x (1-third) x (1 + Third) x... X (1-tenth) x (1 + tenth)

=One in two, three in two, two in three, four in four, three in four 10 × 10 / 9 × 11 / 10
=1 / 2 × (3 / 2 × 2 / 3) × (4 / 3 × 3 / 4) × × (10 / 9 × 9 / 10) × 11 / 10
=1 / 2 × 11 / 10
=11 out of 20

The ratio of 1 / 2, 3 / 4, 5 / 6 and 5 / 4 is the external product

Although the external term of proportion is not invariable, that is to say, the proportion composed of 1 / 2, 3 / 4, 5 / 6 and 5 / 4 may be external term or internal term, but the product of two internal terms = the product of two external terms; therefore, the product of external terms is 5 / 8

What proportion can 1.5, 6, 10 and 12 make up? 2. What proportion can 1 / 2, 5 / 6, 1 / 3 and 1 / 5 make up?

The first question is, what's the ratio
5:6=10:12 5:10=6:12 6:5=12:10 10:5=12:6 10:12=5:6 6:12=5:10 12:10=6:5 12:6=10:5
The second question can be composed of the following proportions:
1/2:5/6=1/5:1/3 1/2:1/5=5/6:1/3 5/6:1/2=1/3:1/5 1/5:1/2=1/3:5/6 1/5:1/3=1/2:5/6 5/6:1/3=1/2:1/5 1/3:1/5=5/6:1/2 1/3:5/6=1/5：1/2

What is the internal product of the four numbers 4.5, 7.5, 1 / 2, 3 / 10?

4.5:7.5 = three tenths: one half
7.5 × half = 3.75

One half, two-thirds and four seventh plus a number to make up the proportion. How many situations do you think there are?
Please reply within one hour. The more answers, the better,

Let this number be
Situation 1
1/2:2/3=4/7:x
1/2x=8/21
x=16/21
Situation 2
1/2:2/3=x:4/7
2/3x=2/7
x=3/7
Situation 3
1/2:4/7=x:2/3
4/7x=1/3
x=7/12
So there are three cases: 16 / 21, 3 / 7, 7 / 12

If the four numbers 4.5, 7.5, 12 and 310 are proportioned, the product of their internal terms is ()
A. 1.35B. 3.75C. 33.75D. 2.25

In order to solve the problem conveniently, we first change 12 and 310 into decimals of 0.5 and 0.3 respectively

The product of the internal terms of 4, 2.5, 1 / 2 and 4 / 5 is ()

Hello,
4×1/2=4/5×2.5,
So the product of internal terms is 4 × 1 / 2 = 2
I hope my answer will help you

1 / 2 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42 + 1 / 56 =? In Chinese characters,

1/2+1/6+1/12+1/20+1/30+1/42+1/56=1/(2*3)+1/(3*4)+...+1/(7*8)=1-1/2+1/2-1/3+..1/7-1/8=1-1/8=7/8

One half + one sixth + one twelfth + one twentieth + one thirtieth + one forty second + one fifty sixth + one seventy-two
Urgent. I'll hand it in tomorrow. I want the simplest one

1/2=1/(1*2)=1-1/2 1/6=1/(2*3)=1/2-1/3 1/12=1/(3*4)=1/3-1/4 .1/72=1/(8*9)=1/8-1/9
So the original formula = 1-1 / 2 + 1 / 2-1 / 3 + 1 / 3-1 / 4 +... + 1 / 8-1 / 9 = 1-1 / 9 = 8 / 9

A simple method of 1 / 2 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42

1 / 2 + 1 / 6 + 1 / 12 + 1 / 20 + 1 / 30 + 1 / 42
=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+1/6-1/7
=1-1/7
=6/7