If two-thirds a equals one-half B, then a is equal to (three-quarters, four-thirds, or two-thirds) B

If two-thirds a equals one-half B, then a is equal to (three-quarters, four-thirds, or two-thirds) B

2/3a=1/2b
Multiply both sides by three
2a=3/2b
Divide two sides by two
a=3/4b
a:b=3/4
Choose three fourths

(- 1 / 2) + (+ 1 / 3) + (- 1 / 4) + (+ 1 / 9) + (+ 1 / 8) + (- 4 / 9)=

Original formula = (- 1 / 2) + (+ 1 / 3) + (- 1 / 4) + (+ 1 / 9) + (+ 1 / 8) + (- 4 / 9)
=[(+1/9)+(-4/9)]+(+1/3)+[(-1/2)+(-1/4)]+(+1/8)
=[-(4/9-1/9)]+(+1/3)+[-(1/2+1/4)]+(+1/8)
=[(-1/3)+(+1/3)]+[(-3/4)+(+1/8)]
=0+[-(3/4-1/8)]
=-(6/8-1/8)
=-5/8

1 / 2-1 + 1 / 3-1 / 2 +... + 1 / 9-1 / 8 + 1 / 10-1 / 9
All 3.14 - π are rational numbers

1 / 2-1 + 1 / 3-1 / 2 +... + 1 / 9-1 / 8 + 1 / 10-1 / 9
=1-1/2+1/2-1/3+…… +1/9-1/10
=1-1/10
=9/10
｜3.14-π｜ =π -3.14