Evaluate this expression. 22/18 − 29/30

Which fraction is closest in value to this expression?

1/6

1/7

2/7

2/5

9514 1404 393

  2/7

Step-by-step explanation:

The actual difference is ...

  22/18 -29/30 = 110/90 -87/90 = 23/90

One way to see which fraction is closest is to divide this value by the fraction and see which result is closest to 1. Of course dividing by a fraction is the same as multiplying by its inverse.

  23/90 × 5/2 = 23/36 . . . . about 2/3 or 6/9

  23/90 × 7/2 = 161/180 . . . about 8/9 -- very nearly 1

  23/90 × 7/1 = 161/90 . . . . about 1 7/9

The closest value to the difference is 2/7.

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You can also compare decimal values. Rounded to 3 decimal places, we have in increasing order ...

  1/7 ≈ 0.143

  1/6 ≈ 0.167 . . . . . . . differs by 0.089

  23/90 ≈ 0.256

  2/7 ≈ 0.286 . . . . . . differs by 0.030 -- closest value

  2/5 ≈ 0.400

tell you what. i'll find the length of the medians and you can fill in the blanks where they belong.

br

b = (2a,0)

r = (a/2,b/2) remember these things are medians. they go to the 1/2 way point of the line opposite the vertex they face.

br^2 =   (2a - a/2)^2 + (0 - b/2)^2

br^2 = (3/2 a) ^2 + b^2 / 4

br^2 = 9/4 a^2 + b^2 / 4   we need to find some relationship between a and b.

let's try ab = bc  

ab = 2a

bc = (2a - a)^2 + (b - 0)^2

bc = sqrt(a^2 + b^2)

ab = bc

2a = sqrt(a^2 + b^2) square both sides.

4a^2 = a^2 + b^2 subtract a^2 from both sides.

sqrt(3a^2) = sqrt(b^2)

sqrt(3)a = b

let's put b into br^2

br^2 = 9/4 a^2 + 3b^2 / 4

br^2 = 12 a^2 / 4

br^2 = 3a^2 

br = sqrt(3) * a

cp

c = (a,b) ; p = (a,0) this is another application of the distance formula, and it is a good one.

cp^2 = (a - a)^2 + (b - 0)^2

cp^2 = 0 + b^2

cp^2 = b^2 which you can see from the diagram. 

cp = sqrt(b^2)

cp = b but b = sqrt(3) * a 

cp = sqrt(3)*a

aq

a = (0,0)

q = (3/2) a, b/2

aq^2 = (3a/2 -0)^2 + (b/2 - 0)^2

aq^2 = 9a^2/4 + b^2/4

but b = sqrt(3) * a 

aq^2 = 9a^2 / 4 + (sqrt(3)*a)^2 /4

aq^2 = 9 a^2/ 4 + 3 a^2 / 4

aq^2 = 12 a^2/4

aq^2 = 3 a^2

aq = (sqrt  3) * a which agrees with the other two.