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

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