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Well 0.166666.... = 1/6. So 5.26666.... - 0.16666.... = 5.1 or 5 1/10. Now add 1/10 + 1/6 = 3/30 + 5/30 = 8/30 = 4/15. So as a mixed number it is 5 4/15, as an improper fraction 79/15.
There is a procedure for working out repeating decimals. The above method recognized what decimal represents 1/6, and found the entire decimal as combination of two fractions. Suppose you did not know what 1/6 was, but you know that 2/3 = 0.66666.... You can use that information. Divide both sides by 10: 2/30 = 0.066666.... So now you have 0.2 + 0.066666.... = 2/10 + 2/30 or 6/30 + 2/30 = 8/30 = 4/15, same as above.
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