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Solve `3/10 - (-5/8).`

When subtracting fractions find the least common denominator. (The lowest multiple of 8 and 10.  This is 40.

Rewrite equivalent fractions as 40th's.

`3/10 = 12/40`

`5/8 = 25/40`

Subtraction means to add the opposite therefore we will rewrite as:

`12/40 + (25/40)` = `37/40`

The solution is `37/40.`

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`3/10 -(-5/8) =3/10 +5/8 =3/(2*5) +5/(2*4) =(3*4)/(2*4*5) +(5*5)/(2*4*5) =(12+25)/40 =37/40`

First step in solving is to observe the sign rule: two minus signs make one plus sign. Then we decompose the numbers under the line (the different denominators) of fractions in such a way as to observe their common multiple. Third step is to bring to a common multiple the numbers under the fraction line (the denominators) by amplifying both fractions with the missing terms. Thus we can consider we have a single fraction with an addition sign in the numerator. Last step is to add the numbers above the line of fraction to obtain the numerator of the fraction.

Answer: 3/10 -(-5/8) =37/40

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