To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50] and the first few multiples of 7 are [7, 14, 21, 28, 35, 42, 49, 56, 63, 70]. The first few multiples they share are [35, 70] making 35 the smallest multiple 5 and 7 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{7 x 7}{5 x 7} \) + \( \frac{8 x 5}{7 x 5} \)

\( \frac{49}{35} \) + \( \frac{40}{35} \)

Now, because the fractions share a common denominator, you can add them:

\( \frac{49 + 40}{35} \) = \( \frac{89}{35} \) = 2\(\frac{19}{35}\)

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{2 x 2}{6 x 2} \) - \( \frac{4 x 1}{12 x 1} \)

\( \frac{4}{12} \) - \( \frac{4}{12} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{4 - 4}{12} \) = \( \frac{0}{12} \) =

The greatest common factor (GCF) is the greatest factor that divides two integers.

To raise a term with an exponent to another exponent, retain the base and multiply the exponents:

To simplify this fraction, first find the greatest common factor between them. The factors of 20 are [1, 2, 4, 5, 10, 20] and the factors of 60 are [1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60]. They share 6 factors [1, 2, 4, 5, 10, 20] making 20 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{20}{60} \) = \( \frac{\frac{20}{20}}{\frac{60}{20}} \) = \( \frac{1}{3} \)