To multiply the fractions 5 2/7, 5/8, and 3 1/2, we first need to convert the mixed fractions to improper fractions.
The first fraction is 5 2/7. To convert it to an improper fraction, multiply the whole number (5) by the denominator (7) and add the numerator (2). So, 5 x 7 + 2 = 37. The denominator remains the same, so the improper fraction is 37/7.
The second fraction is 5/8, which is already a fraction, so no conversion is needed.
The third fraction is 3 1/2. Convert it to an improper fraction by multiplying the whole number (3) by the denominator (2) and adding the numerator (1). So, 3 x 2 + 1 = 7. The denominator remains the same, so the improper fraction is 7/2.
Now we multiply the numerators (37 x 5 x 7) and the denominators (7 x 8 x 2) together.
37 x 5 x 7 = 1295
7 x 8 x 2 = 112
So, the multiplication of the fractions is 1295/112.
To simplify this fraction to its simplest form, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 1295 and 112 is 1. Therefore, the simplest form of the fraction is 1295/112.
If you have access to a scientific calculator, you may be able to use the "a b/c" key to find the simplest form of fractions. For example, to find the simplest form of 18/24, enter 18, press the "a b/c" key, enter 24, and then press the "=" key.