why can you not do this?

You also need to multiply 3 x 1/4, and 1/3 x 5.

So that is 3/4 and 5/3. When you add those to 15 1/12, you get the correct answer

15 & 1/12 + 3/4 + 5/3 = 17 & 1/2

3 1/3 can be written as 3 + 1/3

5 1/4 can be written as 5 + 1/4

When you multiply them together, you get:

(3 + 1/3)(5 + 1/4)

Note that this needs to be foiled out. Doing so gets you this:

3*5 + 3*1/4 + 1/3*5 + 1/3*1/4

15 + 3/4 + 5/3 + 1/12

35/2

It does NOT get you this:

3*5 + 1/3*1/4

(3⅓)(5¼) = (3 + ⅓)(5 + ¼)

By the distributive rule,

(3 + ⅓)(5 + ¼) = 3×5 + ⅓×5 + 3×¼ + ⅓×¼ = 15 + 5/3 + 3/4 + 1/12 = 17.5

3 1/3 x 5 1/4

When performing math operations

on proper fractions, first convert the

proper fractions to improper fractions.

3 1/3 = 10/3

5 1/4 = 21/4

Multiplying the numerators,

10 x 21 = 210

Multiplying the denominators,

3 x 4 = 12

Putting them together,

210/12

Converting back to proper fractions,

17 1/2

¯¯¯¯¯

3 1/3 is (3+1/3)

5 1/4 is (5 + 1/4)

(3+1/3)(5+1/4) now you must foil.

3*5+3*1/4+1/3*5+1/4*1/3=35/2

Or you could expand the fractions.

3 1/3=10/3

5 1/4= 21/4

10/3*21/4=210/12 reduces to 35/2.

Hope this clarifies :)