What rule would work for multiplying mixed numbers?

Answer 1

You could use the FOIL method of multiplying two binomials.

To multiply two binomials (a + b) * (c + d), use FOIL (First, Outside, Inside, Last) to organize multiplication of all terms:

• First: a*c
• Outside: a*d
• Inside: b*c
• Last: b*d

Then add them together. Suppose you want to multiply 1 1/2 times 2 3/4. So write them as two binomials: (1 + 1/2) * (2 + 3/4) then multiply using FOIL:

1*2 + 1*(3/4) + (1/2)*2 + (1/2)*(3/4) = 2 + 3/4 + 1 + 3/8. Change 3/4 to 6/8, then add 3/8 to get 9/8, which simplifies to 1 1/8. Add to the other integers to get 2 + 1 + (1 + 1/8) = 4 1/8.

Note: you could also use some subtraction, for example if one of the terms is 5 15/16, instead of (5 + 15/16) if it's easier, you could represent it as the binomial (6 - 1/16), which is equal to the same number.