Multiplication with Fractions

Today's lesson was pretty easy! It was basically overview of simple multiplication only in a fraction form. Basically when multiplying two fractions together the product is made by just multiplying the two numerators together and the two denominators together.


For Example: a/b * c/d = a * c/b * d

• 3/4 * 1/3 = 3/12 <-- this is also known as 1/4 
• 2/5 * 1/3 = 2/15
• 3/2 * 1/4 = 3/8

Another way of showing this besides just doing it in your head is by making a grid and shading each fraction to get your answer. For instance, if you were using the equation 3/4 * 1/3 you would make a grid with 3 across and 4 down creating a grid of 12 boxes. This is because you base the grid off of the two denominators. (the first denominator is always the amount going down, the second is always the amount going across) Next you should shade in 3/4 of the grid (9 boxes), then you should shade in 1/3 of the boxes (4 boxes). This leaves exactly 3 out of the 12 boxes shaded by both fractions. That makes your answer 3/12.

 Through multiplication familiar property rules apply:

• closure: fraction * fraction = fraction
• commutative: a/b * c/d = c/d * a/b
• associative: (a/b * c/d) * e/f  = a/b * (c/d * e/f)
• distributive: a/b (c/d + or - e/f) = a/b * c/d + or - a/b * e/f
• inverse: for every fractions a/b, a & b do NOT = 0; there exists an b/a so that a/b * b/a = 1 (reciprocal) ---> practice the inverse operation
• identity: a/b * 1 = a/b * 1/1 = a/b