3/8 × 4/9
First, let's see if they can cancel out. Nope. 3 and 8 have no common factors, and neither do 4 and 9.
When you're multiplying fractions together, you can switch out the numerators and denominators (if it helps you visualize things more easily. You won't need to do this step with some practice).
3/8 × 4/9 =
3/9 × 4/8 =
Now three 3 and 9 both have a common factor of 3. Divide them both by that common factor, top and bottom.
3/9 × 4/8 = //Comment: 3 ÷ 3 = 1, 9 ÷ 3 = 3.
1/3 × 4/8 =
4 and 8 likewise have a common factor, but of 4. Divide them both by that common factor. Remember, what you divide or multiply from the top, must also be done with the bottom and vice version. This way it will cancel out.
1/3 × 4/8 = //Comment: 4 ÷ 4 = 1, 8 ÷ 4 = 2.
1/3 × 1/2 =
Now multiply the numerators to each other, and the denominators to each other.
1/3 × 1/2 =
(1 × 1)/(3 × 2) =
1/(3 × 2) =
1/6
That is your answer. To check, we can do the opposite operation. In this case, you can divide the answer by either of the two original fractions and you should get the other. That's a little more advanced though, but a quick and easy way to convert from fraction division to fraction multiplication is to invert the fraction and the division sign to a multiplication sign.
1/6 ÷ 3/8 = 4/9 //Comment: Invert fraction and division sign.
1/6 × 8/3 = 4/9 //Can we cancel out any thing?
1/3 × 8/6 = 4/9
8 and 6 have a common factor of 2. Divide both by that factor.
1/3 × 8/6 = 4/9 //Comment: 8 ÷ 2 = 4, 6 ÷ 2 = 3
1/3 × 4/3 = 4/9
Multiply the numerators together and the denominators together.
1/3 × 4/3 = 4/9
(1 × 4)/(3 × 3) = 4/9
4/(3 × 3) = 4/9
4/9 = 4/9
4/9 = 4/9 which is true. If you like, try it out with 1/6 ÷ 4/9 :)
