Multiplying and dividing fractions are definitely more abstract concepts then adding and subtracting fractions. However, they are quite simple in terms of actually solving the questions. Because the steps are significantly different from adding and subtracting, it can cause some difficulty. Therefore I like to ensure students have a solid grasp of adding and subtracting before transitioning to multiplication and division. In the Ontario Curriculum, students will begin to explore these concepts in grade 5 and the concepts will continue to be explored into grade 8 with increasingly more complex expectations surrounding the skill.
Here is a simple example of an activity that we did with a tutoring clients that consolidated fraction understanding.
When first introducing the skill, students should explore it through fractions that include: one-digit numbers and then two-digit numbers. To solve the question, you multiply the two numerators together and the two denominators together to get the answer.
1/3 x 2/6 = 2/18
2/12 x 2/10 = 4/120
The next step is exploring multiplying fractions with whole numbers. The key here is knowing that a whole number can be represented as the number over 1. Once rewritten, it then follows the same pattern.
1 x 1/2 =
1/1 x 1/2 = 1/2
The next step is to solve questions that have mixed numbers. There are multiple ways of solving these questions. One way of solving the question is to convert the fraction into an improper fraction. Once the fraction is converted to an improper fraction, it again follows the same pattern to solve.
1 1/2 x 3/4 =
3/2 x 3/4 = 9/8
When dividing fractions, the progression of difficulty is similar to multiplication. Dividing fractions is very abstract so we tend to focus my instruction on the numerical steps. When dividing fractions, we turn the division question into a multiplication question by using the KFC method. Then we solve the question, as we would a multiplication question. The KFC method has a catchy name that reminds us of three important steps.
We keep the first number the same.
1/2 ÷ 3/4 =
1/2 stays the same.
We flip the division symbol to multiplication
1/2 ÷ 3/4 =
1/2 x 3/4 =
We change the numerator to the denominator and the denominator to the numerator
1/2 ÷ 3/4 =
1/2 x 4/3 =
Solve the Question
With the KFC method complete, we have turned the question into a multiplication question. We can solve it by multiplying the numerators together and the denominators together.
1/2 x 4/3 = 4/6