Fractions - Multiplication and Division
Concept
- Fractions can be multiplied and divided just like whole numbers.
Theory
Multiplying fractions
Multiplication is simply addition done as many times as the number you need to multiply with. So if 2 x 4 = 2 + 2 +2 + 2, the same rules apply to fractions too.
1/2 x 4 = 1/2 + 1/2 + 1/2 + 1/2 = 2.
But what about if you have to multiply 1/3 x 12. That’s a lot of circles to draw. And what about multiplying 1/3 x 4/5.
A simple rule to multiply fractions:
- Multiply the numerators = new numerator
- Multiply the denominators = new denominator
- numerator / denominator = result.
In pictures ![[/concepts/attachments/fraction-multiplications.png]]
Sometimes you may not have a denominator - for example when you are multiplying by a whole number. But wait, you do - the denominator is 1. Because 4 is the same as 4/1.
Dividing fractions
To understand division you have to understand the concept of a reciprocal. The reciprocal of a/b is b/a. Flip the numerator and denominator and you have the reciprocal.
Let’s now use this concept to perform the following fraction division problem.
1/3 divided by 2 => 1/3 multiplied by 1/2 (reciprocal of 2/1) => 1/6 (answer)
So to divide fractions, you convert it to a multiplication problem and use the steps to multiply as before.
Common Misconceptions
- When multiplying a fraction, say 3/4 times 2, the learner might multiply both numerator and denominator by 2.
- Not remembering that 2 is the same as 2/1.