The butterfly method of adding fractions is a useful trick that children can use when they first learn how to add bits.
It can be unclear to be faced with two fractions and asked to add them together since they look so different from normal integers.
The butterfly method can be a good place for children to start when adding fractions. But, eventually, they can no longer need it as their maths skills develop.
Adding fractions: butterfly method
Before children can add fractions with the butterfly method, they must understand what the numerator is and what the denominator is.
The numerator is the top number of the fraction. It shows how many individual parts are out of the total number of factors. For example, in the fraction ⅖, the numerator is 2, indicating that there are two parts out of a total of 5.
The denominator is the bottom number of the fraction below the line. It shows how many parts there are in total. Using the example above, the denominator of ⅖ is 5. This indicates that there are five parts in total.
Here are the steps for adding fractions using the butterfly method:
- Multiply the numerators and denominators diagonally.
- Add the product of the diagonal pairs of numerators and denominators together. This creates the new numerator.
- Multiply the denominators by each other. This creates a new denominator.
- Simplify the fraction if possible.
Pros and cons of using the butterfly method when adding fractions
Pros
- It is an easy way to introduce children to the concept of adding fractions
- The steps are easy to learn
- The butterfly method includes a handy visual that can help children to remember how to use it
Cons
- Children might memorize the butterfly method without really learning how to add fractions – it doesn’t develop a conceptual understanding or fluency
- It can make adding algebraic fractions much more complicated
- The butterfly method only works for pairs of fractions
- Children need to learn how to add fractions by changing the fractions to equivalent fractions with the same denominator
- It doesn’t work for subtracting fractions
