The Butterfly Method for Fractions with adding subtracting, dividing Flashcards

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The butterfly method, also known as the cross-multiplication method or the Chinese method, is used for multiplying or dividing fractions. The method involves creating a butterfly-like diagram where the numerators and denominators of the fractions are crossed and multiplied diagonally.

The butterfly method is a helpful technique for performing multiplication and division of fractions using mental math. Here are some tips for using the butterfly method with mental math:

1. Simplify the fractions before starting: If possible, simplify the fractions before using the butterfly method. For example, if you are multiplying 2/3 by 6/8, you can simplify 6/8 to 3/4 before using the butterfly method.
2. Use mental multiplication tricks: There are many mental math tricks for multiplying numbers quickly. For example, you can use the distributive property (a x (b + c) = a x b + a x c) to break down one of the fractions into smaller parts. You can also use multiplication tables or mental multiplication strategies such as doubling and halving.
3. Cross-cancel common factors: If the numerator of one fraction is divisible by the denominator of the other fraction, you can cross-cancel the common factor before multiplying. For example, if you are multiplying 2/3 by 6/8, you can cross-cancel the factor of 2 to get 1/3 x 3/4.
4. Simplify as you go: Simplify the product of each diagonal multiplication as you go along. For example, if you are multiplying 2/3 by 6/8, you can simplify 2/8 to 1/4 as you multiply diagonally.
5. Check your answer: After completing the multiplication or division, check your answer by simplifying it to its lowest terms or verifying that it makes sense in the context of the problem.

Here is an example of using the butterfly method for multiplication with mental math:

2/3 x 6/8

Step 1: Simplify the fractions (if possible):

2/3 x 3/4

Step 2: Use mental multiplication tricks:

2 x 3 = 6

3 x 4 = 12

Step 3: Cross-cancel common factors:

2/3 x 3/4 = 1/3 x 1/4

Step 4: Simplify as you go:

1/3 x 1/4 = 1/12

Step 5: Check your answer:

1/12 is already in its lowest terms, so we’re done. The final answer is 2/3 x 6/8 = 1/12.