Why does the butterfly method work in math?

Answer 1

Oh, dude, the butterfly method, or the method of cross-multiplication, works in math because it's just a fancy way of multiplying fractions. When you're multiplying fractions, you're essentially multiplying the numerators together and the denominators together. So, the butterfly method is just a cool visual way to do that. It's like math's way of saying, "Hey, let's make multiplying fractions a bit more interesting."

Answer 2

The butterfly method, also known as the lattice method, works in math because it provides a structured way to multiply multi-digit numbers. By breaking down the multiplication process into smaller steps and organizing the partial products in a grid-like fashion, the butterfly method helps students keep track of their calculations and carry over the correct digits efficiently. This method is particularly useful for visual learners and can help improve understanding of place value and the multiplication algorithm.

Answer 3

Ah, the butterfly method in math is like a gentle dance of numbers. It works because it helps us break down complex multiplication problems into smaller, more manageable steps. Just like how a butterfly gracefully flutters from one flower to another, this method helps us flutter through numbers with ease and grace. Remember, there are many ways to solve a problem in math, and the butterfly method is just one beautiful option.

Answer 4

What the butterfly method does is to make the fractions equivalent fractions with a new denominator (bottom number) the product of the original denominators (bottom numbers). Then to compare/add/subtract the fractions, the numerators (top numerators) can be compared/added/subtracted.

Let the two fractions be a/b and c/d, then the new denominator is bd (b times d). Then the equivalent fractions are:

• a/b ⇒ (a x d)/(b x d) ⇒ ad/bd
• c/d ⇒ (b x c)/(b x d) ⇒ bc/bd