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The butterfly method is making equivalent fractions, just not obviously.

However, the different is that in making equivalent fractions you have to choose the new denominator (ideally this should be the lowest common multiple (LCM) of the denominators to avoid big numbers, but it doesn't have to be), whereas with the butterfly method the new denominator is always the product of the original two denominators.

For example: what is 3/4 + 1/8?

Using LCM:

lcm(4, 8) = 8

→ 3/4 = (3x2)/(4x2) = 6/8 (as 4 goes into 8 two times, multiply top and bottom by 2)

→ 1/8 stays the same as it already has 8 in the denominator

→ 3/4 + 1/8 = 6/8 + 1/8 = (6+1)/8 = 7/8

Using product of the denominators:

4x8 = 32

→ 3/4 = (3x8)/(4x8) = 24/32 (as 4 goes into 32 eight times, multiply top and bottom by 8)

→ 1/8 = (1x4)/(8x4) = 4/32 (as 8 goes into 32 four times, multiply top and bottom by 4)

→ 3/4 + 1/8 = 24/32 + 4/32 = (24+4)/32 = 28/32 = (7x4)/(8x4) = 7/8

Using the butterfly method:

Left antenna: 3x8 = 24

Right antenna: 4x1 = 4

Body: 4x8 = 32

Calculation: (24+4)/8 = 28/32 = (7x4)/(8x4) = 7/8

Which you should notice is the same as the last part of the equivalent fractions method when the product of the denominators is used.

Q: How is the butterfly method different from making equivalent fractions?

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Rational numbers can be expressed as fractions and fractions can be equivalent as for example 3/4 has the same value as 9/12

If you want to make it equivalent you would have to multiply by the same # both so that's how you multiply it. (If you multiply it you have to be making it equivalent)

If the denominators (bottom numbers) are not equal, making equivalent fractions of them so that the denominators are equal. With the denominators equal if the numerators (top numbers) are equal, then the fractions are equal.

Because you can't add or subtract fractions that have different denominators. Making them like fractions, by multiplying so the denominators are the same, you can add and/or subtract them.

The prefix "un-" in unlike fractions indicates that the fractions are not the same or not similar. It helps to highlight that the fractions have different denominators, making them distinct from each other.

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You convert them both to improper fractions by multiplying the denominators by the whole number and then adding the numerator to it. This number goes in the numerator and the denominator stays the same. Then you do this for the other fraction, making sure that the denominators of each fraction are equivalent. Then add the fractions as normal.

There are many equivalent fractions for 2/5, eg. 4/10, 10/25, 20/50. The rule for making an equivalent fraction is; 2/5 = 2x/5x, meaning just multiply the top and bottom by the same number.

Equivalent ratios are ratios that represent different numbers but the relationship between the numbers is same.

The sum of two fractions will only be a whole number if the fractions have a common denominator. When the denominators are different, the sum will be a fraction with a different denominator, making it impossible to be a whole number. Thus, estimating the sum of two fractions will generally result in a fraction, not a whole number.

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