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Grade 4-5 · Fractions · Adding unlike denominators

Butterfly method for adding fractions

0:18 video · Watch on YouTube

2/3 + 1/4 = 11/12. With the butterfly method you multiply across the "wings" (2 x 4 = 8 and 3 x 1 = 3), add them to get the top (8 + 3 = 11), and multiply the denominators for the bottom (3 x 4 = 12).

The butterfly method is a shortcut for finding a common denominator. It works for any two fractions, but the answer may need simplifying at the end, so always check whether the top and bottom share a factor.

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The question, solved step by step

2/3 + 1/4 = ?

  1. Write the fractions side by side: 2/3 and 1/4.
  2. Draw the first wing: multiply the top of 2/3 by the bottom of 1/4. 2 x 4 = 8.
  3. Draw the second wing: multiply the bottom of 2/3 by the top of 1/4. 3 x 1 = 3.
  4. Add the wings to get the new top: 8 + 3 = 11.
  5. Draw the body: multiply the two bottoms. 3 x 4 = 12.
  6. Write the answer: 11/12. It cannot be simplified.

Answer

2/3 + 1/4 = 11/12

The common mistake

Adding the tops and the bottoms: 2/3 + 1/4 = 3/7. A quick check shows it is wrong, because 2/3 is already more than one half and 3/7 is less than one half.

Parent tip

After each answer, ask your child: is this about the size I expected? 2/3 is a bit more than 1/2 and 1/4 is a little, so the total should be a bit under 1. 11/12 fits.

Video transcript

0:00Add fractions the butterfly way! Two thirds plus one fourth.

0:04Draw the wings. Two times four is eight. Three times one is three.

0:09Add them up, eleven. Now the body. Three times four is twelve.

0:14Eleven twelfths!

0:15Now you try one half plus two fifths!

Questions parents ask

How do you add fractions with the butterfly method?

Multiply diagonally to make two "wings", then add the wings for the new numerator. Multiply the two denominators for the new denominator. For 2/3 + 1/4, the wings are 2 x 4 = 8 and 3 x 1 = 3, so the answer is (8 + 3)/12 = 11/12.

Does the butterfly method work for subtracting fractions?

Yes. Make the wings the same way, but subtract instead of add. For 2/3 - 1/4, the wings are 8 and 3, and 8 - 3 = 5, so the answer is 5/12. Keep the first fraction on the left so the wings are subtracted in the right order.

Do you always have to simplify after the butterfly method?

Not always, but check every time. The method multiplies the denominators, so the result can be reducible. For example, 1/2 + 1/6 gives 8/12, which simplifies to 2/3. If the top and bottom share a factor, divide both by it.

What is 1/2 + 2/5 with the butterfly method?

The wings are 1 x 5 = 5 and 2 x 2 = 4. Add them: 5 + 4 = 9. The body is 2 x 5 = 10. So 1/2 + 2/5 = 9/10. This is the practice question from the video.

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