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Finding Common Denominators: Butterfly Method

Finding Common Denominators: Butterfly Method
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Are your students struggling with finding common denominators?

Have them place a copy of this step-by-step approach into their math notebook to help guide them through their work!

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Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
Interpret a fraction as division of the numerator by the denominator (𝘒/𝘣 = 𝘒 ÷ 𝘣). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, 𝘒/𝘣 + 𝘀/π˜₯ = (𝘒π˜₯ + 𝘣𝘀)/𝘣π˜₯.)
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