Middle School Math Huddle Fractions Review & Summary Factors and Multiples 1∙12 2∙6 3∙4 The key to fractions is understanding factors and multiples. 12______ 12 24 36 ______18______ 1∙18 18 2∙9 36 3∙6 54 The GCF of 12 and 18 is 6 The LCM of 12 and 18 is 36 The Greatest Common Factor (GCF) of two number is the largest number that is a factor of both. The Least Common Multiple (LCM) of two numbers is the smallest number that is a multiple of both Simplifying Fractions To simplify a fraction, find the GCF of the numerator and denominator and factor it out. Then cancel the common factor. 𝟏𝟐 𝟏𝟖 = 𝟔∙𝟐 𝟔∙𝟑 = 𝟐 𝟏𝟓 𝟑 𝟐𝟏 = 𝟑∙𝟓 𝟓 = 𝟑∙𝟕 𝟕 Adding and Subtracting Fraction To add or subtract fractions, find the LCM of the two denominators. Then multiply each fraction so that the LCM is the denominator of both. 𝟑 𝟏𝟐 𝟑 ∙ 𝟑 𝟑 𝟏𝟐 𝟗 𝟑𝟔 + + + 𝟒 𝟏 𝟏𝟖 𝟒 𝟒 𝟏 − 𝟔 𝟐 𝟑 𝟏 𝟏 𝟐 𝟏𝟖 𝟐 𝟑 𝟒 𝟔 𝟐 ∙ ∙ − ∙ 𝟖 𝟑 𝟑𝟔 𝟏𝟐 − 𝟏𝟕 𝟏 𝟑𝟔 𝟏𝟐 𝟐 𝟏𝟐 Multiplying and Dividing Fractions To multiply fractions, multiply the numerators and denominators. Simplify if possible. 𝟐 𝟑 𝟔 𝟑 𝟒 𝟏𝟐 ∙ = = 𝟏 𝟒 𝟐 𝟖 𝟐 𝟕 𝟑 𝟐𝟏 ∙ = To divide fractions, invert (flip) the second fraction and multiply. 𝟑 𝟖 𝟐 𝟑 𝟓 𝟏𝟓 𝟓 𝟖 𝟐 𝟏𝟔 ÷ = ∙ = Middle School Math Huddle Fraction Review Practice Pages Instructions: 1) Prepare a solution page by writing “Fraction Review” and your name at the top of the page. 2) For each problem: a) Number a space on your solution page and neatly copy the problem. b) Solve the problem on your White Board, showing all of the steps. c) Neatly copy your solution onto the solution page. d) Leave plenty of space for each problem and use extra pages as needed. Find the Least Common Multiple (LCM) 1) 10 12 2) 12 24 4) 7 8 5) 10 25 3) 4 11 6) 8 9 Simplify (be sure to show GCF and cancellation) 7) 10) 𝟔 8) 𝟖 𝟏𝟒 𝟒𝟐 𝟏𝟓 𝟗 9) 𝟏𝟖 11) 𝟏𝟎 14) 𝟏 𝟐𝟕 𝟏𝟐 12) 𝟓𝟎 𝟖 Find the sum or difference: 13) 𝟏 16) 𝟒 𝟑 𝟗 + − 𝟐 𝟓 𝟏 𝟔 17) 𝟐 − 𝟓 𝟏𝟐 𝟏 𝟑 + 𝟓 𝟏𝟎 15) 𝟑 18) 𝟒 21) 𝟑 𝟏 𝟒 𝟗 + − Find the product or quotient: 19) 𝟒 𝟑 ∙ 𝟗 𝟓 20) 𝟓 𝟖 ÷ 𝟑 𝟒 ∙ 𝟕 𝟐 𝟏 𝟖 𝟏 𝟔