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**Adding and Subtracting Fractions**

By Graeme Henchel

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**Adding Fractions with common denominators**

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**Adding Fractions with different denominators**

Problem: You can’t add fractions with different denominators without getting them ready first. They will be ready to add when they have common denominators Solution: Turn fractions into equivalent fractions with a common denominator that is find the Lowest Common Multiple (LCM) of the two denominators

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**Finding the Lowest Common Denominator**

The lowest common multiple of two numbers is the lowest number in BOTH lists of multiples Multiples of 2 are 2, 4, 6, 8, 10…… Multiples of 3 are 3, 6, 9, 12, ……… What is the lowest common multiple?

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**Finding the Lowest Common Denominator**

The lowest common multiple of two numbers is the lowest number they will BOTH divide into 2 divides into 2, 4, 6, 8….. 3 divides into 3, 6, 9…. What is the lowest number 2 and 3 both divide into?

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**You can’t add fractions with different denominators**

+ The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths Special form of 1

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**Lowest common denominator is 10 so make all fractions tenths**

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**Turn both fractions into twelfths**

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**What is the lowest number BOTH 3 and 7 divide into?**

Finally the fractions are READY to add. I just have to add the numerators 9+14=23 It is 3/3 So I multiply 3/7 by 3/3 It is 7/7 So I multiply 2/3 by 7/7 What is the lowest number BOTH 3 and 7 divide into? Hmmmmm?????? What special form of 1 will change 7 to 21. Hmmmm? What special form of 1 will change 3 to 21. Hmmmm? It is 21. So that is my common denominator Now 3x3=9 and 2x7=14 Now I know the new numerators

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Adding Mixed Numbers Separate the fraction and the whole number sections, add them separately and recombine at the end

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Mixed Number to Improper - Multiply, Add, Put over Denominator (MAD - Makes a circle) 4 ½ 9292 Improper to Mixed Number - Divide Numerator by denominator.

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