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# Adding and subtracting fractions

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### Adding and subtracting fractions

1. 1. Adding and Subtracting Fractions
2. 2. Adding Fractions with common denominators
3. 3. 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
4. 4. Finding the Lowest Common Denominator <ul><li>The lowest common multiple of two numbers is the lowest number in BOTH lists of multiples </li></ul>Multiples of 2 are 2, 4, 6, 8, 10…… Multiples of 3 are 3, 6, 9, 12, ……… What is the lowest common multiple?
5. 5. Finding the Lowest Common Denominator <ul><li>The lowest common multiple of two numbers is the lowest number they will BOTH divide into </li></ul>2 divides into 2, 4, 6, 8….. 3 divides into 3, 6, 9…. What is the lowest number 2 and 3 both divide into?
6. 6. + The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths You can’t add fractions with different denominators Special form of 1 + +
7. 7. Lowest common denominator is 10 so make all fractions tenths
8. 8. Turn both fractions into twelfths
9. 9. What is the lowest number BOTH 3 and 7 divide into? Hmmmmm?????? It is 21. So that is my common denominator What special form of 1 will change 7 to 21. Hmmmm? It is 3/3 So I multiply 3/7 by 3/3 What special form of 1 will change 3 to 21. Hmmmm? It is 7/7 So I multiply 2/3 by 7/7 Now 3x3=9 and 2x7=14 Now I know the new numerators Finally the fractions are READY to add. I just have to add the numerators 9+14=23 +
10. 10. Adding Mixed Numbers <ul><li>Separate the fraction and the whole number sections, add them separately and recombine at the end </li></ul>