Adding & Subtracting Fractions & Mixed Numbers with regrouping

First………let’s remember this ……

How to change a mixed number to an improper fraction 1 9 Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. + 4 = x 2 2

Change this mixed number to an improper fraction 2 20 Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. + 6 = x 3 3

Change this mixed number to an improper fraction 2 17 Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. + 3 = x 5 5

Excellent!!!! Let’s keep moving…….

Adding Mixed Numbers Find the sum. 4 9 1 1 9 + 3 5 9 4 Rewrite the fraction using LCD if denominators are different. 4 9 1 1 9 2. Add or subtract the fractions, then the whole numbers. + 3 3. Simplify if possible. 5 9 4 In this problem, the denominators are the same, so begin with step 2.

Let’s Do More Examples! Find the sum. 7 8 4 9 4 1 1 4 2 1 3 3 5 3 = = + + 8 9 X 2 X 3 1 8 9 8 7 9 9 = 1 4 1 8 10 Add the whole numbers.

Subtracting Mixed Numbers Find the Difference. X 6 3 4 18 7 8 17 20 = 10 3 1 24 X 6 1 8 1 8 1 6 X 4 3 5 X 4 12 4 = 4 = 1 1 - - - 24 20 X 4 X 4 6 8 3 4 5 20 1 4 14 24 7 12 = 6 = 2 = 3 4 7 12 6 2

Now You Try! Find the sum or difference. 3 5 10 6 5 6 10 3 = 4 = 12 10 X 2 10 6 5 6 10 3 = 4 = 12 X 2 9 10 1 12 7 1 + - 15 10 5 10 1 2 3 4 9 12 10 = 1 = 3 = 1 2 3 4 11 3

just like you would with whole numbers. What if I’m supposed to subtract a larger fraction from a smaller fraction?_________ _______________________ Regroup just like you would with whole numbers. 6 + + 9 8 9 7 1 8 13 9 1 4 9 1 10 x x 3 8 - 3 7 9 4 - 6 8 5 6 9 2 3 3 3 3 4 5 = =

Can you regroup with unlike denominators? Sure, but first find the LCD and equivalent fractions. 8 x 7 2 3 21 14 35 21 1 9 x 7 Watch this! 21 5 7 x 3 15 5 - x 3 20 21 3

Let’s see that again! Remember, first find the LCD and equivalent fractions. 5 x 4 2 5 20 8 28 20 1 6 x 4 20 3 4 x 5 15 3 Watch this! - x 5 13 20 2

Then regroup as we have before! Remember to simplify if you need to. How about these! If you have a whole number, make a fraction with 0 in the numerator and the same denominator the mixed number has. 5 8 8 8 7 7 6 1 1 9 3 2 8 4 7 - 5 - 2 6 8 2 3 4 3 3 7 = Then regroup as we have before! Remember to simplify if you need to.

Now, you try!!!! 6 2 8 10 8 9 7 1 4 1 4 6 12 18 30 18 = = 1 10 = = 3 8 3 8 - 3 7 9 14 18 4 = - = 8 9 7 8 5 16 18 5 3 =

Remember, you can also convert each mixed number into an improper fraction and use the butterfly method.