Fraction Operations Nichole Kurtz “The hardest part of math last week was multiplication quiz.” - Student 1 Fraction Operations Nichole Kurtz

Once upon a time, in a far away math classroom, there was a little girl named Amy who struggled with fractions…

She decided to write a letter to her favorite fourth grade teacher because she knew Mrs. Jones would help. Her first letter said,

Dear Mrs. Jones, Today in class we reviewed addition and subtraction of fractions. Mrs. Smith said + does not equal . If 4 +8 =12, why is this not true? - Amy

Dear Amy, I’m so glad to hear from you! That is a great question! It is true that 4 + 8 = 12, but with fractions it works a little differently. Remember you need a common denominator.

+ = Think of it as separate pieces of a pie. is equivalent to and can stay the same. So, + = - Mrs. Jones

Dear Mrs. Jones, I’m still confused. How do I find a common denominator? - Amy

Dear Amy, Do you remember when we found the least common multiple between two numbers? Let’s look at the numbers 4 and 6. List all of the multiples of each, then choose the smallest.

Multiples of 4: 8, 12, 16, 20… Multiples of 6: 12, 18, 24, 30 Multiples of 4: 8, 12, 16, 20… Multiples of 6: 12, 18, 24, 30... The LCM of 4 and 6 is 12. So, if you want to add and , the common denominator is 12. - Mrs. Jones

Dear Mrs. Jones, Does it work the same with subtraction? My teacher said - = . How can this be true? - Amy

Dear Amy, Yes, you still need to find the LCM for the denominator, then subtract the numerators. or - = - Mrs. Jones

Dear Mrs. Jones, Thank you! That makes sense. Now I have a question about a division problem. It asks what is / ? How do I know which fraction to flip? - Amy

Dear Amy, Remember to flip the second fraction and multiply. It would look like this: x Then, you would multiply straight across. So, 1 x 6 = 6 and 2 x 1 = 2. Then, 6 / 2 = 3. - Mrs. Jones

Dear Mrs. Jones, I am really starting to understand this! I also have a question about reciprocals. My teacher said I need to find the reciprocal of . What does this mean? - Amy

Dear Amy, That is a very good question. You need to find a number that you can multiply by to get 1. The reciprocal would be because x = = 1. - Mrs. Jones

Dear Mrs. Jones, Oh! That is easier than I thought. You have helped me so much! When would I ever really use this kind of math in real life, though? - Amy

Dear Amy, You might be surprised to know that there are many uses for this kind of math. If you want to bake a pie, you might need to multiply or divide fractions to get the recipe right!

Fractions can also be written in different forms, such as decimals and percents. For example, is the same as 0.25 and 25%!

We use decimals everyday with money, and stores use percentages during sales. Keep practicing and working hard! You’re doing great! - Mrs. Jones

Glossary Fraction – A number that names a part or set of a region Denominator – The bottom number in a fraction Equivalent Fractions – Two (or more) fractions representing the same value

Glossary Least Common Multiple – The smallest number that can be evenly divided by both integers Numerator – The top number in a fraction. Reciprocal – Two numbers whose product (in multiplication) is 1.

Glossary Decimal – A number in the base 10 system Percent – A ratio comparing a number to 100

Textbook Reference Foresman, S. (1999). Middle school math. Addison Wesley Longman, Inc.