Adding Fractions:

Gaining facility in adding fractions is the first step in mastering all the fractional operations: addition, subtractions, multiplication and division.

Probably starting in fourth grade math, and then receiving strong emphasis in fifth grade math and sixth grade math, your child learned the operations for fractions.

That is, how to do the four arithmetic operations of addition, subtraction, multiplication and division with fractions, or with combinations of fractions, mixed numbers and whole numbers.

The next step, and this topic is addressed throughout the middle school years, is Applications of Fractions. That means understanding when to use the different operations in the context of real life fractions situations.

This page is focusing solely on the real-life application of adding fractions.

If your upper elementary or middle school child really doesn’t know the fraction operations of addition confidently, and doesn't know how or when to get a common denominator, you really need to work with him first on learning these basic steps. (Scroll down to the end of this article to see my TOP recommended fractions practice materials!)

OK, so assuming your child knows how to do operations with fractions pretty well, let’s look at the applications. The real trick for this is recognizing the English words that point to the given operation. Another way to look at it is, recognizing the typical situations that relate to a given operation.

Here's a simple problem involving adding fractions to see if your child knows how to compute:

• Judy babysat for the Miller’s for 1 1/2 hours and for the Carbuncle’s for 2 3/4 hours, how many hours did she babysit all together?

1 2/4 hours + 2 3/4 hours (get common denominator)

3 5/4 hours (add the whole numbers and add the numerators)

4 1/4 hours (make it a proper fraction)

How is your child supposed to know to add fractions to solve this problem? Looking at the language, the key phrase is “all together,” that suggests grouping or joining or adding together.

Looking at the concept of the problem, two separate things are going to be viewed as a whole. Judy’s separate babysitting jobs are going to be viewed as one group of hours.

That is the addition concept.

Here are some other examples showing some varieties of wording.

• Billy Bob bought a 7 1/2 pound bag of cement and a 1 3/4 pound tub of Spackle at the Home Depot. When he carried it out to his pick-up truck, how much weight was he carrying?

Here, we didn’t put in the words, “all together” but the idea is the exact same and it’s still addition. You would add the two separate weights to get the total, which would be the answer.

• Eugene owned 3 pieces of property. One was 1 3/4 acres, one was 2 7/10 acres, one was 1 1/2 acres. How much property did Eugene own?

If your child can't, unassisted, accurately compute the simple adding fractions problems I've given above, it's time for you to take action!

Your child needs help understanding the basics of adding fractions.

This is not necessarily a sign of a learning difficulty, but more likely that your child's teacher never spent enough time teaching and practicing adding fractions.

(I consider that a math education crime! Your child was robbed of the opportunity of practicing this skill in the classroom, until mastery was reached. Adding fractions is a vital math skill that will be used over and over in middle school math and high school math.)

It takes weeks of incremental skills development and practice to gain facility with adding fractions!!! Did your child's teacher give him that? (You may be interested to read about some of the problems in today's American Math education to learn more about this phenomenon.)

To help your child bridge his or her knowledge gap, here are my TOP RECOMMENDED practice books for you to use with your child.

I only recommend products that I have used successfully in my classrooms, and in my own home with my children. (Cost matters too. We can buy good math practice books and tools without breaking the bank!)

For 4th Grade Math Practice:

• Kumon 4th grade math practice books are well presented and organized. At $6.95, its a great value compared to other math workbooks!
• For homeschoolers and those interested in more intense math practice at home: I would recommend this Saxon Publishing 4th grade math practice book. I have not only successfully used the Saxon materials in the classroom, but I have contributed and edited a text book for them. Their math materials are superior!
• And, I'm positive your children will love these as much as mine do. These fun fractions tiles will help visually demonstrate the operation of adding fractions. Use them as you're working out fractions problems together with your child.

• Kumon 5th grade math practice books are tops for zeroing in on one skill and working on incremental fractions skill development. At only $6.95 (and eligible for FREE Shipping from amazon.com) they are a real bargain!
• For Homeschoolers and parents who want more intense at-home math practice, you should consider the practice books and products in Saxon Math's excellent series of math instruction books.

• Kumon 6th grade math practice booksare tops for zeroing in on one skill and working on incremental fractions skill development. At only $6.95 (and eligible for FREE Shipping from amazon.com) they are a real bargain!
• For Homeschoolers and parents who want more intense at-home math practice, you should consider the practice books and products in Saxon Math's excellent series of math instruction books.