Teaching Mixed Numbers: How to Add and Subtract Mixed Numbers

Teaching Tips for Adding and Subtracting Mixed Numbers

Review Background Knowledge

Before tackling mixed numbers, students need to be at ease with several fraction concepts. The logical order in which to review them is as follows:

Denominators are names: Numerators tell how many parts there are; denominators name how many parts are in a whole. Examples: 1/2 is not the same as its denominator 2; 1/4 is not the same as 4; 1/2 and 1/4 are parts of a whole; 2 and 4 are whole numbers

Equivalent fractions: Fractions that look different but represent the same amount are equivalent (e.g., 1/2 = 2/4 = 4/8). If you multiply both a numerator and a denominator by the same number, you'll have an equivalent fraction; the same is true if you divide both numerator and denominator by the same number.

Adding and subtracting fractions: Fractions can be added only when the denominator (or name) is the same. If you want to add or subtract two fractions, you must change them to equivalent fractions with the same denominator.

Common denominators: If you had time, you could rewrite every fraction in the world so that they all had the same denominator (or name). The trick is to find one number, the common denominator, which can be divided by each and every one of the denominators.

Remainders in division: The remainder in a division problem may be written as a fraction. The remainder becomes the numerator and the divisor becomes the denominator.

Introduce New Concepts for Mixed Numbers

Teach each of these concepts in order, making sure the students fully understand before moving to the next one. Use as many illustrations as needed until the children fully comprehend.

Four Kinds of Numbers

Whole number: numbers without fractions, such as 3 or 10

Proper fraction: a fraction where the numerator is smaller than the denominator, like 3/10

Improper fraction: a fraction where the numerator is larger than the denominator, as in the case of 10/3

Mixed number: a combination of a whole number and a proper fraction, such as 3 1/3

Draw Improper Fractions

Help children to visualize improper fractions with circles; draw 4 for this illustration. Color 3 of the circles, divide the 4th one into 3 equal parts and color 1 part. State that you colored 3 1/3 circles.

Next, divide the first 3 circles into 1/3. Count all of the thirds (including the 1/3 colored in the 4th circle) and write '10/3.'

Convert Mixed Numbers to Improper Fractions

Using the circles above, you changed a mixed number (3 1/3) to an improper fraction (10/3). You could demonstrate every problem that way, by drawing pictures and counting parts.

A faster way is to multiply the whole number (3) by the denominator (also a 3) and add the numerator (1) to the answer: 3 x 3 = 9; 9 + 1 = 10. Write the 10 as the numerator, and keep the 3 as the denominator (10/3). Compare with the fraction you got as a result of drawing pictures and counting parts.

Change Improper Fractions to Mixed Numbers

Explain to your students that usually you don't want to leave a problem's final solution in the form of an improper fraction. You must be able to convert the improper fraction to a mixed number, by dividing the larger numerator by the smaller denominator. Example: convert 10/3, 10 ÷ 3 = 3 with a remainder of 1, or 3 1/3

Add and Subtract Mixed Numbers

The steps for adding and subtracting mixed numbers are:

1. Line up the whole numbers just as you would for any other addition or subtraction problem.
2. Keep the fractions with their whole numbers.
3. Change all of the fractions so they have common denominators, and rewrite the new mixed numbers to the right of the originals, like this:

5 1/3 = 5 2/6
3 1/6 = 3 1/6

Enter either the + or - sign for the problems. Draw the sum/difference line and do the math for the problem on the right:

If you were adding, the sum is 8 3/6. Reduce the fraction to the final answer of 8 1/2. If you subtracted, the difference is 2 1/6.

If the fraction in a sum is an improper fraction, show how you change the improper fraction to a mixed number, and then add the whole numbers together.

Make It Fun

To add a little spice, find stories, poems, jokes, songs or games for any or all of the concepts or have the children make up their own. For example, you might use the MathSmart Fraction card game or dominoes to help reinforce concepts in an entertaining way. A recording of the song Fraction Rock by Joe Crone can help students with equivalent fractions.

A helpful reference for you and other teachers is Painless Fractions by Alyece B. Cummings, a step-by-step guide for teaching fractions. Even worksheet problems are included.