If you’re working on adding and subtracting fractions with your students, make sure that you’re using various strategies. It’s important to show students how to use visual models in addition to the standard algorithm.
In 4th grade, students mostly work on adding and subtracting fractions with like denominators.
By 5th grade, unlike denominators are used for adding and subtracting both fractions and mixed numbers.
Creating a fraction model is important in showing students why they only add or subtract the numerators instead of the denominators.
Adding with like denominators
In the example image below with like denominators, students would create a rectangle to represent one whole with columns to show how many pieces are in the whole. In the addition example, the fractions being added are out of ninths, so they would create a single rectangle with 9 columns. To represent the first fraction, they would shade in 3 of the 9 columns using one color, and then can use the same or a different color to shade in 1 more column to represent the 1/9 being added. Once these two are shaded in, the model now has 4/9 shaded.
Subtracting with like denominators
In the subtraction example, students would create a rectangle with 12 columns, shading in 11 of them to represent 11/12. To subtract 4/12 from this, they cross out 4 of the 11 shaded pieces. The number of shaded columns that remain would be the difference. In this case, the answer is 7/12.
Adding with Unlike denominators
To add fractions with unlike denominators using a visual model, you would first create models to represent each of the fractions, then find equivalent fractions with the same denominator. To do this, you have to find the least common multiple of the two fractions and then use the LCM as their common denominator.
In the example problem below, the LCD of 1/4 and 3/5 is 20. Each fraction model will need to have 20 pieces. The first fraction (1/4) has 4 columns, so we need to split the 4 columns into 5 rows in order to make 20 pieces. The second fraction (3/5) has 5 columns, so you would need to create 4 rows in order to have 20 total pieces. Now we can see the equivalent fractions for each of the original fractions: 1/4 = 5/20 and 3/5 = 12/20. Finally, add the equivalent fractions to get a final answer of 17/20.
Subtracting with Unlike denominators
To subtract two fractions with unlike denominators, start by creating fraction models for each fraction in the problem. They need to have a common denominator, so find the least common multiple of both denominators.
For 4/5 and 1/3, the LCM is 15, so the common denominator is 15. Next, create equivalent fractions using the common denominator. The first fraction (4/5) has 5 columns, so we need to create 3 rows in order to have 15 pieces. The second fraction (1/3) needs to have 5 rows. The first fraction now has 12 of the 15 pieces shaded (12/15). We will need to subtract the number of pieces in the second fraction model from the first. To do this, cross out 5 of the 12 shaded pieces. The remaining shaded columns that are not crossed out is the answer: 7/15.
When using the standard algorithm to find the sum or difference of two fractions with unlike denominators, I teach my students to write their original fractions vertically. The reason I teach it this way, is because I like them to get the visual of creating their equivalent fractions to the side and to show what they’re multiplying both the numerator and denominator by to get the equivalent fractions.
Again, students will need to:
- Find the least common multiple of each fraction to find the common denominator.
- Create equivalent fractions.
- Determine what to multiply the denominator in the original fraction by to get the common denominator.
- Multiply the numerator by the same number as in step 3 (I like to draw an arrow from the original fraction to the equivalent fraction and show the multiplication in-between. It also helps with checking for student errors.)
- Add or subtract the equivalent fractions.
Creating consistent strategies for adding and subtracting fractions will help your students to gain a strong understanding of the skill. While they may not like showing their work, it’s very important for them to do so in order for you, as the teacher, to determine any misconceptions they may develop and intervene when necessary.
- adding the numerator AND the denominator of two fractions
- multiplying the denominators of both fractions to find the least common denominator, instead of finding their LEAST common multiple (while this isn’t wrong, it can create the need to simplify the answer at the end more frequently)
Need a Resource?
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