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Adding and Subtracting Fractions 3/5

In grade 5, students are asked to add and subtract fractions. This skill is also repeated in grade 5, 6, 7, and 8 with increasingly complex components. We will focus on 3 skills.

1. Adding fractions with the same denominator

Adding fractions requires the student to understand what the denominator represents and that what we are adding together are the parts that we have in each fraction. Going back and representing these fractions as drawings can be really powerful in terms of the student understanding how and why we do what we do.

The basic steps:

  • Add the numerators together

  • Keep the denominator the same

2. Subtracting fractions with the same denominator

Subtracting fractions requires the same conceptual understanding that is needed for adding fractions. Once your child understands adding fractions, the only thing that changes is that we subtract instead of add.

The basic steps:

  • Subtract the second numerator from the first numerator

  • Keep the denominator the same

3. Adding and Subtracting with different denominators

When the denominators are different, it definitely adds complexity to the question. Representing the fractions as drawings highlights why we need to add a step before adding or subtracting.

The basic steps:

  • Rewrite the fractions so that both fractions have the same denominator (easier said then done)

  • follow the steps for adding or subtracting

There are two different methods for rewriting fractions so they have the denominator.

  1. Cross Multiplying - this is the most common method and likely the method you are familiar with. It involves multiplying the denominators together to form a new denominator. You then have to multiply the numerator by the opposite denominator

For example:

4x3 = 12 (new denominator)

1x3 = 3 (new numerator)

1x4 = 4 (new numerator)

Then you find the sum of 3 and 4 which equals 7.

2. Drawing / Diagram - this is an excellent way to understand the 'why' behind the cross multiplying method. Why does it work?

By creating an array that is 4x3 you can easily represent both 1/4 and 1/3. Then count up how many parts are within one whole (in this case 12). That 12 is your new denominator. Then count up how many parts are shaded in on 1/4 (the answer 3) and how many parts are shaded in on 1/3 (the answer 4). Then add the two parts together (4+3=7) to get your new numerator. The answer is thus 7/12.

We also made an Instagram video that highlights how these two methods work.

We want students to understand the why and how of adding and subtracting fractions. Because multiplying and dividing have additional and different steps, students can become confused when switching back and forth between the skills. As a result, during tutoring we pursue mastery and automaticity with these steps. Taking breaks and revisiting the skill to ensure competency.

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