Rule of Four: Adding and Subtracting Fractions

Lesson Plan - Get It!

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Just like the number of seasons in a year or the number of years a president serves, the number 4 shows up all around us.

• And guess what?

It even plays a big role when discussing fractions through the Rule of Four!

Remember that a fraction is a way to show part of a whole. You’ll see it written as a number on top (the numerator) and a number on the bottom (the denominator).

Check out this example.

Here, 1 is the numerator, and 4 is the denominator. The denominator tells you how many equal parts make up the whole, while the numerator tells you how many of those parts you have.

Keep an eye on the denominator because it becomes important when adding and subtracting fractions!

Imagine you had two fractions, and you wanted to add them together, like these pieces of kiwi pie.

Here’s what happens.

That is one whole pie!

You simply added the numerators (1 + 2 = 3), and since the denominators were already the same (3), they stayed that way. Fractions with the same denominator are called like fractions.

• But what happens when your fractions have different denominators?

Figure it out using this example.

Since the denominators aren’t the same, you can’t just add them together.

But don’t worry! The Rule of Four is here to help with four easy steps for adding unlike fractions.

Step 1: Find the Least Common Denominator (LCD)

Start by listing the multiples of each denominator. In this case, the multiples of 3 and 5.

3: 3, 6, 9, 12, 15...

5: 5, 10, 15...

The least common multiple (LCM) here is 15.

Step 2: Convert Each Fraction to the LCD

Now, convert each fraction so they have the same denominator.

Remember, you can multiply each fraction by a form of one (like ²/₂ or ³/₃) to keep its value the same.

You can multiply ²/₃ by ⁵/₅ to equal ¹⁰/₁₅.

You can multiply ¹/₅ by ³/₃ to equal ³/₁₅.

Now, both fractions have like denominators.

Step 3: Add the Numerators and Keep the Denominator

Step 4: Simplify the Answer

Lastly, see if you can simplify your answer.

In this case, ¹³/₁₅ is already in its simplest form!

The Rule of Four works the same way when subtracting fractions.

Try a subtraction example.

Start with step 1 of the Rule of Four and work through the problem.

Step 1: Find the Least Common Denominator

The denominators are 3 and 4.

3: 3, 6, 9,12...

4: 4, 8,12...

The LCD is 12.

Step 2: Convert Each Fraction

• How do you get the denominators to be the same?

Multiply ²/₃ by ⁴/₄ to get ⁸/₁₂.

Multiply ²/₄ by ³/₃ to get ⁶/₁₂.

Step 3: Subtract the Numerators

Step 4: Simplify

Look at ²/₁₂.

You can divide both by 2 to get ¹/₆. This is the simplified answer!

• Are you ready to practice more?

Head to the Got It? section for fun activities and games to help you master adding and subtracting fractions using the Rule of Four!