5 Ways to Subtract Fractions with Unlike Denominators

Understanding Fractions and Denominators

Fractions are a way to represent part of a whole. They consist of two parts: the numerator and the denominator. The numerator is the number on top, and it represents the number of equal parts you have. The denominator is the number on the bottom, and it represents the total number of equal parts the whole is divided into.

When dealing with fractions, we often need to perform arithmetic operations like addition and subtraction. However, when the denominators are unlike, it can get a bit tricky. In this article, we’ll explore five ways to subtract fractions with unlike denominators.

Method 1: Finding the Least Common Multiple (LCM)

One way to subtract fractions with unlike denominators is to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly.

For example, let’s say we want to subtract ¹⁄₄ from ³⁄₆. The denominators are 4 and 6. To find the LCM, we can list the multiples of each denominator:

• Multiples of 4: 4, 8, 12, 16,…
• Multiples of 6: 6, 12, 18, 24,…

The first number that appears in both lists is 12, so the LCM is 12. Now, we can rewrite the fractions with the LCM as the denominator:

• ¹⁄₄ = ³⁄₁₂
• ³⁄₆ = ⁶⁄₁₂

Now, we can subtract the fractions:

• ⁶⁄₁₂ - ³⁄₁₂ = ³⁄₁₂

🤔 Note: Finding the LCM can be time-consuming, but it's a good method to use when the denominators are small.

Method 2: Using Equivalent Fractions

Another way to subtract fractions with unlike denominators is to use equivalent fractions. Equivalent fractions are fractions that have the same value, but different denominators.

For example, let’s say we want to subtract ¹⁄₄ from ³⁄₆. We can rewrite the fractions as equivalent fractions with the same denominator:

• ¹⁄₄ = ²⁄₈
• ³⁄₆ = ⁴⁄₈

Now, we can subtract the fractions:

• ⁴⁄₈ - ²⁄₈ = ²⁄₈

📝 Note: Using equivalent fractions can be a quick and easy way to subtract fractions with unlike denominators.

Method 3: Using the Butterflies Method

The butterflies method is a visual way to subtract fractions with unlike denominators. It involves drawing two butterflies with the same shape, but different sizes.

For example, let’s say we want to subtract ¹⁄₄ from ³⁄₆. We can draw two butterflies with 4 and 6 parts, respectively:

Butterfly 1 (4 parts): * 1 part shaded

Butterfly 2 (6 parts): * 3 parts shaded

Now, we can subtract the fractions by subtracting the number of shaded parts:

• 3 parts (Butterfly 2) - 1 part (Butterfly 1) = 2 parts

Since the butterflies have different sizes, we need to find the LCM of the denominators to find the total number of parts. In this case, the LCM is 12. So, we can rewrite the answer as:

• ²⁄₁₂

🦋 Note: The butterflies method is a fun and visual way to subtract fractions with unlike denominators.

Method 4: Using a Number Line

A number line is a visual representation of numbers on a line. We can use a number line to subtract fractions with unlike denominators.

For example, let’s say we want to subtract ¹⁄₄ from ³⁄₆. We can draw a number line with the fractions marked:

• 0, ¹⁄₄, ¹⁄₂, ³⁄₄, 1
• 0, ¹⁄₆, ¹⁄₃, ¹⁄₂, ²⁄₃, ³⁄₄, 1

Now, we can subtract the fractions by moving along the number line:

• Start at ³⁄₄ (the starting point)
• Move ¹⁄₄ to the left (the amount to subtract)
• End at ¹⁄₂ (the answer)

Since the number line has different units, we need to find the LCM of the denominators to find the total number of units. In this case, the LCM is 12. So, we can rewrite the answer as:

• ⁶⁄₁₂

📏 Note: Using a number line is a great way to visualize the subtraction of fractions with unlike denominators.

Method 5: Using a Calculator

Finally, we can use a calculator to subtract fractions with unlike denominators. Most calculators have a built-in function for adding and subtracting fractions.

For example, let’s say we want to subtract ¹⁄₄ from ³⁄₆. We can enter the fractions into the calculator:

• ³⁄₆ - ¹⁄₄ =

The calculator will give us the answer:

• ¹⁄₂

📊 Note: Using a calculator is a quick and easy way to subtract fractions with unlike denominators.

Subtracting fractions with unlike denominators can be a challenge, but there are several methods we can use to make it easier. Whether we use the LCM, equivalent fractions, the butterflies method, a number line, or a calculator, we can find the answer with a little practice and patience.

Related Terms:

• Fraction addition and subtraction worksheet
• Fraction Worksheet Grade 5
• Multiplication mixed number worksheet
• Multiplying Fractions worksheet pdf