5 Ways to Master Unlike Fractions

Understanding Unlike Fractions

Unlike fractions are fractions that have different denominators, making them difficult to compare or add directly. However, with the right techniques and strategies, you can master unlike fractions and become proficient in solving mathematical problems that involve them.

1. Finding the Least Common Multiple (LCM)

One of the key strategies for working with unlike fractions is to find the Least Common Multiple (LCM) of the denominators. The LCM is the smallest multiple that both denominators can divide into evenly. To find the LCM, you can list the multiples of each denominator and find the smallest common multiple.

🤔 Note: Finding the LCM is essential for adding or subtracting unlike fractions.

For example, let’s say we have two unlike fractions: ¹⁄₄ and ¹⁄₆. To find the LCM, we can list the multiples of 4 and 6:

Multiples of 4: 4, 8, 12, 16, 20,… Multiples of 6: 6, 12, 18, 24, 30,…

The smallest common multiple is 12, so the LCM of 4 and 6 is 12.

2. Converting Unlike Fractions to Like Fractions

Once you have found the LCM, you can convert the unlike fractions to like fractions by multiplying the numerator and denominator of each fraction by the necessary factor.

For example, let’s say we have two unlike fractions: ¹⁄₄ and ¹⁄₆. We have already found the LCM, which is 12. To convert these fractions to like fractions, we can multiply the numerator and denominator of each fraction by the necessary factor:

¹⁄₄ = (1 x 3) / (4 x 3) = ³⁄₁₂ ¹⁄₆ = (1 x 2) / (6 x 2) = ²⁄₁₂

Now we have two like fractions: ³⁄₁₂ and ²⁄₁₂.

3. Adding and Subtracting Unlike Fractions

Now that we have converted the unlike fractions to like fractions, we can add or subtract them directly.

For example, let’s say we want to add ¹⁄₄ and ¹⁄₆. We have already converted these fractions to like fractions:

³⁄₁₂ + ²⁄₁₂ = ⁵⁄₁₂

To subtract unlike fractions, we can follow the same steps:

³⁄₁₂ - ²⁄₁₂ = ¹⁄₁₂

4. Multiplying Unlike Fractions

Multiplying unlike fractions is straightforward. We can multiply the numerators and denominators of each fraction directly.

For example, let’s say we want to multiply ¹⁄₄ and ¹⁄₆:

(1 x 1) / (4 x 6) = ¹⁄₂₄

5. Dividing Unlike Fractions

Dividing unlike fractions is also straightforward. We can invert the second fraction (i.e., flip the numerator and denominator) and then multiply.

For example, let’s say we want to divide ¹⁄₄ by ¹⁄₆:

(1 x 6) / (4 x 1) = ⁶⁄₄

We can simplify this fraction by dividing both the numerator and denominator by 2:

⁶⁄₄ = ³⁄₂

By mastering these five strategies, you can become proficient in working with unlike fractions and tackle even the most challenging mathematical problems with confidence.

In summary, working with unlike fractions requires finding the LCM, converting unlike fractions to like fractions, and then performing arithmetic operations. With practice and patience, you can master unlike fractions and take your math skills to the next level.

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