91Ó°ÊÓ

When adding fractions, it's crucial to find a common denominator. This can be found using the least common multiple (LCM). The LCM of two or more numbers is the smallest number that is a multiple of each of them.
For example, the LCM of 3 and 2 is 6 because 6 is the smallest number divisible by both 3 and 2.
Knowing the LCM helps us rewrite fractions so they have the same denominator. This way, we can add or subtract them easily.

• Find LCM
• Rewrite fractions with the LCM as denominator
• Add or subtract fractions

For instance, in our example of adding \(\backslash frac{2}{3}\) and \(\backslash frac{1}{2}\), we found that the LCM of 3 and 2 is 6. So we rewrote \(\backslash frac{2}{3}\) as \(\backslash frac{4}{6}\) and \(\backslash frac{1}{2}\) as \(\backslash frac{3}{6}\). This made it easy to add them.

A common denominator is needed to perform addition or subtraction of fractions. It's simply a shared denominator.
In our problem, we needed to add \(\backslash frac{2}{3}\) and \(\backslash frac{1}{2}\). We couldn't do this directly because the denominators are different.

• Rewrite fractions so they have the same denominator
• The LCM helps in finding this common denominator
• Add the numerators once the denominators are the same

Let's convert these fractions:

• \(\backslash frac{2}{3}\) to \(\backslash frac{4}{6}\)
• \(\backslash frac{1}{2}\) to \(\backslash frac{3}{6}\)

Now it's easy to add them: \( \backslash frac{4}{6} + \backslash frac{3}{6} = \backslash frac{7}{6}\).

Squaring fractions means to multiply a fraction by itself. If you have a fraction \( \backslash frac{a}{b} \), squaring it will give \( \backslash frac{a^2}{b^2} \).
In our example, after adding the fractions, we got \( \backslash frac{7}{6} \). To square this result, we squared both the numerator and the denominator:

• Numerator: \( 7^2 = 49 \)
• Denominator: \( 6^2 = 36 \)

Therefore, \( \backslash left( \backslash frac{7}{6} \backslash right)^2 = \backslash frac{49}{36} \).
This technique can be applied to any fraction. Just remember to square both the numerator and the denominator separately.