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Mixed numbers can seem a bit confusing at first, but with a little practice, they become easy to understand. A mixed number combines a whole number with a fraction. In the problem, the number given is expressed as a mixed number: 5.18 \(\frac{2}{3}\). Here, 5 is the whole number, 0.18 is the decimal part, and \(\frac{2}{3}\) is the fractional part.

Mixed numbers are useful for representing numbers that are not whole, giving a complete picture of values that involve parts and wholes combined. For instance, if you have 5 whole cakes and another \(\frac{2}{3}\) of a cake, this can be represented neatly as the mixed number 5 \(\frac{2}{3}\). Understanding how to handle mixed numbers is essential in math because it helps in tasks like addition or subtraction involving non-integers.

• Whole Number: The entire amount or full parts, in this case, 5.
• Decimal: Can be easily changed into a fraction to complete the blend.
• Fraction: Represents a part of a whole, such as \(\frac{2}{3}\) in the exercise.

One of the key skills in dealing with numbers is converting a decimal into a fraction. This is particularly useful when dealing with mixed numbers or performing precise calculations. In the exercise, the decimal 0.18 needed to be converted to a fraction.

To convert 0.18 into a fraction, follow these steps:

• Write the decimal as a fraction with the decimal digits as the numerator and the appropriate power of 10 as the denominator: 0.18 becomes \(\frac{18}{100}\).
• Simplify the fraction by finding the greatest common divisor of the numerator and the denominator. For \(\frac{18}{100}\), dividing by the common factor of 2 gives \(\frac{9}{50}\).

This conversion is beneficial for calculations as fractions are often easier to manage mathematically than decimals. The ability to switch between decimals and fractions can aid significantly in algebraic manipulation and in solving complex mathematical problems.

Finding the least common multiple (LCM) is crucial when adding or subtracting fractions with different denominators. The least common multiple is the smallest number that is a multiple of each of the denominators involved.

In this exercise, to add the fractions \(\frac{5}{1}, \frac{9}{50}, \) and \(\frac{2}{3}\), their denominators were 1, 50, and 3. The least common multiple of these numbers is 150.

• To find the LCM, list the multiples of each denominator until you find the smallest common one. In this case, 150 is the smallest number that 1, 50, and 3 all divide into evenly.
• Once the LCM is determined, convert each fraction to an equivalent fraction with the LCM as the new denominator.

By using the least common multiple, fractions become easier to add, since they share a common denominator, allowing straightforward addition of their numerators. Mastering LCM helps in simplifying operations involving fractions and makes calculations more straightforward.